Tectonophysics 156 (1988) 1-20 Elsevier Science Publishers BV Amsterdam - Printed in The Netherlands

Review

Magnetic susceptibility petrofabrics and strain

GRAHAM JOHN BORRADAILE

Department of Geology LAkehead University Thunder Bay Onto P7B 5pound1 (Canada)

(Received July 6 1987 revised version accepted April 18 1988)

Abstract

Borradaile GJ bull 1988 Magnetic susceptibility petrofabrics and strain-a review Tectonophysics 156 1-20

Magnetic susceptibility is a non-destructive technique for quantifying the average fabric of a small sample of rock The interpretation of the magnetic fabric is not always straightforward However the principal directions of the magnitude ellipsoid of susceptibility commonly show orientations consistent with the kinematic interpretations of folds shear zones and other structural features The directions may correspond with the orientations of strained objects or with the planar-linear mineral orientations There will usually be multiple mineralogical sources of susceptibility often involving silicates If the sources are known or ifmiddotthe susceptibility can be attributed to a single mineral species it may be possible to establish a correlation between the strain ellipsoid and the susceptibility ellipsoid This correlation will be of principal directions in many instances and occasionally there may be a weak correlation of strain magnitudes as well In other circumstances it may be possible to establish a correlation between changes in susceptibility and the strain Nevertheless magnetic fabric studies are not routine substitutes for strain analysis Even where information on strain is not provided the magnetic fabrics (and sub fabrics) yield a measure of the preferred crystallographic orientation or preferred dimensional orientation of the minerals that may be integrated profitably with other petro fabric data Experimental deformation of certain synthetic aggregates indicates that directions of magnetic susceptibility spin rapidly with advancing strain especially where the matrix grains undergo crystal-plastic deformation In certain experiments simple shear appears to cbange the intensity of magnetic fabric more effectively than pure shear Experiments indicate also that the initial anisotropy of a rock-like material is not easily overprinted by deformation whereas field studies are equivocal

Introduction specimens (usually pieces of drill-core with a length = 082 x diameter) Its most attractive feashy

This review draws the attention of structural ture is that it sums the magnetic contributions of geologists to the value of magnetic fabrics but all components of the rock and presents an avershyindicates current limitations in their interpretashy age bulk fabric description Its relationship with tion Note is also made of some relevant complexishy fabric of the rock arises because the most magnetishyties of rock deformation that are not always emshy cally susceptible minerals can have distributions phasised in geophysical studies of shape orientations or lattice orientations inshy

Shape changes and some aspects of kinematic fluenced by the kinematic history of the fabric If histories of rocks especially tectonically deformed these influences apply similarly to the rest of the rocks may be inferred from grain and mineral rocks fabric then the magnitude ellipsoid of susshyfabrics These procedures are time-consuming difshy ceptibility may be a faithful representation of the ficult and require the presence of special strucshy total fabric tures or textures In contrast the anisotropy of There is a wealth of literature on the magnetic magnetic susceptibility may be determined rapidly susceptibility of rocks (Hrouda 1982 Urrutiashyfrom a wide range of rocks in suitably shaped Fucugauchi and Odabchian 1982 Zavoyskiy

0040-195188$0350 (11988 Elsevier Science Publishers BV

2

1982 Park 1983) Textbooks discuss applications (Tariing 1983) and instrumentation (Collinson 1983) detailed studies date from 1942 (Ising) The earliest uses concern sediments and sedimentary rocks Rees (1967) and Hamilton et al (1968) showed experimentally that the movement of sedishyment produces characteristic susceptibility patshyterns Numerous field studies either foresaw or followed this work with inferences of paleocurrent trends and stratification planes from the principal directions of Magnetic suceptibility (eg Hamshyilton 1963 Graham 1966 Crimes and Oldershaw 1967 Van den Ende 1975 Hamilton and Rees 1970 1971 Hrouda and Janak 1971)

A similar theme has been followed by workers on volcanic or other igneous rocks in which cryptic flow fabrics of the magma have been inferred from the orientation of the magnetic susceptibility ellipsoid (Khan 1962 Hrouda and Chlupacova 1980) Mimetic igneous fabrics have also been discerned (Hrouda et al 1971) Magmatic flow fabrics and their magnetic anisotropy have been simulated experimentally (Wing-Fatt and Stacey 1966) The alteration of magmatic rocks (Hrouda et aI 1972 Lapointe et al 1986) the fabrics of ore deposits (Schwarz 1974 Hrouda et al 1985) and the deformational history of a chondritic meteorite (Hamano and Yomida 1982) have all been studied through their magnetic fabrics

Most studies have concentrated on deformed rocks since their petrofabrics are noticeably anisoshytropic (Graham 1954) For example Singh et al (1975) Hrouda (1976) Kneen (1976) Wood et al 1976 Kligfield et al (1977) and Stott and Schwerdtner (1981) all were able to compare the principal directions of the susceptibility ellipsoid with the principal fabric elements in slates and low grade schists

Magnetic susceptibility anisotropy and mineralogy

Susceptibility is a measure of the response of the material to an applied magnetic field This can be considered under three main classes (eg Uyeda et al 1963 Strangway 1970 Owens and Bamshyford 1976) for minerals which are responding to weak applied fields of the same order of magnishytude as the Earths field The majority of rock-forshy

ming minerals are either paramagnetic or diamagshynetic In the paramagnetic case the magnetisation (M) induced in the mineral is considered to supshyport an applied weak field or magnetic intensity (H) weakly in a linear fashion

M=kmiddotH

For the diamagnetic case k is negative For rockshyforming minerals k is typically small about 1 X

10-4 SI unitsunit vol for some paramagnetic minerals and typically -1 x 10-5 SI unitsvol for diamagnetic minerals (Susceptibility is also sometimes given in cgs units which are 1(411) of an SI unit) In geology it is also sometimes exshypressed on a unit mass basis as the specific susshyceptibility (X) rather than a unit volume basis (k) It is useful to report the densities so that comparishyson can be made between results reported in the two schemes For diamagnetic and paramagnetic minerals the anisotropy of susceptibility is conshytrolled by the crystallographic orientations of the mineral grains and is not appreciably influenced by grain shape The anisotropies of paramagnetic matrix-forming minerals are quite high (see Table 1) by comparison with diamagnetic minerals (see Table 2)

Although they usually occur as accessory minerals a third important class are the ferrishymagnetic minerals Magnetite and hematite are most important although pyrrhotite can make a significant contribution (Fuller 1964 Rochette 1987) The susceptibilities of natural examples of these minerals are sensitive to composition but are positive and are large by comparison with the paramagnetic and diamagnetic rock-forming minerals (Typical approximate values are 5 SI unitsvol for magnetite and 6 X 10- 3 SI unitsvol for hematite)

The response of magnetite depends non-linshyearly on the strength of the applied field but for the low fields at which routine susceptibility deshyterminations are made the susceptibility anishysotropy of magnetite is controlled by the shape of the mineral grain as long as the grains are wellshyspaced (There may be differences in the deshytermination of the magnitude of susceptibility beshycause of its slight dependence of the field strength (Smith and Banerjee 1987) however the effects

3

TABLE 1 netic fabric (Uyeda et aI 1963) Thus the susceptshySusceptibility data for common metamorphic minerals ibility anisotropy of magnetite will in practice

Mineral Minimum anisotropies

k max kin k min kan

(SI unitsvol XlO- 6 )

---Actinolite 1076 0982 0947 3560

Actinolite 1083 1027 0899 6500

Hornblende 1347 0917 0809 8920

Crocidolite 1052 0992 0958 333

Glaucophane 1094 1006 0908 787

Chlorite 1093 1060 0864 358

Chlorite 1287 1058 0734 70

Chlorite 1128 1023 0866 1550

Chlorite 1063 1020 0921 370

Biotite 1114 1106 0812 1230

Biotite 1098 1095 0832 1180

Biotite a 1107 1096 0824 998

Biotite bull 1108 1107 0814 1290

Phlogopite 1098 1091 0838 1180

Muscovite 1159 1052 0820 165

From Borradaile et al (1987) where further details may be

found

bull Pure specimens by personal communication through Karel Zapletai from Hrouda et al (1985a) These specimens also

show good agreement between the mean susceptibility reo

ported here and the susceptibility predicted theoretically

from the precisely determined compositions)

on anisotropy are expected to be small) Magshynetite is the only mineral of importance in which the grain shape fabriC directly influences the mag-

TABLE 2

A Weakly susceptible rockforming minerals (units are Sljvol x 10-6 )

Mineral Mean k St Reference dev

Plagioclase -278 034 Borradaile et al (1987)

(oligoclase)

Quartz -134 080 Hrouda (1986)

Calcite -138 034 Voight and Kinoshita (1907)

Talc +54 082 Borradaile et al (1987)

B Anisotropy of weakly susceptible minerals

Mineral Anisotropy Reference

ratio

kckab

Quartz 101 Voight and Kinoshita (1907) Nye (1957)

Calcite 111 Voight and Kinoshita (1907)

Owens and Rutter (1978)

depend on the particular habit of the grains in question and which is nearly equidimensional for detrital examples For example detrital magnetite has been reported with an anisotropy of 1108 0964 0936 by the author and Rees (1965) reports another example with susceptibilities in the ratio 106 097 097 Hydrothermal magshynetites (Heider et aI 1987) can have much higher dimensional anisotropies (eg 2 1) as do some magmatic examples The problems arising from the shape effects of magnetite are compounded by the grouping of grains to form elongate masses There can be tectonic causes for this for example where pre-existing magnetites have been strung together to form elongate domains by pressure solution or other forms of metamorphic differshyentiation In sediments trains of magnetite grains may be formed by colonial bacteria (Karlin et aI 1987 Chang et aI 1987)

Hematite has an enormous intrinsic crystalloshygraphic magnetic anisotropy with maximum susshyceptibility parallel to its basal planes and a ratio of maximum to minimum susceptibility reported as gt 100 (Table 3) These extreme anisotropies for single crystals are not realised from polycrystalline samples a minimum anisotropy estimated from Hargraves (1959) and Hrouda et ai (1985b) is

127 122 056 In the case of hematite-bearing metasediments even with intensely developed petro fabric anishysotropies (Kneen 1976) the magnetic anisotropies are typically only

1023 0993 0983 Hematite like the paramagnetic and diamagnetic rock-forming minerals yields a component of magnetic fabric to the rock that is influenced primarily by the crystallographic alignment of the anisotropic grains Other ore minerals also have large susceptibility anisotropies (Table 3) but these are relatively rare in metamorphic rocks

Mineralogical sources of magnetic susceptibility in rocks

The magnetic fabric relates primarily to the petrofabric of the significantly susceptible mineral

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TABLE 3

Susceptibility and anisotropy of iron minerals (units are Slfvol)

A Anisotropy controlled by shape (Borradaile et aI 1987)

Mineral k max k int kinin Mean value

Magnetite (crushed metamorphic) 1063 0989 0951 58

Magnetite (detrital) 1108 0964 0936

B Crystallographic anisotropy

Mineral Anisotropy ratio Maximum susceptibility value Reference

Hematite gt 100 1 1 x 10 - 2 basal planes Uyeda et al (1963)

Pyrrhotite c 10000 1 10 basal planes Schwarz (1974)

Pyrrhotite 1024 368 0027 Rochette (1988) 910 391 0028

Ilmenite-hematite 15 1 04 basal planes Uyeda et al (1963)

C Mean values of other iron minerals (Carmichael 1982)

Mineral Mean susceptibility (approximate)

Magnetite 62

Ilmenite 18

Pyrrhotite 15

Titanomagnetite 001

Hematite 0007 Siderite 0005

Limonite 0003

Pyrite 0001

species If all the minerals in a rock have similar magnitudes of susceptibility then it should be expected that the magnetic susceptibility ellipsoid bears some close relationship to the gross petroshyfabric However where the susceptibility is chiefly carried by an accessory mineral the susceptibility ellipsoid will only be represerttative of the rocks fabric to the degree that the accessory minerals imitate and are coeval with the host fabric Hitherto most papers on deformed rocks col1shycentrated on rocks in which the accessory iron oxides particularly magnetite and hematite were the dominant source of susceptibility However the incoming of pyrrhotite at the expense of pyrite during progressive metamorphism may also conshytribute to the susceptibility of certain greenschist facies metamorphic rocks (Rochette 1987 Borshyradaile et al in press)

Bulk susceptibility values are readily available (International Critical Tables 1929 Weast and Astle 1978 Carmichael 1982) whereas anishy

sotropy data are rarer beginning with the report of Voight and Kinoshita (1907) The earliest deshyterminations used sufficiently large fragments of single crystals and the same approach continues

- shy(0) (b)

Fig 1 It is possible to physical1y arrange anisometric minerals into linear (a) and planar (b) fabrics as shown One can then

detennine the susceptibilities of the cubical specimens in the

directions I m and n and these yield minimum estimates of

the anisotropies of the minerals This simple method enables one to estimate the minimum anisotropy of susceptibility of

the actual fine-grained minerals separated from a metamorphic rock

5

T p bull B2 bull BI diSC -snoped

middotM C2

rod -shoped

-I 0 t~1 1~2 1~3 14 s 16 t~1 pi

Fig 2 Susceptibility anisotropies of metamorphic minerals separated from metamorphic rocks (from Borradaile et al 1987) and the field (stippled) of common metamorphic rocks (from Hrouda et al 1978) P and T are explained in the Appendix AI AZ-actinolite BI etc-biotite CI etc-chlorite CR-crocidolite G-g1aucophane H-bomblende M-muscovite

P-phJogopite Triangle-metamorphic magnetite partly crushed triangle in circle-detrital magnetite

for ore minerals (Uyeda et al 1963 Schwarz 1974 1975 Rochette 1988) hornblende (Parry reported in Wagner et al 1981) augite and calcite (Owens and Bamford 1976) and quartz (Hrouda 1986) However for many rock-forming metamorshyphic minerals large single crystals are unavailable or have unrepresentative compositions To overshycome this problem samples large enough for deshytermination can be synthesised by orienting small (c 1 mm) grains into an aggregate (Borradaile et al 1986) This technique can be applied to any markedly anisometric single-crystal grains that can be physically manipulated or magnetically arranged into a strong preferred crystallographic orientation (Fig 1) The technique yields a minishymum estimate of the anisotropy because it is not possible to produce a perfect alignment of crystalshylographic axes in this manner Nevertheless it is the only practical method at the present time for isolating the contribution of specific mineral grains with fme-grained habits to the susceptibility and anisotropy of susceptibility of a given rock

Anisotropy data for some important rock-forshyming minerals mainly from metamorphic rocks and some bulk anisoir~py data for other imshyportant minerals are given in Table 1 and Fig 2

Contributions to whole-rock susceptibility and its anisotropy

Initially most work on metamorphic or deshyformed rocks concentrated on examples in which the susceptibility was due to iron oxides However several workers have addressed the more general situation in which there may be paramagnetic

contributions also (Coward and Whalley 1979 Henry 1983 Rochette and Vialon 1984 Borshyradaile et al 1986 Lamarche and Rochette 1987) or even diamagnetic contributions (Hrouda 1986) Such effects become important where magnetite is present in small amounts usually less than 1 wt in a rock that has a matrix of moderately susceptishyble silicates Detailed magnetic studies have been undertaken involving magnetic susceptibility deshyterminations at different field strengths (Coward and Whalley 1979 Hrouda and Jelinek in press) at different temperatures (Rochette and Vialon 1984) and the effects of temperature on remanent magnetisation (KJigfield et al 1982) Such studies have identified the mineralogical source of the susceptibility However those techniques are not routine and it may be beneficial to physically separate the minerals in a few typical samples so that susceptibility measurements may be carried out on these individually

Henry (1983) and Henry and Daly (1983) inshyferred multiple sources of susceptibility from the measurements directly by using multiple specishymens of similar lithologies but different intensities of fabric The method uses a plot of principal susceptibilities of individual specimens against their mean or bulk susceptibility The data for each of the principal susceptibilities lie on straight lines that intersect at a point that has equal values on both graph axes This can be considered as a gradual transition in anisotropies from the most anisotropic case at the right of the graph through lesser anisotropies to a theoretically predictable equivalent isotropic case in which all principal susceptibilities equal the mean susceptibility (Fig

6

10-4

o

ki (i I 10 3) [ellsem ]

e~

~~T ~~I

eQ e ~ 0 v~ e~ - 1 ~~fFel e~ gt

$ ~~ I V( (shy~+ middot~eQ ~( e

(- bull v ( oJ ~ ~~e9 r ~ u 1 I I bull 1

+ 1 mosl anisolropic + specimen

leasl anisolropic specimen

i ( bull k [ellsem]

o 10-4

Fig 3 Diagram from Henry (1983) showing the variation in anisotropy of adjacent specimens or parts of a specimen The axes are individual principal susceptibilities (vertical) and the

mean or bulk susceptibility (horizontal)

3) This pattern was predicted by Henrys model of additive combinations of ferrimagnetic contrishybutions from traces of magnetite with contribushytions from paramagnetic silicates In a natural example the range in anisotropies on his special plot could be an indication of the degree to which mineralogical constitution affects the magnetic anshyisotropy of a rock Other influences cannot be ruled out however The variation in mineral comshyposition between different specimens or the variashytion in the degree to which the ferrimagnetic grains have similar preferred orientations to the other mineral grains could al~o playa role

Studies of susceptibility at low temperatures and of remanent and saturation magnetisation have confirmed that there are paramagnetic conshytributions from silicates and that these can swamp the ferrimagnetic contributions (Coward and Whalley 1979 Henry and Daly 1983 Rochette and Vialon 1984) These contributions cannot yet be attributed to a specific mineral without physishycally separating the grains (Hrouda and Jelinek in press)

The reverse procedure predicting whole-rock anisotropy from multiple mineralogical sources is easier Consider a rock with a perfect preferred crystallographic fabric of mica grains with their basal planes perfectly parallel and their long axes perfectly aligned in that plane In the simple case of a monomineralic rock with perfectly aligned

grains the mineral anisotropy is equal to the anisotropy of the rock If susceptibility contrishybutions from different mineral sources can be summed as Henry (1983) and Hrouda (1986) sugshygest the effect of adding a small proportion of magnetite to a paramagnetic matrix can be predicshyted For simplicity assume that the magnetite grains are dispersed and present as a small trace ( lt 1) with a perfect shape alignment coaxial with the preferred crystallographic fabric of the matrix Although magnetite has an enormous susshyceptibility magnitude its anisotropy (directly reshy

lated to its shape) is usually small especially if it is of detrital origin On the other hand metamorshyphic silicates have moderate susceptibility magnishytudes but very high anisotropies (Table 1) (Whether the susceptibility anisotropy is intrinsic or due to inclusions is immaterial here)

The magnetic anisotropies of metamorphic silicate grains are more extreme than those of most metamorphic rocks Thus a trace of magshynetite combined with much mica in a schist proshyduces an anisotropy intermediate between that of the minerals In Fig 4 this thought experiment is carried out using model rocks with 60 plagioclase (a diamagnetic matrix with almost negligible susceptibility) traces of magnetite in the proportions stated on the figure and about 40 of the named metamorphic silicate From Fig 4 it can be seen that the anisotropy of the rock is virtually equal to that of magnetite if the latter is present as gt 1 This is important for those intershypretations of magnetic fabrics in terms of March-type analysis (see below) in which disshyseminated markers are virtually solely responsible for the magnetic fabric But where the magnetite is present in smaller proportions the anisotropy of the rock may be influenced more by the composishytion of the rock than by its petrofabric or strain Thus compositional variation between specimens could produce differences in anisotropy even if the specimens had identical fabrics or strains

Recently a mathematical model has been inshyvestigated in which paramagnetic silicates are the only source of susceptibility (Hrouda 1987) With increasing preferred crystallographic orientation the anisotropy is shown to increase until it equals that of the crystal lattice Hrouda notes that this

14

13

1-2

I-I

t1-0 I-I -2 13 k2k3 Fig 4 Flinn-type diagram of susceptibility anisotropies for hypothetical rocks indicating the effects of variable proporshytions of magnetite and a paramagnetic mineral Each rook is represented by a tie-line and is composed of approximately 40$ of the named mineral plus magnetite (in the small fraction indicated by the numbers on the tie-line) and 60$ feldspar As the proportion of magnetite in the rock is increased (from 10-6

at the distal end of the tie-line in each case) the magnetic anisotropy of the rock decreases towards the anisotropy of magnetite The anisotropy of the particular magnetite chosen in these models is located near the convergence of the tie-lines

(From Borradaile 1987b)

relationship can be disturbed by the smallest traces of ferrimagnetic material and is difficult to calibrate in terms of strain Moreover a general difficulty of this type of mathematical model (both in magnetic fabrics and petrofabrics) is that it treats the grains as dispersed crystallites of no finite size which are free to develop their ideal crystal shape In nature grains are in contact and in the case of paramagnetic silicates in metamorshyphic tectonites their preferred orientations pose special problems For example grains with crystalshylographic orientations at high angles to the preshyferred orientation (schistosity) are restricted in growth Thus their reduced volumes will decrease their contribution to the rock anisotropy (see Fig 13b)

Magnetic anisotropy and finite strain

Principal susceptibility directions

In rocks with strong tectonic fabrics the prinshycipal magnetic susceptibility directions are often

7

parallel to prominent structural directions (Kligshyfield et al 1977) or related to fold geometry (Owens and Bamford 1976) For example the minimum susceptibili ty is usually perpendicular to a primary cleavage The maximum susceptibility may be parallel to the maximum extension in the rock (eg Fig 6b) contained in the cleavage and defined by stretched objects or mineral lineations (eg Singh et aI 1975 Kligfield et aI 1977 Coward and Whalley 1979 Rathore 1979 Goldshystein 1980) In contrast the maximum susceptibilshyity may be parallel to the intersection lineation of bedding and cleavage (eg Hrouda 1976 also Fig 5)

These two different patterns have been intershypreted in a number of ways One interpretation is that the maximum susceptibility is parallel always to the maximum extension It implies that the intersection lineation of bedding and cleavage is the maximum extension direction This appears to be unusual because an intersection lineation is the fortuitous interference of a tectonic fabric with the disturbed bedding surfaces In some areas the magnetic fabrics may be reasonably consistent in orientation while the (single-generation) fold hinges and intersection lineations may vary conshysiderably in orientation (Fig 6) There is no good reason for supposing that the intersection lineashytion must necessarily have some genetic relation to the strain ellipsoid

Another interpretation is that maximum susshyceptibilities occur parallel to intersection lineashytions because of heterogeneous combinations of sub fabrics If some portions of the rock retain a

bedding

cleole

bull maximum susceptibilify

intermediote susceptibility bull minimum sUKeptibihly

Fig 5 Principal susceptibility directions in Hercynian slates with a single tectonic fabric Note the maximum susceptibilishyties close to the intersection lineation of cleavage and bedding and the minimum susceptibility perpendicular to bedding

(From Borradaile and Tarling 1981)

8

bull -l-A~

~xL 0--~

~

b)0)

SUSCfptiblhtibullbull bull mcaimum in~rmtdIQt bull mntnlUtl

X IMOn fOld plunQl I inttotcon liMohon

Fig 6 Susceptibility orientations and major fold plunges in Archean slates with a single tectonic fabric Despite the varishyation in fold plunge ( sheath folds or periclinal folds) the metamorphic and magnetic fabrics are reasonably consistently

oriented in different adjacent parts of the area (From Borradaile and Brown 1987)

bedding parallel oblate magnetic fabric due to sedimentation then this may interfere with the fabric due to tectonic causes Under the right circumstances which are not too special this comshybination may produce maximum susceptibilities parallel to cleavage and bedding or perpendicular to the stretching direction (Fig 7) For this exshyplanation to be valid indeed for this arrangement of susceptibility axis to be detectable the interfershying subfabrics must be present on scales smaller than the sample size used in susceptibility deshyterminations (usually about 10 em3) Recently bedding-parallel fabrics have been detected in

L L

0 IIbullbulllli0 degiOo bull

(a) (b)

susceptibilities bull mo int-dio 0 mi

Fig 7 Variation in principal susceptibility orientations in meta-sandstones with a single tectonic fabric L indicates the grain elongation in the schistosity plane which is horizontal in these diagrams In some cases the maximum susceptibility is nearly parallel to the grain elongation (b) in others it is

perpendicular (a) (Borradai1e and Tarling 1984)

stylolitic cl~voge dOmOin

Fig 8 Where a tectonic fabric develops a domainal texture such as in stylolitic cleavage there may be distinct contribushytions of magnetic anisotropy from different parts of the rock Qeavage zones may contribute a tectonic susceptibility anishysotropy while inter-cleavage domains may still retain a sedimiddot mentary magnetic fabric The susceptibility determination for

the rock blends the two fabrics

metasediments with isoclinal sheath folds (Borshyradaile et al bull in press)

A third explanation similar to the previous one has been given for rocks that have been very weakly strained with pressure solution as the deshyformation mechanism lbis mechanism often proshyduces a regular domainal tectonic fabric of closely spaced laminae which concentrate insoluble material (including iron oxides and paramagnetic silicates) in thin sheets between rock that retains a sedimentary fabric Where laminae are more closely spaced than the width of the core used to determine susceptibility the net susceptibility is a combination of sedimentary and tectonic contrishybutions In this case the maximum susceptibility is often parallel to the intersection lineation of the domains (stylolitic cleavage) and bedding (Fig 8) Rochette and Vialon (1984) note that heterogeshyneous fabrics combining magnetic sub-fabrics of different ages prohibit any kind of quantitative correlation of strain and susceptibility

In mylonite zones (Goldstein 1980) and in major shear zones (Rathore 1985) magnetic fabrics have orientations that indicate maximum susceptshyibilities compatible with maximum extension dishyrections Similarly minimum susceptibilities are reported perpendicular to schistosities or foliashytions The relationship to boudinage directions and mineral stretching lineations has been cited to support the contention that there is a one-ta-one correspondence of strain axes and principal susshyceptibility directions in some cases Hrouda (1979 reported 1977) seems to have been the first person

9

to have considered the combining effects of magshynetic fabrics of different ages He described early susceptibility fabrics by a tensor P superimposed tectonic fabrics by a tensor D and suggested that they combine to form a resultant susceptibility tensor R by

D P = R or D = R p- 1

Goldstein (1980) applied the same approach to mylonitic fabrics Some authors have simply asshysumed that it is permissible to use the orientations of magnetic fabrics within shear zones rather like a schistosity to determine the amount and sense of shear Similar studies have been carried out subsequently on shear zones up to a regional scale in extent (eg Rathore 1985) However in experishymental shear zones the author has found that earlier magnetic fabrics are difficult to overprint and magnetic fabric maybe an unreliable kineshymatic indicator

Magnitudes ofsusceptibility and magnitudes ofstrain

The relationship between the shape of the magshynitude ellipsoid of susceptibility and the intensity of the tectonic fabric is more complex than the relationship between directions as discussed in the previous section Usually comparisons have been attempted between the shapes of the susceptshyibility and finite strain ellipsoids The latter is usually derived from some macroscopic straiI) marker such as pebbles concretions lappilli or rotated sand-dikes (eg Rathore 1979 Borradaile and Tarling 19811984 Rathore and Henry 1982 Clendenen et at 1988 Hirt et al 1988) Reducshytion spots have been used as strain markers from time to time however their pre-metamorphic origin is not always certain and in the Welsh examples some outcrops have susceptibilities that are too low to give reproducible magnetic fabrics

The susceptibility ellipsoid normally plots much nearer the origin of the Flinn-diagram than does the strain ellipsoid (Fig 9) In some cases logashyrithmic plots (Fig 10) help in their discrimination The relationships between strain and magnetic fabric are not straightforward The most strained samples in an outcrop do not necessarily have the most extreme magnetic anisotropies This is shown

a or L

20-1 AI IfIOOltfrc ItJtedtlDoloty 0IItN11tOy

JWUiOl2L1LL bull for QIdfl c~1 f~~

O for fktlPOf lCIStl ( ~ I

15

ol~~ ~bOrF 10 15 20 B

Fig 9 Strain ellipsoid data determined by de-straining analyshysis for quartz clasts and for feldspar clasts and the susceptibilshy

ity anisotropy in meta-sandstones a XY b - YZ where X lt Y lt Z L and F are the equivalent ratios for the magnetic susceptibility There is a single schistose tectonic fabric Data for the same hand-specimens are connected by tie-lines There is no simple relationship between the magnitude of strain and

intensity of magnetic fabric (Borradaile and Tarling 1984)

by the crossing tie-lines in Fig 9 Moreover there is always some question as to the validity of the comparison since the strain is commonly heterogeshyneous on the scale of a thin section whereas the homogeneously strained markers are much larger Susceptibility is usually measured from a sample about 10 cm3

so that the susceptibility tensor will be defined on a smaller scale than the strain tensor Another approach although less common in the literature is to compare the susceptibility

t log a (log l)

~ ~

~ +~ iii~iffl ~

0 lr b ~ C-_~~

0 ~J 04 ~tgt~J-~

~~~I ~~Q

0middot1

az

~ llZ I

o CH 02 0middot4 0middot6 08 1middot0 IZ

- log b (log F)

bull ST~AIN EItIPSOIO SHAPE SUSCEPTISILITY ELUPSOID SHAPE

Fig 10 Strain ellipsoid data and susceptibility data for four outcrops of slate (l to IV) with a single tectonic fabric connected by tie-lines and presented on a logarithmic Flinn-dishy

agram (From Borradaile and Tarling 1981)

bull bull bull bull

10

003

Mj maximum (i -I) values

006 I intermediate I

( i bull 2 l values 1 ~~---------~~------

- 003 -lmiddotmiddot - 006

bull bull III(L -middot00

II I

minimum (imiddot 3) values

I NmiddotI 000

Fig 11 Nonnalised measures of principal susceptibility magnishytudes (M) and o( principal strain magnitudes (Ni ) (or specishymens o( a metavolcanic rock with a single tectonic fabric There is no correlation between minimum values of susceptibilshyity and strain nor between intennediate values etc Nevertheshyless it would be possible to infer a correlation incorrectly by considering all the data laquo(or maximum intermediate and minimum susceptibilities) simultaneously (From Borradaile

and Mothersill 1984)

fabric with the petrofabric of a slightly smaller sample detennined by means of X-ray texture goniometry (eg Wood et al 1976 Hrouda et al 1985b) This overcomes the criticism that different scales will be sampled but there is the added complication of interpreting the texture goniomeshyter data in terms of finite strain (Oertel 1983)

One of the earliest attempts to relate the strain and susceptibility tensors was by Kneen (1976) She plotted ratios of principal strains against ratios of principal susceptibilities and inferred correlashytions Similar studies that compared strain ratios with susceptibility anisotropy used special loga-

M 02

rithmic parameters to normalise values (Wood et al 1976 Rathore 1979 1980 Rathore and Henry 1982 Kligfield et al 1982) These are termed IV (for strain) and M (for susceptibility) where i = 1 2 or 3 for the appropriate principal value The actual algebraic definition of N and M varies in the literature and care should be taken in comparshying data from one paper to another) Unforshytunately in most of these cases the authors plotted the data for all three principal directions on the same axes and generally established correlation coefficients for the maximum intermediate and minimum values simultaneously Strictly speaking this is invalid (Fig 11) and in one instance the correlation of anisotropies attempted in this manner has been disproved (Borradaile and Mothersill 1984)

This may give a discouraging view of the correshylations of strain and susceptibility but the data already published do give some indication that correlations may exist although weaker than origishynally claimed For example comparing data for just minimum (normalised) strains and minimum (normalised) susceptibilities it is possible to reshycognise modest correlations between susceptibility and strain in the case of the Welsh slates (eg Wood et al 1976) here in Fig 12 Clendenen et al (1988) have recently recognised that this kind of weaker correlation between the strain of conshycretions and susceptibility can be statistically sigshynificant

Thus although weak correlations of the kind

klk2 =(XY) may exist these must only be of local siginificance

I I I bullbullbullbullbullbullbull bull

I ttl bullbull~

ol------------r ------ shy bull V

~- fmiddot I maximum (i1) and -0middot2 r I intermediate (middot 2 ) values

minimum values (i 3) I

~~~____~____~I~____~ Nj -~ -~ 0 ~

Fig 12 Nonnalised measures of principal susceptibilities (M) and of principal strains (Ni ) for slates with a single tectonic fabric Note that a weak correlation exists between minimum strains and minimum susceptibilities (From Wood et al 1976)

11

Q Z p Marchian rofafion

S ~ b

t1- y p 0- Zr +y~

k X L oL

X SI bull bull S

Fig 13 a Theoretical outline of the March model as applied to the rotation and preferred orientation of phyUosilicate grains For strain axes X ~ Y ~ Z the rotation of a pole p of a platelet is shown schematically as is the rotation of the long axis of a rod-like element Such elements are considered to be dispersed and perfectly rigid b Schematic cross-section of a typical natural preferred orientation of phyllosilicate grains defining a schistosity Sl Grains with less favoured orientations are truncated and their volumetric contribution to the magnetic fabric may be reduced Usually the pattern of

preferred orientation can only be explained by the March model to a limited degree

and it seems unduly optimistic to consider them as universal relationships that may be extrapolated from one region to another Within a single reshygion with a limited range of deformation mechashynisms and lithological uniformity it might be posshysible to extrapolate some correlations of magnetic fabric with strain

The approaches reviewed so far in this section are essentially empirical and in most cases the susceptibility was attributed to disseminated magshynetite The studies of Coward and Whalley (1979) and of Henry and Daly (1983) were exceptions they recognised multiple sources of susceptibility and Kligfield et al (1982) also investigated the sources thoroughly The latter authors demonshystrated susceptibility anisotropy was due to iron oxides whose distributions and orientations were controlled mimetically by their position on the surfaces of the oolites used as strain markers The other studies mentioned adopt the premise or imply that magnetite grains were distributed throughout the rocks and were tectonically aligned to produce a magnetite shape-fabric which in turn dictated the magnetic fabric The underlying mechanistic model that appears to have influenced this train of thought is attributed to March (1932) This model (eg Wood et al 1976) outlines the situation in which platy elements that do not impinge upon oneanother and that are preferably randomly oriented in their initial configuration

become systematically re-oriented by homogeshyneous strain and are not impeded by the matrix (Fig 13a) Consequently the orientation-distribushytion of the poles to these platelets after constantshyvolume strain is directly related to the strain Thus for a given direction i the strain e is related to the normalised density (d) of platelet poles by

emiddot = d(-1j3 - 1 I bull

In the structural geology literature some considershyation has been given to the aspect ratios of the platelets as well as accompanying volume changes of tqe aggregate (Tullis 1976 Tullis and Wood 1975) However these modifications still fall short of reality The March model is difficult to adapt to three-dimensional grains and even more difficult to reconcile with the premises of passive beshyhaviour and non-impingement of the rotating grains on each other A worse shortcoming is the inherent assumption that the grains are spatially separated whereas in a typical metamorphic rock the variation in orientation imposes restrictions on the degree to which differently oriented crystals grow (Fig 13b) Nevertheless it has found applishycations in magnetic studies (eg Cogne and Gapais 1986) and studies of comparable mathematical models (Hrouda 1980) and is frequently cited in petrofabric studies (Oertel 1983)

Hrouda (1987) has extended these arguments to situations in which it is known that paramagnetic

12

sheet silicates such as chlorite and biotite0

dominate the anisotropy of susceptibility An inshyteresting development of this study is that in slates of the Carpathians in which the anisotropy is due to paramagnetic phyllosilicates the degree of anishysotropy is proportional to the bulk or mean susshyceptibility This has also been reported in Archean slates (Borradaile et aI in press)

Strain response models and multiple sources of susshy

ceptibility

Owens (1974) first drew attention to two imshyportant items that must be taken into account in any interpretation of susceptibility anisotropy in terms of strain Firstly the mineralogical source of the susceptibility should be defined If there are multiple sources of susceptibility the direct applishycation of the simple March model or any other model assuming a penetrative homogeneous magshynetic response is invalid Rochette and Vialon (1984) and Henry (1983) enforced this argument in different ways Slight variations in the proporshytions of minerals with different magnetic anishysotropies may under certain circumstances proshyduce changes in the bulk anisotropy that override any changes in anisotropy due to strain (Borshyradaile 1987b)

The second major point raised by Owens was that the actual strain response model has a major influence on the way in which the anisotropy accumulates from the pre-strain situation For simplicity he considered three models The first was a lineplane model that we can compare to the March model already referred to above (Fig 13a) The second was the viscous or Jeffery model in which the magnetic grain is likened to a rigid ellipsoid undergoing strain-induced motion in a viscous medium The third passive model likens the magnetic grains to passive strain markers Structural geologists may compare this to the model proposed by Ramsays school of structshyural geology to approximate the shape and conseshyquent orientation changes of for example a tectonically deforming passive ellipsoidal marker by the Rrcp equations see Fig 14 (Borradaile 1987a) Care should be taken with the term passhysive some geophysicists use the term to refer to

$e85 ~_068 fRo= 15 ~t=135

C)-shystrain ellipse (j) ~5middot Rs= 20 0_01409lt

Ro= 15 iff=15

original possive passive markers markers after strain

Fig 14 The R rlt1gt model Particles with the original orientashy J

tions (8) shown as a result of strain indicated by the strain ellipse take up new orientations (lt1raquo At the same time the ratios of the original shapes (R1f) change to final shapes (Ry2) The shape-ratio of the strain ellipse is 2 1 as indicated

the lineplane or March model and where they do not appear to imply any similarity to the Rrcp model (eg Cogne and Gapais 1986)

The mechanical response is usually neglected in the correlation of strains and susceptibility anishysotropies Indeed it is likely that many rocks and many types of deformation mechanisms are unsuishytable for establishing a correlation using the preshymises of simple mathematical models involving a single mode of deformation For example if there are relict components of sedimentary magnetic fabrics mixed with the tectonic fabrics or magshynetic fabrics of different tectonic ages a model assuming homogeneity will fail Similarly deforshymation structures that produce domainal fabrics that differently influence the magnetic fabric will cause complications if the magnetic fabric is samshypled on a scale that does not take this into account In particulate flow (Fig 15) the movement of grains may be poorly ordered Some grains move more than their neighbours rotate more or even exchange neighbours despite the fact that on a suitably large polygranular scale the strain may be approximately homogeneous Movement in polyshygranular units is also possible (Fig 16) as has been shown by experiments on analog materials (Means 1977) The scale on which magnetic susceptibility is defined will determine whether or not this preshysents a problem

The deformation mechanisms may be still more complicated The deformation may cause the rock

I bull

13

(01 (bl

Fig IS Particulate flow of a simulated (two-dimensional) aggregate Deformation proceeds from (a) through (c) The motions of particles is somewhat disordered whereas on a large scale the strain may appear to be approximately homogeneous as shown by the

strain ellipse defined by the black particles

J mm Fig 16 Experimentally produced particulate flow of groups of alum grains involving intergranular displacement surfaces

(From Means 1977)

et

deformation gt

bull00 bull

Fig 17 Possible deformation processes in metamorphic rocks that could be significant in the evolution of magnetic fabrics c -intergranular displacement surfaces (may be invisible) d-ductile (may be plastic) deformation of grains e-styloshylitie surfaces and grain-truncation f -penetration of grains g -microfaults (cleavage slip) h-rotation of blocks or groups of grains between faults or other discontinuities m-pressureshysolution material transfer (may be out of system) n-new

minerals crystallise

to be a discontinuum on various scales Lozenges of rock may rotate mass removal may occur loshycally or even to outside the system while grains plastically deform by intercrystalline processes and slide and roll past oneanother (Fig 16) At the same time new minerals may form with their crystallographic orientations controlled by the contemporary stress system Any of these factors could complicate the strain-response model of the rock and the development of its magnetic fabric While all of these processes are unlikely to occur at once the roles of several of these (or others not discussed) have to be assessed before the magnetic fabric can be correlated with the bulk strain Amongst these complications probably the most common one is the growth of new minerals as for example in phyllites schists and gneisses In these cases the explanation of schistosity may be bound up with the origin of the metamorphic texture more than with the strain of the rock (Fig 17) (Borradaile et at 1986)

Experimental studies

Although there has been some early interest in the effects of stress on magnetic susceptibility (eg Nagata 1966 1970 Kean et al 1976) this was associated with strains within the elastic limit Of interest here are the susceptibility changes that occur with large strains due to deformation that is macroscopically ductile if not actually plastic at the crystalline level The problem in the laboratory

bullbull bull bullbull bull bull

bullbull

14

environment is that even at the slowest strain rates that are practicable (10- 6 to 10-9 S-I) most rocks and minerals are not sufficiently ductile at room temperature to fail by the natural mechanisms of metamorphic rocks

Owens and Rutter (1978) first tackled this subshyject with a study of marbles and of calcite Alshythough the diamagnetic susceptibility of calcite is low the mineral is relatively easily deformed in a plastic manner at moderate confining pressures It is also stable at modest experimental temperatures so that Owens and Rutter were able to enhance the ductility by using temperatures up to 500 0 C in combination with pressures of 150 to 300 MPa (15 to 3 kbar) at strain-rates of approximately 10 - 4 to 10 - s s - 1 They achieved strains up to 50 axial-symmetrical (coaxial) shortening of the cylindrical specimens

The marbles they used had essentially isotropic magnetic and optical-crystallographic fabrics inishytially The magnetic anisotropy rapidly reached a plateau intensity at about 45 shortening The optical fabrics and the susceptibility fabric rapidly became axisymmetric to the shortening axis of the specimens This study didmiddot much to confirm the value of magnetic fabrics as indicators of strain and kinematics of deformation but most natural studies are based on ferrirnagnetic or parashymagnetic materials

Natural paramagnetic and ferrimagnetic matershyials are difficult to deform in a realistic manner without raising the temperature Heating will not normally be possible without inducing mineralogishycal changes that might mask susceptibility changes due to deformation Borradaile and Alford (1987) approached this problem by using a synthetic aggregate of sand enriched with magnetite that was cemented with commercial Portland cement The latter has a negligible (diamagnetic) susceptshyibility in comparison with the aggregate and pershymitted the aggregate to shorten by 35 in a ductile manner by axial symmetrical shortening The deshyformation did not involve cataclasis of the sand grains Rather the deformation was accommodshyated by the shearing of the cement gel This pershymitted a grain-shape alignment to develop by rollshying and sliding of the grains The magnetite grains were of the same grain-size as the matrix sand so

bulll1pl -04

bull 03

02 bull bull

01 bullbull01 02 03 04 In (XZ)

00 I I bull I I ~

11 12 13 14 15 (XI Z)

Fig 18 A correlation between the change in degree (fl) of susceptibility anisotropy and the strain ratio in some pure shear experiments on synthetic magnetite-bearing sandshy

stones (From Borradaile and Alford 1987)

that these experiments essentially addressed the problem of the rotational behaviour of the clasts (In most natural sandstones the iron oxide grains are much smaller than the sand clasts) The experiments were at carefully controlled strainshyrates of 5 x 10 - 6 S - 1 and confining pressures of 150 MPa (15 kbar) The maximum and intershymediate principal directions of susceptibility of these specimens rotated very rapidly towards the plane of flattening at rates exceeding the rate of rotation of a line undergoing homogeneous strain (cf the lineplane model) It was inferred that the magnetites rotated rigidly possibly with some plastic deformation The rotation was even more rapid when the matrix was composed of calcite instead of silicate mineral grains For initial susshyceptibility fabrics that were suitably oriented it was found that the change in the degree of anishysotropy was related to the strain by a power law (Fig 18) This serves to emphasise the importance of the initial magnetic fabric Relatively little can be deduced of the strain history from the final magnetic fabric alone Just as the initial ellipsoidal shape and orientation is of paramount importance in the strain analysis of ellipsoidal objects so is a knowledge of similar information for the initial magnetic fabric ellipsoid Although a power law relationship between the change in orientation of specially oriented magnetic fabrics exists in cershytain axial-symmetrical ( pure shear) experiments

15

In ( kmox kim J Calcite -cement - magnetite Q9g~gotes

at 150 MPo 05

04

XZHI XZmiddotH403 --

~ U-C3Z ~ AC -10 SHEAR ZOHEt ~ PURE SHEAR

02

t 01 XZ 20 XZ -115

In (kint kmln )

-0 02 03 04 -05 06 -07 os

bull Fig 19 The paths of incremental changes in magnetic anishysotropy are shown for the experimental deformation of syntheshysised calcite-cement-magnetite specimens The pure shear test produces little change in anisotropy even though the XZ strain ratio reaches 135 In contrast the changes produced in a shear zone (transpressive) are much greater despite the fact

that the ultimate XZ strain ratio for the zone is only 114

it is premature to make extrapolations to nature at the present state of knowledge

Recent work on experimental shear zones of synthetic materials at 150 MPa extends these conshyclusions to the case of transpressive deformation -a non-coaxial strain history (Borradaile and Alshyford in press) The susceptibility ellipsoids rotate rapidly toward stable orientations in which the minimum susceptibility is at a high angle to the shear zone boundaries The magnetic anisotropy changes very rapidly in the shear zones they produce a stronger magnetic fabric than axial symmetrical shortening at the same strain This is shown for two typical incremental- tests on the same synthetic calcite-matrix material at 150 Mpa in Fig 19 A further complication recognised in the experiments is that the magnetic fabrics may be planar (F gt L) whereas the mineral fabrics are constricted (a gt b) or plane strain (a = b) It is not known if these observations are transferable to natural shear zones

Conclusions

The interpretation of natural magnetic fabrics may be more complex than was initially recogshynised but progressive changes in magnetic anishysotropy do occur sympathetically with regional strain gradients despite accompanying regional

metamorphism (eg Hrouda and Janak 1976 Hrouda 1976 Coward and Whalley 1979) Indeed Rochette (1987) has shown that the metashymorphic production of pyrrhotite can enhance the susceptibility and produce a magnetically detectashyble isograd Also in certain rocks there are at least weak correlatiCfls between ratios of principal strains and the ratios of principal susceptibilities Numerous examples of the parallelism of principal susceptibility directions and structural directions (or even principal strain directions) support the contention that genetic relationships do exist beshytween strain and susceptibility in some cases Nevshyertheless these correlations are not universal and it is not possible to predict which natural situashytions will yield susceptibility data that _will faithshyfully represent principal strain directions or prinshycipal strain magnitudes or both For exampl~ magnetic fabrics do not always seem to be reliable kinematic indicators for shear zones and in the case of polyphase deformation later magnetic fabrics do not uniformly overprint earlier ones Magnetic fabrics should not be used for routine methods of strain analysis without further study A more profitable avenue is to determine how the susceptibility and strain tensors relate taking account of the actual strain-response model (deshyformation mechanisms) and the actual minerashylogical sources of susceptibility in that rock inshycluding phases produced by metamorphism A fruitful approach would be to consider the tensorial combination of coexisting magnetic subshyfabrics and successive episodes of magnetic fabric development along the lines initiated by Hrouda (1979)

Relationships between susceptibility and strain are in vogue However the earliest uses of magshynetic studies simply to investigate bulk petroshyfabrics are not yet been fully developed or inshytegrated with detailed petrofabric studies by optishycalor X-ray means Furthermore studies of remashynence and of susceptibility at different field strengths can yield information on magnetic subshyfabrics of different grain-sizes or different mineralogy This information is essential in the study of metamorphism of magnetic phases as well as their preferred orientation The anisotropy of remanence is also a profitable area of study

16 _

because only the ferrimagnetic traces contribute to that sub-fabric

Finally the nondestructive nature of magnetic fabric analysis provides a tool for investigating the progressive deformation or progressive metamorshyphism of a single specimen in laboratory experishyments Experiments on synthetii aggregates indishycate that the initial anisotropy of materials is not easily overprinted by small strains at low tempershyature They demonstrate also that the magnetic fabric ellipsoid spins very rapidly where the chief magnetic mineral is magnetite This is more noticeable when the matrix grains undergo crystal-plastic deformation Experimental shear zones produce greater changes in magnetic shape fabrics than axial-symmetrical shortening (pure shear) at the same strain they can also produce magnetic fabrics differing in symmetry from the grain fabric Such results develop an awareness for the greater complexities of natural structures

Acknowledgments

I wish to thank the Natural Sciences and Enshygineering Research Council of Canada for the continuing support of my work Frantisek Hrouda and Brian Bayly are thanked for constructive criticism of this article Karel Zapletal is thanked for some data on biotite Mel Friedman and Jan Tullis provided helpful reviews

Postscript

Since this paper was accepted for publication P Rochette has drawn attention to unusual inshyverse magnetic fabrics probably produced by single-domain magnetite (Thesis University of Grenoble 1988211 pp)

APPENDIX

Presentation of anisotropy of susceptibility

Magnetic susceptibility is a second rank tensor property conveniently envisaged as a magnitude ellipsoid (see Hrouda 1982 p 38) with three principal axes k max bull kim and k min or k ll bull kn k 33 The average or bulk susceptibility is comshy

monly defined as the arithmetic mean of the three principal values (Ellwood et al 1986-Symshyposium recommendations) but it is not clear why the arithmetic mean is a more appropriate represhysentation of bulk susceptibility than the geometric mean Susceptibility anisotropies for rocks are so low (Figs 9 and 10) that there is often little difference between these two expressions For exshyample seventeen specimens of strongly strained fine schist of the English Borrowdale Volcanic Series have principal susceptibilities in the ratio 104 102 0943 ~

Hrouda (1982) lists 25 different parameters that have been used at various times to represent anishysotropy The most useful are sometimes termed the magnetic lineation and the magnetic foliashytion

L = kmaxkint and F= kintkmin

Note that some authors chose alternative definishytions for Land F (eg Coward 1976) The parameters L and F are plotted vertically and horizontally respectively and compare directly with the ratios used to describe the strain ellipsoid on a Flinn-diagram

a=XY and b= YZ where X 2 Y ~ Z are the principal strains In some instances it is clearer if the natural logarithms of L F and of a and b are plotted

If the ratios of principal susceptibilities are listed individually it is helpful to normalise them so that their product is unity The normalised versions of the principal susceptibilities are related to their ratios by the following relations

kmax = L 2 3 bull pl3

kml

= L -13 F I 3

k = L -13 bull F- 23mm

It is advisable also to present a mean (bulk) susceptibility value This enables the reader to assess the significance of the results (Conference recommendations Ellwood et al 1986) Unforshytunately this has often not been done in the past Commonly one finds that anisotropies are poorly reproducible for rocks with susceptibility lt 10-4

SIjvol Providing cones of confidence about principal directions and standard errors for prinshycipal magnitudes is also useful in this regard

bull

30

2-5

20

-5

10 F=~ WI shy - middotmiddotV j Y

0 5 20 25 30 35

F =(klnkmin)

Fig AI The relationship between Jelineks (1981) P and T parameters and the conventional anisotropy parameters L and

F

The ratios L and F like their counterparts in strain (a and b) are very useful in describing the ellipsoids shape or sense of anisotropy However the distance of the point (L F) from the origin is also a measure of the degree of anisotropy that is to say its departure from sphericity Jelineks (1981) parameters pi and T overcome this T represents sense of anisotropy and ranges from -1 (prolate) to + 1 (oblate) pi (gt 1) expresses degree of anisotropy These are defined as

[ 2(In k -In k~]T= -1

In k itM - In k min 1

pi = exp [ 2( af + a ~ + a~ ) ] ~ where a1 = In(kmaxkb) etc and kb = (kmax k inl

kmin )(l3) The relationship of p and T to L and F is shown in Fig AI

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17

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Rochetle P 1987 Metamorphic control of the mineralogy of black shales in the Swiss Alps toward the use of magnetic isograds Eanh Planet Sci Lett 84 446-456

Rochette P 1988 Relation entre deformation et metamorshy

f

bull

phisme Alpin dans les schistes noirs Helvetiques Iapport de la fabrique magnetique Geodin Acta 2 (in press)

Rochette P and Vialon P 1984 Development of planar and linear fabrics in Dauphinois shales and slates (French Alps) studied by magnetic anisotropy and its mineralogical conshytrol J Struct Geo 6 33-38

Schwarz E 1974 Magnetic fabrics in massive sulfide deposits Can J Earth Sci 11 1669-1675

Schwartz EJ 1975 Magnetic properties of pyrrhotite and their use in applied geology and geophysics Geo Surv Can Pap 74-59 24 pp

Singh J (now Rathore J) Sanderson DJ and Tariing DH 1975 The magnetic susceptibility anisotropy of deformed rocks from North Cornwall England Tectonophysics 27 141-153

Smith GM and Banetjee SK bull 1987 The dependence of weak field susceptibility on applied magnetic field Phys Earth Planet Inter 46 71-76

Stott GM and Schwerdtner WM 1981 A structural analyshysis of the central part of the Shebandowan metavolcanicshymetasedimentary belt Ontario Dep Mines Toronto Final Repbull Onto Geosci Res Rep No 5349 44 pp

Strangway DW 1970 History of the Earths Magnetic Field McGraw-Hili New York NY 168 pp

Tarling DH 1983 Paleomagnetism Chapman and Hall London 379 pp

Tullis TEbull 1976 Experiments on the origin of slaty cleavage and schistosity Geo Soc Am Bull 87 745-753

Tullis TE and Wood DS 1975 Correlation of finite strain from both reduction bodies and preferred orientation of mica in slate from Wales Geol Soc Am Bull 86 632-638

Urrutia-Fucugauchi J and Odabachian Y 1982 A Bibiograshyphy of Magnetic Susceptibility Anisotropy of Rocks Inshystituto de Geofisica Universidad Nacional Autonoma de Mexico Mexico 42 pp

Uyeda S Fuller MD Belshe JC and Girdler RW 1963 Anisotropy of magnetic susceptibility of rocks and minershyals J Geophys Res 68 279-291

Van den Ende C 1975 On the origin of anisotropy of magshynetic susceptibility in Permian Redbeds from the western part of the Dome de Barrot (S France) In GJ Borradaile et al (Editors) Progress in Geodynamics North-Holland Pub Co Amsterdam pp 176-189

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20

II

Wing-Fatt L and Stacey FD 1966 Magnetic anisotropy of laboratory materials in which magma flow is simulated Pure AppJ Geophys 6478-80

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Zavoyskiy VN 1982 Use of magnetic susceptibility tensor for solving problems in structural geology Izv Akad Nauk SSSR Earth Phys Ser 18 217-223

3

TABLE 1 netic fabric (Uyeda et aI 1963) Thus the susceptshySusceptibility data for common metamorphic minerals ibility anisotropy of magnetite will in practice

Mineral Minimum anisotropies

k max kin k min kan

(SI unitsvol XlO- 6 )

---Actinolite 1076 0982 0947 3560

Actinolite 1083 1027 0899 6500

Hornblende 1347 0917 0809 8920

Crocidolite 1052 0992 0958 333

Glaucophane 1094 1006 0908 787

Chlorite 1093 1060 0864 358

Chlorite 1287 1058 0734 70

Chlorite 1128 1023 0866 1550

Chlorite 1063 1020 0921 370

Biotite 1114 1106 0812 1230

Biotite 1098 1095 0832 1180

Biotite a 1107 1096 0824 998

Biotite bull 1108 1107 0814 1290

Phlogopite 1098 1091 0838 1180

Muscovite 1159 1052 0820 165

From Borradaile et al (1987) where further details may be

found

bull Pure specimens by personal communication through Karel Zapletai from Hrouda et al (1985a) These specimens also

show good agreement between the mean susceptibility reo

ported here and the susceptibility predicted theoretically

from the precisely determined compositions)

on anisotropy are expected to be small) Magshynetite is the only mineral of importance in which the grain shape fabriC directly influences the mag-

TABLE 2

A Weakly susceptible rockforming minerals (units are Sljvol x 10-6 )

Mineral Mean k St Reference dev

Plagioclase -278 034 Borradaile et al (1987)

(oligoclase)

Quartz -134 080 Hrouda (1986)

Calcite -138 034 Voight and Kinoshita (1907)

Talc +54 082 Borradaile et al (1987)

B Anisotropy of weakly susceptible minerals

Mineral Anisotropy Reference

ratio

kckab

Quartz 101 Voight and Kinoshita (1907) Nye (1957)

Calcite 111 Voight and Kinoshita (1907)

Owens and Rutter (1978)

depend on the particular habit of the grains in question and which is nearly equidimensional for detrital examples For example detrital magnetite has been reported with an anisotropy of 1108 0964 0936 by the author and Rees (1965) reports another example with susceptibilities in the ratio 106 097 097 Hydrothermal magshynetites (Heider et aI 1987) can have much higher dimensional anisotropies (eg 2 1) as do some magmatic examples The problems arising from the shape effects of magnetite are compounded by the grouping of grains to form elongate masses There can be tectonic causes for this for example where pre-existing magnetites have been strung together to form elongate domains by pressure solution or other forms of metamorphic differshyentiation In sediments trains of magnetite grains may be formed by colonial bacteria (Karlin et aI 1987 Chang et aI 1987)

Hematite has an enormous intrinsic crystalloshygraphic magnetic anisotropy with maximum susshyceptibility parallel to its basal planes and a ratio of maximum to minimum susceptibility reported as gt 100 (Table 3) These extreme anisotropies for single crystals are not realised from polycrystalline samples a minimum anisotropy estimated from Hargraves (1959) and Hrouda et ai (1985b) is

127 122 056 In the case of hematite-bearing metasediments even with intensely developed petro fabric anishysotropies (Kneen 1976) the magnetic anisotropies are typically only

1023 0993 0983 Hematite like the paramagnetic and diamagnetic rock-forming minerals yields a component of magnetic fabric to the rock that is influenced primarily by the crystallographic alignment of the anisotropic grains Other ore minerals also have large susceptibility anisotropies (Table 3) but these are relatively rare in metamorphic rocks

Mineralogical sources of magnetic susceptibility in rocks

The magnetic fabric relates primarily to the petrofabric of the significantly susceptible mineral

4

TABLE 3

Susceptibility and anisotropy of iron minerals (units are Slfvol)

A Anisotropy controlled by shape (Borradaile et aI 1987)

Mineral k max k int kinin Mean value

Magnetite (crushed metamorphic) 1063 0989 0951 58

Magnetite (detrital) 1108 0964 0936

B Crystallographic anisotropy

Mineral Anisotropy ratio Maximum susceptibility value Reference

Hematite gt 100 1 1 x 10 - 2 basal planes Uyeda et al (1963)

Pyrrhotite c 10000 1 10 basal planes Schwarz (1974)

Pyrrhotite 1024 368 0027 Rochette (1988) 910 391 0028

Ilmenite-hematite 15 1 04 basal planes Uyeda et al (1963)

C Mean values of other iron minerals (Carmichael 1982)

Mineral Mean susceptibility (approximate)

Magnetite 62

Ilmenite 18

Pyrrhotite 15

Titanomagnetite 001

Hematite 0007 Siderite 0005

Limonite 0003

Pyrite 0001

species If all the minerals in a rock have similar magnitudes of susceptibility then it should be expected that the magnetic susceptibility ellipsoid bears some close relationship to the gross petroshyfabric However where the susceptibility is chiefly carried by an accessory mineral the susceptibility ellipsoid will only be represerttative of the rocks fabric to the degree that the accessory minerals imitate and are coeval with the host fabric Hitherto most papers on deformed rocks col1shycentrated on rocks in which the accessory iron oxides particularly magnetite and hematite were the dominant source of susceptibility However the incoming of pyrrhotite at the expense of pyrite during progressive metamorphism may also conshytribute to the susceptibility of certain greenschist facies metamorphic rocks (Rochette 1987 Borshyradaile et al in press)

Bulk susceptibility values are readily available (International Critical Tables 1929 Weast and Astle 1978 Carmichael 1982) whereas anishy

sotropy data are rarer beginning with the report of Voight and Kinoshita (1907) The earliest deshyterminations used sufficiently large fragments of single crystals and the same approach continues

- shy(0) (b)

Fig 1 It is possible to physical1y arrange anisometric minerals into linear (a) and planar (b) fabrics as shown One can then

detennine the susceptibilities of the cubical specimens in the

directions I m and n and these yield minimum estimates of

the anisotropies of the minerals This simple method enables one to estimate the minimum anisotropy of susceptibility of

the actual fine-grained minerals separated from a metamorphic rock

5

T p bull B2 bull BI diSC -snoped

middotM C2

rod -shoped

-I 0 t~1 1~2 1~3 14 s 16 t~1 pi

Fig 2 Susceptibility anisotropies of metamorphic minerals separated from metamorphic rocks (from Borradaile et al 1987) and the field (stippled) of common metamorphic rocks (from Hrouda et al 1978) P and T are explained in the Appendix AI AZ-actinolite BI etc-biotite CI etc-chlorite CR-crocidolite G-g1aucophane H-bomblende M-muscovite

P-phJogopite Triangle-metamorphic magnetite partly crushed triangle in circle-detrital magnetite

for ore minerals (Uyeda et al 1963 Schwarz 1974 1975 Rochette 1988) hornblende (Parry reported in Wagner et al 1981) augite and calcite (Owens and Bamford 1976) and quartz (Hrouda 1986) However for many rock-forming metamorshyphic minerals large single crystals are unavailable or have unrepresentative compositions To overshycome this problem samples large enough for deshytermination can be synthesised by orienting small (c 1 mm) grains into an aggregate (Borradaile et al 1986) This technique can be applied to any markedly anisometric single-crystal grains that can be physically manipulated or magnetically arranged into a strong preferred crystallographic orientation (Fig 1) The technique yields a minishymum estimate of the anisotropy because it is not possible to produce a perfect alignment of crystalshylographic axes in this manner Nevertheless it is the only practical method at the present time for isolating the contribution of specific mineral grains with fme-grained habits to the susceptibility and anisotropy of susceptibility of a given rock

Anisotropy data for some important rock-forshyming minerals mainly from metamorphic rocks and some bulk anisoir~py data for other imshyportant minerals are given in Table 1 and Fig 2

Contributions to whole-rock susceptibility and its anisotropy

Initially most work on metamorphic or deshyformed rocks concentrated on examples in which the susceptibility was due to iron oxides However several workers have addressed the more general situation in which there may be paramagnetic

contributions also (Coward and Whalley 1979 Henry 1983 Rochette and Vialon 1984 Borshyradaile et al 1986 Lamarche and Rochette 1987) or even diamagnetic contributions (Hrouda 1986) Such effects become important where magnetite is present in small amounts usually less than 1 wt in a rock that has a matrix of moderately susceptishyble silicates Detailed magnetic studies have been undertaken involving magnetic susceptibility deshyterminations at different field strengths (Coward and Whalley 1979 Hrouda and Jelinek in press) at different temperatures (Rochette and Vialon 1984) and the effects of temperature on remanent magnetisation (KJigfield et al 1982) Such studies have identified the mineralogical source of the susceptibility However those techniques are not routine and it may be beneficial to physically separate the minerals in a few typical samples so that susceptibility measurements may be carried out on these individually

Henry (1983) and Henry and Daly (1983) inshyferred multiple sources of susceptibility from the measurements directly by using multiple specishymens of similar lithologies but different intensities of fabric The method uses a plot of principal susceptibilities of individual specimens against their mean or bulk susceptibility The data for each of the principal susceptibilities lie on straight lines that intersect at a point that has equal values on both graph axes This can be considered as a gradual transition in anisotropies from the most anisotropic case at the right of the graph through lesser anisotropies to a theoretically predictable equivalent isotropic case in which all principal susceptibilities equal the mean susceptibility (Fig

6

10-4

o

ki (i I 10 3) [ellsem ]

e~

~~T ~~I

eQ e ~ 0 v~ e~ - 1 ~~fFel e~ gt

$ ~~ I V( (shy~+ middot~eQ ~( e

(- bull v ( oJ ~ ~~e9 r ~ u 1 I I bull 1

+ 1 mosl anisolropic + specimen

leasl anisolropic specimen

i ( bull k [ellsem]

o 10-4

Fig 3 Diagram from Henry (1983) showing the variation in anisotropy of adjacent specimens or parts of a specimen The axes are individual principal susceptibilities (vertical) and the

mean or bulk susceptibility (horizontal)

3) This pattern was predicted by Henrys model of additive combinations of ferrimagnetic contrishybutions from traces of magnetite with contribushytions from paramagnetic silicates In a natural example the range in anisotropies on his special plot could be an indication of the degree to which mineralogical constitution affects the magnetic anshyisotropy of a rock Other influences cannot be ruled out however The variation in mineral comshyposition between different specimens or the variashytion in the degree to which the ferrimagnetic grains have similar preferred orientations to the other mineral grains could al~o playa role

Studies of susceptibility at low temperatures and of remanent and saturation magnetisation have confirmed that there are paramagnetic conshytributions from silicates and that these can swamp the ferrimagnetic contributions (Coward and Whalley 1979 Henry and Daly 1983 Rochette and Vialon 1984) These contributions cannot yet be attributed to a specific mineral without physishycally separating the grains (Hrouda and Jelinek in press)

The reverse procedure predicting whole-rock anisotropy from multiple mineralogical sources is easier Consider a rock with a perfect preferred crystallographic fabric of mica grains with their basal planes perfectly parallel and their long axes perfectly aligned in that plane In the simple case of a monomineralic rock with perfectly aligned

grains the mineral anisotropy is equal to the anisotropy of the rock If susceptibility contrishybutions from different mineral sources can be summed as Henry (1983) and Hrouda (1986) sugshygest the effect of adding a small proportion of magnetite to a paramagnetic matrix can be predicshyted For simplicity assume that the magnetite grains are dispersed and present as a small trace ( lt 1) with a perfect shape alignment coaxial with the preferred crystallographic fabric of the matrix Although magnetite has an enormous susshyceptibility magnitude its anisotropy (directly reshy

lated to its shape) is usually small especially if it is of detrital origin On the other hand metamorshyphic silicates have moderate susceptibility magnishytudes but very high anisotropies (Table 1) (Whether the susceptibility anisotropy is intrinsic or due to inclusions is immaterial here)

The magnetic anisotropies of metamorphic silicate grains are more extreme than those of most metamorphic rocks Thus a trace of magshynetite combined with much mica in a schist proshyduces an anisotropy intermediate between that of the minerals In Fig 4 this thought experiment is carried out using model rocks with 60 plagioclase (a diamagnetic matrix with almost negligible susceptibility) traces of magnetite in the proportions stated on the figure and about 40 of the named metamorphic silicate From Fig 4 it can be seen that the anisotropy of the rock is virtually equal to that of magnetite if the latter is present as gt 1 This is important for those intershypretations of magnetic fabrics in terms of March-type analysis (see below) in which disshyseminated markers are virtually solely responsible for the magnetic fabric But where the magnetite is present in smaller proportions the anisotropy of the rock may be influenced more by the composishytion of the rock than by its petrofabric or strain Thus compositional variation between specimens could produce differences in anisotropy even if the specimens had identical fabrics or strains

Recently a mathematical model has been inshyvestigated in which paramagnetic silicates are the only source of susceptibility (Hrouda 1987) With increasing preferred crystallographic orientation the anisotropy is shown to increase until it equals that of the crystal lattice Hrouda notes that this

14

13

1-2

I-I

t1-0 I-I -2 13 k2k3 Fig 4 Flinn-type diagram of susceptibility anisotropies for hypothetical rocks indicating the effects of variable proporshytions of magnetite and a paramagnetic mineral Each rook is represented by a tie-line and is composed of approximately 40$ of the named mineral plus magnetite (in the small fraction indicated by the numbers on the tie-line) and 60$ feldspar As the proportion of magnetite in the rock is increased (from 10-6

at the distal end of the tie-line in each case) the magnetic anisotropy of the rock decreases towards the anisotropy of magnetite The anisotropy of the particular magnetite chosen in these models is located near the convergence of the tie-lines

(From Borradaile 1987b)

relationship can be disturbed by the smallest traces of ferrimagnetic material and is difficult to calibrate in terms of strain Moreover a general difficulty of this type of mathematical model (both in magnetic fabrics and petrofabrics) is that it treats the grains as dispersed crystallites of no finite size which are free to develop their ideal crystal shape In nature grains are in contact and in the case of paramagnetic silicates in metamorshyphic tectonites their preferred orientations pose special problems For example grains with crystalshylographic orientations at high angles to the preshyferred orientation (schistosity) are restricted in growth Thus their reduced volumes will decrease their contribution to the rock anisotropy (see Fig 13b)

Magnetic anisotropy and finite strain

Principal susceptibility directions

In rocks with strong tectonic fabrics the prinshycipal magnetic susceptibility directions are often

7

parallel to prominent structural directions (Kligshyfield et al 1977) or related to fold geometry (Owens and Bamford 1976) For example the minimum susceptibili ty is usually perpendicular to a primary cleavage The maximum susceptibility may be parallel to the maximum extension in the rock (eg Fig 6b) contained in the cleavage and defined by stretched objects or mineral lineations (eg Singh et aI 1975 Kligfield et aI 1977 Coward and Whalley 1979 Rathore 1979 Goldshystein 1980) In contrast the maximum susceptibilshyity may be parallel to the intersection lineation of bedding and cleavage (eg Hrouda 1976 also Fig 5)

These two different patterns have been intershypreted in a number of ways One interpretation is that the maximum susceptibility is parallel always to the maximum extension It implies that the intersection lineation of bedding and cleavage is the maximum extension direction This appears to be unusual because an intersection lineation is the fortuitous interference of a tectonic fabric with the disturbed bedding surfaces In some areas the magnetic fabrics may be reasonably consistent in orientation while the (single-generation) fold hinges and intersection lineations may vary conshysiderably in orientation (Fig 6) There is no good reason for supposing that the intersection lineashytion must necessarily have some genetic relation to the strain ellipsoid

Another interpretation is that maximum susshyceptibilities occur parallel to intersection lineashytions because of heterogeneous combinations of sub fabrics If some portions of the rock retain a

bedding

cleole

bull maximum susceptibilify

intermediote susceptibility bull minimum sUKeptibihly

Fig 5 Principal susceptibility directions in Hercynian slates with a single tectonic fabric Note the maximum susceptibilishyties close to the intersection lineation of cleavage and bedding and the minimum susceptibility perpendicular to bedding

(From Borradaile and Tarling 1981)

8

bull -l-A~

~xL 0--~

~

b)0)

SUSCfptiblhtibullbull bull mcaimum in~rmtdIQt bull mntnlUtl

X IMOn fOld plunQl I inttotcon liMohon

Fig 6 Susceptibility orientations and major fold plunges in Archean slates with a single tectonic fabric Despite the varishyation in fold plunge ( sheath folds or periclinal folds) the metamorphic and magnetic fabrics are reasonably consistently

oriented in different adjacent parts of the area (From Borradaile and Brown 1987)

bedding parallel oblate magnetic fabric due to sedimentation then this may interfere with the fabric due to tectonic causes Under the right circumstances which are not too special this comshybination may produce maximum susceptibilities parallel to cleavage and bedding or perpendicular to the stretching direction (Fig 7) For this exshyplanation to be valid indeed for this arrangement of susceptibility axis to be detectable the interfershying subfabrics must be present on scales smaller than the sample size used in susceptibility deshyterminations (usually about 10 em3) Recently bedding-parallel fabrics have been detected in

L L

0 IIbullbulllli0 degiOo bull

(a) (b)

susceptibilities bull mo int-dio 0 mi

Fig 7 Variation in principal susceptibility orientations in meta-sandstones with a single tectonic fabric L indicates the grain elongation in the schistosity plane which is horizontal in these diagrams In some cases the maximum susceptibility is nearly parallel to the grain elongation (b) in others it is

perpendicular (a) (Borradai1e and Tarling 1984)

stylolitic cl~voge dOmOin

Fig 8 Where a tectonic fabric develops a domainal texture such as in stylolitic cleavage there may be distinct contribushytions of magnetic anisotropy from different parts of the rock Qeavage zones may contribute a tectonic susceptibility anishysotropy while inter-cleavage domains may still retain a sedimiddot mentary magnetic fabric The susceptibility determination for

the rock blends the two fabrics

metasediments with isoclinal sheath folds (Borshyradaile et al bull in press)

A third explanation similar to the previous one has been given for rocks that have been very weakly strained with pressure solution as the deshyformation mechanism lbis mechanism often proshyduces a regular domainal tectonic fabric of closely spaced laminae which concentrate insoluble material (including iron oxides and paramagnetic silicates) in thin sheets between rock that retains a sedimentary fabric Where laminae are more closely spaced than the width of the core used to determine susceptibility the net susceptibility is a combination of sedimentary and tectonic contrishybutions In this case the maximum susceptibility is often parallel to the intersection lineation of the domains (stylolitic cleavage) and bedding (Fig 8) Rochette and Vialon (1984) note that heterogeshyneous fabrics combining magnetic sub-fabrics of different ages prohibit any kind of quantitative correlation of strain and susceptibility

In mylonite zones (Goldstein 1980) and in major shear zones (Rathore 1985) magnetic fabrics have orientations that indicate maximum susceptshyibilities compatible with maximum extension dishyrections Similarly minimum susceptibilities are reported perpendicular to schistosities or foliashytions The relationship to boudinage directions and mineral stretching lineations has been cited to support the contention that there is a one-ta-one correspondence of strain axes and principal susshyceptibility directions in some cases Hrouda (1979 reported 1977) seems to have been the first person

9

to have considered the combining effects of magshynetic fabrics of different ages He described early susceptibility fabrics by a tensor P superimposed tectonic fabrics by a tensor D and suggested that they combine to form a resultant susceptibility tensor R by

D P = R or D = R p- 1

Goldstein (1980) applied the same approach to mylonitic fabrics Some authors have simply asshysumed that it is permissible to use the orientations of magnetic fabrics within shear zones rather like a schistosity to determine the amount and sense of shear Similar studies have been carried out subsequently on shear zones up to a regional scale in extent (eg Rathore 1985) However in experishymental shear zones the author has found that earlier magnetic fabrics are difficult to overprint and magnetic fabric maybe an unreliable kineshymatic indicator

Magnitudes ofsusceptibility and magnitudes ofstrain

The relationship between the shape of the magshynitude ellipsoid of susceptibility and the intensity of the tectonic fabric is more complex than the relationship between directions as discussed in the previous section Usually comparisons have been attempted between the shapes of the susceptshyibility and finite strain ellipsoids The latter is usually derived from some macroscopic straiI) marker such as pebbles concretions lappilli or rotated sand-dikes (eg Rathore 1979 Borradaile and Tarling 19811984 Rathore and Henry 1982 Clendenen et at 1988 Hirt et al 1988) Reducshytion spots have been used as strain markers from time to time however their pre-metamorphic origin is not always certain and in the Welsh examples some outcrops have susceptibilities that are too low to give reproducible magnetic fabrics

The susceptibility ellipsoid normally plots much nearer the origin of the Flinn-diagram than does the strain ellipsoid (Fig 9) In some cases logashyrithmic plots (Fig 10) help in their discrimination The relationships between strain and magnetic fabric are not straightforward The most strained samples in an outcrop do not necessarily have the most extreme magnetic anisotropies This is shown

a or L

20-1 AI IfIOOltfrc ItJtedtlDoloty 0IItN11tOy

JWUiOl2L1LL bull for QIdfl c~1 f~~

O for fktlPOf lCIStl ( ~ I

15

ol~~ ~bOrF 10 15 20 B

Fig 9 Strain ellipsoid data determined by de-straining analyshysis for quartz clasts and for feldspar clasts and the susceptibilshy

ity anisotropy in meta-sandstones a XY b - YZ where X lt Y lt Z L and F are the equivalent ratios for the magnetic susceptibility There is a single schistose tectonic fabric Data for the same hand-specimens are connected by tie-lines There is no simple relationship between the magnitude of strain and

intensity of magnetic fabric (Borradaile and Tarling 1984)

by the crossing tie-lines in Fig 9 Moreover there is always some question as to the validity of the comparison since the strain is commonly heterogeshyneous on the scale of a thin section whereas the homogeneously strained markers are much larger Susceptibility is usually measured from a sample about 10 cm3

so that the susceptibility tensor will be defined on a smaller scale than the strain tensor Another approach although less common in the literature is to compare the susceptibility

t log a (log l)

~ ~

~ +~ iii~iffl ~

0 lr b ~ C-_~~

0 ~J 04 ~tgt~J-~

~~~I ~~Q

0middot1

az

~ llZ I

o CH 02 0middot4 0middot6 08 1middot0 IZ

- log b (log F)

bull ST~AIN EItIPSOIO SHAPE SUSCEPTISILITY ELUPSOID SHAPE

Fig 10 Strain ellipsoid data and susceptibility data for four outcrops of slate (l to IV) with a single tectonic fabric connected by tie-lines and presented on a logarithmic Flinn-dishy

agram (From Borradaile and Tarling 1981)

bull bull bull bull

10

003

Mj maximum (i -I) values

006 I intermediate I

( i bull 2 l values 1 ~~---------~~------

- 003 -lmiddotmiddot - 006

bull bull III(L -middot00

II I

minimum (imiddot 3) values

I NmiddotI 000

Fig 11 Nonnalised measures of principal susceptibility magnishytudes (M) and o( principal strain magnitudes (Ni ) (or specishymens o( a metavolcanic rock with a single tectonic fabric There is no correlation between minimum values of susceptibilshyity and strain nor between intennediate values etc Nevertheshyless it would be possible to infer a correlation incorrectly by considering all the data laquo(or maximum intermediate and minimum susceptibilities) simultaneously (From Borradaile

and Mothersill 1984)

fabric with the petrofabric of a slightly smaller sample detennined by means of X-ray texture goniometry (eg Wood et al 1976 Hrouda et al 1985b) This overcomes the criticism that different scales will be sampled but there is the added complication of interpreting the texture goniomeshyter data in terms of finite strain (Oertel 1983)

One of the earliest attempts to relate the strain and susceptibility tensors was by Kneen (1976) She plotted ratios of principal strains against ratios of principal susceptibilities and inferred correlashytions Similar studies that compared strain ratios with susceptibility anisotropy used special loga-

M 02

rithmic parameters to normalise values (Wood et al 1976 Rathore 1979 1980 Rathore and Henry 1982 Kligfield et al 1982) These are termed IV (for strain) and M (for susceptibility) where i = 1 2 or 3 for the appropriate principal value The actual algebraic definition of N and M varies in the literature and care should be taken in comparshying data from one paper to another) Unforshytunately in most of these cases the authors plotted the data for all three principal directions on the same axes and generally established correlation coefficients for the maximum intermediate and minimum values simultaneously Strictly speaking this is invalid (Fig 11) and in one instance the correlation of anisotropies attempted in this manner has been disproved (Borradaile and Mothersill 1984)

This may give a discouraging view of the correshylations of strain and susceptibility but the data already published do give some indication that correlations may exist although weaker than origishynally claimed For example comparing data for just minimum (normalised) strains and minimum (normalised) susceptibilities it is possible to reshycognise modest correlations between susceptibility and strain in the case of the Welsh slates (eg Wood et al 1976) here in Fig 12 Clendenen et al (1988) have recently recognised that this kind of weaker correlation between the strain of conshycretions and susceptibility can be statistically sigshynificant

Thus although weak correlations of the kind

klk2 =(XY) may exist these must only be of local siginificance

I I I bullbullbullbullbullbullbull bull

I ttl bullbull~

ol------------r ------ shy bull V

~- fmiddot I maximum (i1) and -0middot2 r I intermediate (middot 2 ) values

minimum values (i 3) I

~~~____~____~I~____~ Nj -~ -~ 0 ~

Fig 12 Nonnalised measures of principal susceptibilities (M) and of principal strains (Ni ) for slates with a single tectonic fabric Note that a weak correlation exists between minimum strains and minimum susceptibilities (From Wood et al 1976)

11

Q Z p Marchian rofafion

S ~ b

t1- y p 0- Zr +y~

k X L oL

X SI bull bull S

Fig 13 a Theoretical outline of the March model as applied to the rotation and preferred orientation of phyUosilicate grains For strain axes X ~ Y ~ Z the rotation of a pole p of a platelet is shown schematically as is the rotation of the long axis of a rod-like element Such elements are considered to be dispersed and perfectly rigid b Schematic cross-section of a typical natural preferred orientation of phyllosilicate grains defining a schistosity Sl Grains with less favoured orientations are truncated and their volumetric contribution to the magnetic fabric may be reduced Usually the pattern of

preferred orientation can only be explained by the March model to a limited degree

and it seems unduly optimistic to consider them as universal relationships that may be extrapolated from one region to another Within a single reshygion with a limited range of deformation mechashynisms and lithological uniformity it might be posshysible to extrapolate some correlations of magnetic fabric with strain

The approaches reviewed so far in this section are essentially empirical and in most cases the susceptibility was attributed to disseminated magshynetite The studies of Coward and Whalley (1979) and of Henry and Daly (1983) were exceptions they recognised multiple sources of susceptibility and Kligfield et al (1982) also investigated the sources thoroughly The latter authors demonshystrated susceptibility anisotropy was due to iron oxides whose distributions and orientations were controlled mimetically by their position on the surfaces of the oolites used as strain markers The other studies mentioned adopt the premise or imply that magnetite grains were distributed throughout the rocks and were tectonically aligned to produce a magnetite shape-fabric which in turn dictated the magnetic fabric The underlying mechanistic model that appears to have influenced this train of thought is attributed to March (1932) This model (eg Wood et al 1976) outlines the situation in which platy elements that do not impinge upon oneanother and that are preferably randomly oriented in their initial configuration

become systematically re-oriented by homogeshyneous strain and are not impeded by the matrix (Fig 13a) Consequently the orientation-distribushytion of the poles to these platelets after constantshyvolume strain is directly related to the strain Thus for a given direction i the strain e is related to the normalised density (d) of platelet poles by

emiddot = d(-1j3 - 1 I bull

In the structural geology literature some considershyation has been given to the aspect ratios of the platelets as well as accompanying volume changes of tqe aggregate (Tullis 1976 Tullis and Wood 1975) However these modifications still fall short of reality The March model is difficult to adapt to three-dimensional grains and even more difficult to reconcile with the premises of passive beshyhaviour and non-impingement of the rotating grains on each other A worse shortcoming is the inherent assumption that the grains are spatially separated whereas in a typical metamorphic rock the variation in orientation imposes restrictions on the degree to which differently oriented crystals grow (Fig 13b) Nevertheless it has found applishycations in magnetic studies (eg Cogne and Gapais 1986) and studies of comparable mathematical models (Hrouda 1980) and is frequently cited in petrofabric studies (Oertel 1983)

Hrouda (1987) has extended these arguments to situations in which it is known that paramagnetic

12

sheet silicates such as chlorite and biotite0

dominate the anisotropy of susceptibility An inshyteresting development of this study is that in slates of the Carpathians in which the anisotropy is due to paramagnetic phyllosilicates the degree of anishysotropy is proportional to the bulk or mean susshyceptibility This has also been reported in Archean slates (Borradaile et aI in press)

Strain response models and multiple sources of susshy

ceptibility

Owens (1974) first drew attention to two imshyportant items that must be taken into account in any interpretation of susceptibility anisotropy in terms of strain Firstly the mineralogical source of the susceptibility should be defined If there are multiple sources of susceptibility the direct applishycation of the simple March model or any other model assuming a penetrative homogeneous magshynetic response is invalid Rochette and Vialon (1984) and Henry (1983) enforced this argument in different ways Slight variations in the proporshytions of minerals with different magnetic anishysotropies may under certain circumstances proshyduce changes in the bulk anisotropy that override any changes in anisotropy due to strain (Borshyradaile 1987b)

The second major point raised by Owens was that the actual strain response model has a major influence on the way in which the anisotropy accumulates from the pre-strain situation For simplicity he considered three models The first was a lineplane model that we can compare to the March model already referred to above (Fig 13a) The second was the viscous or Jeffery model in which the magnetic grain is likened to a rigid ellipsoid undergoing strain-induced motion in a viscous medium The third passive model likens the magnetic grains to passive strain markers Structural geologists may compare this to the model proposed by Ramsays school of structshyural geology to approximate the shape and conseshyquent orientation changes of for example a tectonically deforming passive ellipsoidal marker by the Rrcp equations see Fig 14 (Borradaile 1987a) Care should be taken with the term passhysive some geophysicists use the term to refer to

$e85 ~_068 fRo= 15 ~t=135

C)-shystrain ellipse (j) ~5middot Rs= 20 0_01409lt

Ro= 15 iff=15

original possive passive markers markers after strain

Fig 14 The R rlt1gt model Particles with the original orientashy J

tions (8) shown as a result of strain indicated by the strain ellipse take up new orientations (lt1raquo At the same time the ratios of the original shapes (R1f) change to final shapes (Ry2) The shape-ratio of the strain ellipse is 2 1 as indicated

the lineplane or March model and where they do not appear to imply any similarity to the Rrcp model (eg Cogne and Gapais 1986)

The mechanical response is usually neglected in the correlation of strains and susceptibility anishysotropies Indeed it is likely that many rocks and many types of deformation mechanisms are unsuishytable for establishing a correlation using the preshymises of simple mathematical models involving a single mode of deformation For example if there are relict components of sedimentary magnetic fabrics mixed with the tectonic fabrics or magshynetic fabrics of different tectonic ages a model assuming homogeneity will fail Similarly deforshymation structures that produce domainal fabrics that differently influence the magnetic fabric will cause complications if the magnetic fabric is samshypled on a scale that does not take this into account In particulate flow (Fig 15) the movement of grains may be poorly ordered Some grains move more than their neighbours rotate more or even exchange neighbours despite the fact that on a suitably large polygranular scale the strain may be approximately homogeneous Movement in polyshygranular units is also possible (Fig 16) as has been shown by experiments on analog materials (Means 1977) The scale on which magnetic susceptibility is defined will determine whether or not this preshysents a problem

The deformation mechanisms may be still more complicated The deformation may cause the rock

I bull

13

(01 (bl

Fig IS Particulate flow of a simulated (two-dimensional) aggregate Deformation proceeds from (a) through (c) The motions of particles is somewhat disordered whereas on a large scale the strain may appear to be approximately homogeneous as shown by the

strain ellipse defined by the black particles

J mm Fig 16 Experimentally produced particulate flow of groups of alum grains involving intergranular displacement surfaces

(From Means 1977)

et

deformation gt

bull00 bull

Fig 17 Possible deformation processes in metamorphic rocks that could be significant in the evolution of magnetic fabrics c -intergranular displacement surfaces (may be invisible) d-ductile (may be plastic) deformation of grains e-styloshylitie surfaces and grain-truncation f -penetration of grains g -microfaults (cleavage slip) h-rotation of blocks or groups of grains between faults or other discontinuities m-pressureshysolution material transfer (may be out of system) n-new

minerals crystallise

to be a discontinuum on various scales Lozenges of rock may rotate mass removal may occur loshycally or even to outside the system while grains plastically deform by intercrystalline processes and slide and roll past oneanother (Fig 16) At the same time new minerals may form with their crystallographic orientations controlled by the contemporary stress system Any of these factors could complicate the strain-response model of the rock and the development of its magnetic fabric While all of these processes are unlikely to occur at once the roles of several of these (or others not discussed) have to be assessed before the magnetic fabric can be correlated with the bulk strain Amongst these complications probably the most common one is the growth of new minerals as for example in phyllites schists and gneisses In these cases the explanation of schistosity may be bound up with the origin of the metamorphic texture more than with the strain of the rock (Fig 17) (Borradaile et at 1986)

Experimental studies

Although there has been some early interest in the effects of stress on magnetic susceptibility (eg Nagata 1966 1970 Kean et al 1976) this was associated with strains within the elastic limit Of interest here are the susceptibility changes that occur with large strains due to deformation that is macroscopically ductile if not actually plastic at the crystalline level The problem in the laboratory

bullbull bull bullbull bull bull

bullbull

14

environment is that even at the slowest strain rates that are practicable (10- 6 to 10-9 S-I) most rocks and minerals are not sufficiently ductile at room temperature to fail by the natural mechanisms of metamorphic rocks

Owens and Rutter (1978) first tackled this subshyject with a study of marbles and of calcite Alshythough the diamagnetic susceptibility of calcite is low the mineral is relatively easily deformed in a plastic manner at moderate confining pressures It is also stable at modest experimental temperatures so that Owens and Rutter were able to enhance the ductility by using temperatures up to 500 0 C in combination with pressures of 150 to 300 MPa (15 to 3 kbar) at strain-rates of approximately 10 - 4 to 10 - s s - 1 They achieved strains up to 50 axial-symmetrical (coaxial) shortening of the cylindrical specimens

The marbles they used had essentially isotropic magnetic and optical-crystallographic fabrics inishytially The magnetic anisotropy rapidly reached a plateau intensity at about 45 shortening The optical fabrics and the susceptibility fabric rapidly became axisymmetric to the shortening axis of the specimens This study didmiddot much to confirm the value of magnetic fabrics as indicators of strain and kinematics of deformation but most natural studies are based on ferrirnagnetic or parashymagnetic materials

Natural paramagnetic and ferrimagnetic matershyials are difficult to deform in a realistic manner without raising the temperature Heating will not normally be possible without inducing mineralogishycal changes that might mask susceptibility changes due to deformation Borradaile and Alford (1987) approached this problem by using a synthetic aggregate of sand enriched with magnetite that was cemented with commercial Portland cement The latter has a negligible (diamagnetic) susceptshyibility in comparison with the aggregate and pershymitted the aggregate to shorten by 35 in a ductile manner by axial symmetrical shortening The deshyformation did not involve cataclasis of the sand grains Rather the deformation was accommodshyated by the shearing of the cement gel This pershymitted a grain-shape alignment to develop by rollshying and sliding of the grains The magnetite grains were of the same grain-size as the matrix sand so

bulll1pl -04

bull 03

02 bull bull

01 bullbull01 02 03 04 In (XZ)

00 I I bull I I ~

11 12 13 14 15 (XI Z)

Fig 18 A correlation between the change in degree (fl) of susceptibility anisotropy and the strain ratio in some pure shear experiments on synthetic magnetite-bearing sandshy

stones (From Borradaile and Alford 1987)

that these experiments essentially addressed the problem of the rotational behaviour of the clasts (In most natural sandstones the iron oxide grains are much smaller than the sand clasts) The experiments were at carefully controlled strainshyrates of 5 x 10 - 6 S - 1 and confining pressures of 150 MPa (15 kbar) The maximum and intershymediate principal directions of susceptibility of these specimens rotated very rapidly towards the plane of flattening at rates exceeding the rate of rotation of a line undergoing homogeneous strain (cf the lineplane model) It was inferred that the magnetites rotated rigidly possibly with some plastic deformation The rotation was even more rapid when the matrix was composed of calcite instead of silicate mineral grains For initial susshyceptibility fabrics that were suitably oriented it was found that the change in the degree of anishysotropy was related to the strain by a power law (Fig 18) This serves to emphasise the importance of the initial magnetic fabric Relatively little can be deduced of the strain history from the final magnetic fabric alone Just as the initial ellipsoidal shape and orientation is of paramount importance in the strain analysis of ellipsoidal objects so is a knowledge of similar information for the initial magnetic fabric ellipsoid Although a power law relationship between the change in orientation of specially oriented magnetic fabrics exists in cershytain axial-symmetrical ( pure shear) experiments

15

In ( kmox kim J Calcite -cement - magnetite Q9g~gotes

at 150 MPo 05

04

XZHI XZmiddotH403 --

~ U-C3Z ~ AC -10 SHEAR ZOHEt ~ PURE SHEAR

02

t 01 XZ 20 XZ -115

In (kint kmln )

-0 02 03 04 -05 06 -07 os

bull Fig 19 The paths of incremental changes in magnetic anishysotropy are shown for the experimental deformation of syntheshysised calcite-cement-magnetite specimens The pure shear test produces little change in anisotropy even though the XZ strain ratio reaches 135 In contrast the changes produced in a shear zone (transpressive) are much greater despite the fact

that the ultimate XZ strain ratio for the zone is only 114

it is premature to make extrapolations to nature at the present state of knowledge

Recent work on experimental shear zones of synthetic materials at 150 MPa extends these conshyclusions to the case of transpressive deformation -a non-coaxial strain history (Borradaile and Alshyford in press) The susceptibility ellipsoids rotate rapidly toward stable orientations in which the minimum susceptibility is at a high angle to the shear zone boundaries The magnetic anisotropy changes very rapidly in the shear zones they produce a stronger magnetic fabric than axial symmetrical shortening at the same strain This is shown for two typical incremental- tests on the same synthetic calcite-matrix material at 150 Mpa in Fig 19 A further complication recognised in the experiments is that the magnetic fabrics may be planar (F gt L) whereas the mineral fabrics are constricted (a gt b) or plane strain (a = b) It is not known if these observations are transferable to natural shear zones

Conclusions

The interpretation of natural magnetic fabrics may be more complex than was initially recogshynised but progressive changes in magnetic anishysotropy do occur sympathetically with regional strain gradients despite accompanying regional

metamorphism (eg Hrouda and Janak 1976 Hrouda 1976 Coward and Whalley 1979) Indeed Rochette (1987) has shown that the metashymorphic production of pyrrhotite can enhance the susceptibility and produce a magnetically detectashyble isograd Also in certain rocks there are at least weak correlatiCfls between ratios of principal strains and the ratios of principal susceptibilities Numerous examples of the parallelism of principal susceptibility directions and structural directions (or even principal strain directions) support the contention that genetic relationships do exist beshytween strain and susceptibility in some cases Nevshyertheless these correlations are not universal and it is not possible to predict which natural situashytions will yield susceptibility data that _will faithshyfully represent principal strain directions or prinshycipal strain magnitudes or both For exampl~ magnetic fabrics do not always seem to be reliable kinematic indicators for shear zones and in the case of polyphase deformation later magnetic fabrics do not uniformly overprint earlier ones Magnetic fabrics should not be used for routine methods of strain analysis without further study A more profitable avenue is to determine how the susceptibility and strain tensors relate taking account of the actual strain-response model (deshyformation mechanisms) and the actual minerashylogical sources of susceptibility in that rock inshycluding phases produced by metamorphism A fruitful approach would be to consider the tensorial combination of coexisting magnetic subshyfabrics and successive episodes of magnetic fabric development along the lines initiated by Hrouda (1979)

Relationships between susceptibility and strain are in vogue However the earliest uses of magshynetic studies simply to investigate bulk petroshyfabrics are not yet been fully developed or inshytegrated with detailed petrofabric studies by optishycalor X-ray means Furthermore studies of remashynence and of susceptibility at different field strengths can yield information on magnetic subshyfabrics of different grain-sizes or different mineralogy This information is essential in the study of metamorphism of magnetic phases as well as their preferred orientation The anisotropy of remanence is also a profitable area of study

16 _

because only the ferrimagnetic traces contribute to that sub-fabric

Finally the nondestructive nature of magnetic fabric analysis provides a tool for investigating the progressive deformation or progressive metamorshyphism of a single specimen in laboratory experishyments Experiments on synthetii aggregates indishycate that the initial anisotropy of materials is not easily overprinted by small strains at low tempershyature They demonstrate also that the magnetic fabric ellipsoid spins very rapidly where the chief magnetic mineral is magnetite This is more noticeable when the matrix grains undergo crystal-plastic deformation Experimental shear zones produce greater changes in magnetic shape fabrics than axial-symmetrical shortening (pure shear) at the same strain they can also produce magnetic fabrics differing in symmetry from the grain fabric Such results develop an awareness for the greater complexities of natural structures

Acknowledgments

I wish to thank the Natural Sciences and Enshygineering Research Council of Canada for the continuing support of my work Frantisek Hrouda and Brian Bayly are thanked for constructive criticism of this article Karel Zapletal is thanked for some data on biotite Mel Friedman and Jan Tullis provided helpful reviews

Postscript

Since this paper was accepted for publication P Rochette has drawn attention to unusual inshyverse magnetic fabrics probably produced by single-domain magnetite (Thesis University of Grenoble 1988211 pp)

APPENDIX

Presentation of anisotropy of susceptibility

Magnetic susceptibility is a second rank tensor property conveniently envisaged as a magnitude ellipsoid (see Hrouda 1982 p 38) with three principal axes k max bull kim and k min or k ll bull kn k 33 The average or bulk susceptibility is comshy

monly defined as the arithmetic mean of the three principal values (Ellwood et al 1986-Symshyposium recommendations) but it is not clear why the arithmetic mean is a more appropriate represhysentation of bulk susceptibility than the geometric mean Susceptibility anisotropies for rocks are so low (Figs 9 and 10) that there is often little difference between these two expressions For exshyample seventeen specimens of strongly strained fine schist of the English Borrowdale Volcanic Series have principal susceptibilities in the ratio 104 102 0943 ~

Hrouda (1982) lists 25 different parameters that have been used at various times to represent anishysotropy The most useful are sometimes termed the magnetic lineation and the magnetic foliashytion

L = kmaxkint and F= kintkmin

Note that some authors chose alternative definishytions for Land F (eg Coward 1976) The parameters L and F are plotted vertically and horizontally respectively and compare directly with the ratios used to describe the strain ellipsoid on a Flinn-diagram

a=XY and b= YZ where X 2 Y ~ Z are the principal strains In some instances it is clearer if the natural logarithms of L F and of a and b are plotted

If the ratios of principal susceptibilities are listed individually it is helpful to normalise them so that their product is unity The normalised versions of the principal susceptibilities are related to their ratios by the following relations

kmax = L 2 3 bull pl3

kml

= L -13 F I 3

k = L -13 bull F- 23mm

It is advisable also to present a mean (bulk) susceptibility value This enables the reader to assess the significance of the results (Conference recommendations Ellwood et al 1986) Unforshytunately this has often not been done in the past Commonly one finds that anisotropies are poorly reproducible for rocks with susceptibility lt 10-4

SIjvol Providing cones of confidence about principal directions and standard errors for prinshycipal magnitudes is also useful in this regard

bull

30

2-5

20

-5

10 F=~ WI shy - middotmiddotV j Y

0 5 20 25 30 35

F =(klnkmin)

Fig AI The relationship between Jelineks (1981) P and T parameters and the conventional anisotropy parameters L and

F

The ratios L and F like their counterparts in strain (a and b) are very useful in describing the ellipsoids shape or sense of anisotropy However the distance of the point (L F) from the origin is also a measure of the degree of anisotropy that is to say its departure from sphericity Jelineks (1981) parameters pi and T overcome this T represents sense of anisotropy and ranges from -1 (prolate) to + 1 (oblate) pi (gt 1) expresses degree of anisotropy These are defined as

[ 2(In k -In k~]T= -1

In k itM - In k min 1

pi = exp [ 2( af + a ~ + a~ ) ] ~ where a1 = In(kmaxkb) etc and kb = (kmax k inl

kmin )(l3) The relationship of p and T to L and F is shown in Fig AI

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17

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4

TABLE 3

Susceptibility and anisotropy of iron minerals (units are Slfvol)

A Anisotropy controlled by shape (Borradaile et aI 1987)

Mineral k max k int kinin Mean value

Magnetite (crushed metamorphic) 1063 0989 0951 58

Magnetite (detrital) 1108 0964 0936

B Crystallographic anisotropy

Mineral Anisotropy ratio Maximum susceptibility value Reference

Hematite gt 100 1 1 x 10 - 2 basal planes Uyeda et al (1963)

Pyrrhotite c 10000 1 10 basal planes Schwarz (1974)

Pyrrhotite 1024 368 0027 Rochette (1988) 910 391 0028

Ilmenite-hematite 15 1 04 basal planes Uyeda et al (1963)

C Mean values of other iron minerals (Carmichael 1982)

Mineral Mean susceptibility (approximate)

Magnetite 62

Ilmenite 18

Pyrrhotite 15

Titanomagnetite 001

Hematite 0007 Siderite 0005

Limonite 0003

Pyrite 0001

species If all the minerals in a rock have similar magnitudes of susceptibility then it should be expected that the magnetic susceptibility ellipsoid bears some close relationship to the gross petroshyfabric However where the susceptibility is chiefly carried by an accessory mineral the susceptibility ellipsoid will only be represerttative of the rocks fabric to the degree that the accessory minerals imitate and are coeval with the host fabric Hitherto most papers on deformed rocks col1shycentrated on rocks in which the accessory iron oxides particularly magnetite and hematite were the dominant source of susceptibility However the incoming of pyrrhotite at the expense of pyrite during progressive metamorphism may also conshytribute to the susceptibility of certain greenschist facies metamorphic rocks (Rochette 1987 Borshyradaile et al in press)

Bulk susceptibility values are readily available (International Critical Tables 1929 Weast and Astle 1978 Carmichael 1982) whereas anishy

sotropy data are rarer beginning with the report of Voight and Kinoshita (1907) The earliest deshyterminations used sufficiently large fragments of single crystals and the same approach continues

- shy(0) (b)

Fig 1 It is possible to physical1y arrange anisometric minerals into linear (a) and planar (b) fabrics as shown One can then

detennine the susceptibilities of the cubical specimens in the

directions I m and n and these yield minimum estimates of

the anisotropies of the minerals This simple method enables one to estimate the minimum anisotropy of susceptibility of

the actual fine-grained minerals separated from a metamorphic rock

5

T p bull B2 bull BI diSC -snoped

middotM C2

rod -shoped

-I 0 t~1 1~2 1~3 14 s 16 t~1 pi

Fig 2 Susceptibility anisotropies of metamorphic minerals separated from metamorphic rocks (from Borradaile et al 1987) and the field (stippled) of common metamorphic rocks (from Hrouda et al 1978) P and T are explained in the Appendix AI AZ-actinolite BI etc-biotite CI etc-chlorite CR-crocidolite G-g1aucophane H-bomblende M-muscovite

P-phJogopite Triangle-metamorphic magnetite partly crushed triangle in circle-detrital magnetite

for ore minerals (Uyeda et al 1963 Schwarz 1974 1975 Rochette 1988) hornblende (Parry reported in Wagner et al 1981) augite and calcite (Owens and Bamford 1976) and quartz (Hrouda 1986) However for many rock-forming metamorshyphic minerals large single crystals are unavailable or have unrepresentative compositions To overshycome this problem samples large enough for deshytermination can be synthesised by orienting small (c 1 mm) grains into an aggregate (Borradaile et al 1986) This technique can be applied to any markedly anisometric single-crystal grains that can be physically manipulated or magnetically arranged into a strong preferred crystallographic orientation (Fig 1) The technique yields a minishymum estimate of the anisotropy because it is not possible to produce a perfect alignment of crystalshylographic axes in this manner Nevertheless it is the only practical method at the present time for isolating the contribution of specific mineral grains with fme-grained habits to the susceptibility and anisotropy of susceptibility of a given rock

Anisotropy data for some important rock-forshyming minerals mainly from metamorphic rocks and some bulk anisoir~py data for other imshyportant minerals are given in Table 1 and Fig 2

Contributions to whole-rock susceptibility and its anisotropy

Initially most work on metamorphic or deshyformed rocks concentrated on examples in which the susceptibility was due to iron oxides However several workers have addressed the more general situation in which there may be paramagnetic

contributions also (Coward and Whalley 1979 Henry 1983 Rochette and Vialon 1984 Borshyradaile et al 1986 Lamarche and Rochette 1987) or even diamagnetic contributions (Hrouda 1986) Such effects become important where magnetite is present in small amounts usually less than 1 wt in a rock that has a matrix of moderately susceptishyble silicates Detailed magnetic studies have been undertaken involving magnetic susceptibility deshyterminations at different field strengths (Coward and Whalley 1979 Hrouda and Jelinek in press) at different temperatures (Rochette and Vialon 1984) and the effects of temperature on remanent magnetisation (KJigfield et al 1982) Such studies have identified the mineralogical source of the susceptibility However those techniques are not routine and it may be beneficial to physically separate the minerals in a few typical samples so that susceptibility measurements may be carried out on these individually

Henry (1983) and Henry and Daly (1983) inshyferred multiple sources of susceptibility from the measurements directly by using multiple specishymens of similar lithologies but different intensities of fabric The method uses a plot of principal susceptibilities of individual specimens against their mean or bulk susceptibility The data for each of the principal susceptibilities lie on straight lines that intersect at a point that has equal values on both graph axes This can be considered as a gradual transition in anisotropies from the most anisotropic case at the right of the graph through lesser anisotropies to a theoretically predictable equivalent isotropic case in which all principal susceptibilities equal the mean susceptibility (Fig

6

10-4

o

ki (i I 10 3) [ellsem ]

e~

~~T ~~I

eQ e ~ 0 v~ e~ - 1 ~~fFel e~ gt

$ ~~ I V( (shy~+ middot~eQ ~( e

(- bull v ( oJ ~ ~~e9 r ~ u 1 I I bull 1

+ 1 mosl anisolropic + specimen

leasl anisolropic specimen

i ( bull k [ellsem]

o 10-4

Fig 3 Diagram from Henry (1983) showing the variation in anisotropy of adjacent specimens or parts of a specimen The axes are individual principal susceptibilities (vertical) and the

mean or bulk susceptibility (horizontal)

3) This pattern was predicted by Henrys model of additive combinations of ferrimagnetic contrishybutions from traces of magnetite with contribushytions from paramagnetic silicates In a natural example the range in anisotropies on his special plot could be an indication of the degree to which mineralogical constitution affects the magnetic anshyisotropy of a rock Other influences cannot be ruled out however The variation in mineral comshyposition between different specimens or the variashytion in the degree to which the ferrimagnetic grains have similar preferred orientations to the other mineral grains could al~o playa role

Studies of susceptibility at low temperatures and of remanent and saturation magnetisation have confirmed that there are paramagnetic conshytributions from silicates and that these can swamp the ferrimagnetic contributions (Coward and Whalley 1979 Henry and Daly 1983 Rochette and Vialon 1984) These contributions cannot yet be attributed to a specific mineral without physishycally separating the grains (Hrouda and Jelinek in press)

The reverse procedure predicting whole-rock anisotropy from multiple mineralogical sources is easier Consider a rock with a perfect preferred crystallographic fabric of mica grains with their basal planes perfectly parallel and their long axes perfectly aligned in that plane In the simple case of a monomineralic rock with perfectly aligned

grains the mineral anisotropy is equal to the anisotropy of the rock If susceptibility contrishybutions from different mineral sources can be summed as Henry (1983) and Hrouda (1986) sugshygest the effect of adding a small proportion of magnetite to a paramagnetic matrix can be predicshyted For simplicity assume that the magnetite grains are dispersed and present as a small trace ( lt 1) with a perfect shape alignment coaxial with the preferred crystallographic fabric of the matrix Although magnetite has an enormous susshyceptibility magnitude its anisotropy (directly reshy

lated to its shape) is usually small especially if it is of detrital origin On the other hand metamorshyphic silicates have moderate susceptibility magnishytudes but very high anisotropies (Table 1) (Whether the susceptibility anisotropy is intrinsic or due to inclusions is immaterial here)

The magnetic anisotropies of metamorphic silicate grains are more extreme than those of most metamorphic rocks Thus a trace of magshynetite combined with much mica in a schist proshyduces an anisotropy intermediate between that of the minerals In Fig 4 this thought experiment is carried out using model rocks with 60 plagioclase (a diamagnetic matrix with almost negligible susceptibility) traces of magnetite in the proportions stated on the figure and about 40 of the named metamorphic silicate From Fig 4 it can be seen that the anisotropy of the rock is virtually equal to that of magnetite if the latter is present as gt 1 This is important for those intershypretations of magnetic fabrics in terms of March-type analysis (see below) in which disshyseminated markers are virtually solely responsible for the magnetic fabric But where the magnetite is present in smaller proportions the anisotropy of the rock may be influenced more by the composishytion of the rock than by its petrofabric or strain Thus compositional variation between specimens could produce differences in anisotropy even if the specimens had identical fabrics or strains

Recently a mathematical model has been inshyvestigated in which paramagnetic silicates are the only source of susceptibility (Hrouda 1987) With increasing preferred crystallographic orientation the anisotropy is shown to increase until it equals that of the crystal lattice Hrouda notes that this

14

13

1-2

I-I

t1-0 I-I -2 13 k2k3 Fig 4 Flinn-type diagram of susceptibility anisotropies for hypothetical rocks indicating the effects of variable proporshytions of magnetite and a paramagnetic mineral Each rook is represented by a tie-line and is composed of approximately 40$ of the named mineral plus magnetite (in the small fraction indicated by the numbers on the tie-line) and 60$ feldspar As the proportion of magnetite in the rock is increased (from 10-6

at the distal end of the tie-line in each case) the magnetic anisotropy of the rock decreases towards the anisotropy of magnetite The anisotropy of the particular magnetite chosen in these models is located near the convergence of the tie-lines

(From Borradaile 1987b)

relationship can be disturbed by the smallest traces of ferrimagnetic material and is difficult to calibrate in terms of strain Moreover a general difficulty of this type of mathematical model (both in magnetic fabrics and petrofabrics) is that it treats the grains as dispersed crystallites of no finite size which are free to develop their ideal crystal shape In nature grains are in contact and in the case of paramagnetic silicates in metamorshyphic tectonites their preferred orientations pose special problems For example grains with crystalshylographic orientations at high angles to the preshyferred orientation (schistosity) are restricted in growth Thus their reduced volumes will decrease their contribution to the rock anisotropy (see Fig 13b)

Magnetic anisotropy and finite strain

Principal susceptibility directions

In rocks with strong tectonic fabrics the prinshycipal magnetic susceptibility directions are often

7

parallel to prominent structural directions (Kligshyfield et al 1977) or related to fold geometry (Owens and Bamford 1976) For example the minimum susceptibili ty is usually perpendicular to a primary cleavage The maximum susceptibility may be parallel to the maximum extension in the rock (eg Fig 6b) contained in the cleavage and defined by stretched objects or mineral lineations (eg Singh et aI 1975 Kligfield et aI 1977 Coward and Whalley 1979 Rathore 1979 Goldshystein 1980) In contrast the maximum susceptibilshyity may be parallel to the intersection lineation of bedding and cleavage (eg Hrouda 1976 also Fig 5)

These two different patterns have been intershypreted in a number of ways One interpretation is that the maximum susceptibility is parallel always to the maximum extension It implies that the intersection lineation of bedding and cleavage is the maximum extension direction This appears to be unusual because an intersection lineation is the fortuitous interference of a tectonic fabric with the disturbed bedding surfaces In some areas the magnetic fabrics may be reasonably consistent in orientation while the (single-generation) fold hinges and intersection lineations may vary conshysiderably in orientation (Fig 6) There is no good reason for supposing that the intersection lineashytion must necessarily have some genetic relation to the strain ellipsoid

Another interpretation is that maximum susshyceptibilities occur parallel to intersection lineashytions because of heterogeneous combinations of sub fabrics If some portions of the rock retain a

bedding

cleole

bull maximum susceptibilify

intermediote susceptibility bull minimum sUKeptibihly

Fig 5 Principal susceptibility directions in Hercynian slates with a single tectonic fabric Note the maximum susceptibilishyties close to the intersection lineation of cleavage and bedding and the minimum susceptibility perpendicular to bedding

(From Borradaile and Tarling 1981)

8

bull -l-A~

~xL 0--~

~

b)0)

SUSCfptiblhtibullbull bull mcaimum in~rmtdIQt bull mntnlUtl

X IMOn fOld plunQl I inttotcon liMohon

Fig 6 Susceptibility orientations and major fold plunges in Archean slates with a single tectonic fabric Despite the varishyation in fold plunge ( sheath folds or periclinal folds) the metamorphic and magnetic fabrics are reasonably consistently

oriented in different adjacent parts of the area (From Borradaile and Brown 1987)

bedding parallel oblate magnetic fabric due to sedimentation then this may interfere with the fabric due to tectonic causes Under the right circumstances which are not too special this comshybination may produce maximum susceptibilities parallel to cleavage and bedding or perpendicular to the stretching direction (Fig 7) For this exshyplanation to be valid indeed for this arrangement of susceptibility axis to be detectable the interfershying subfabrics must be present on scales smaller than the sample size used in susceptibility deshyterminations (usually about 10 em3) Recently bedding-parallel fabrics have been detected in

L L

0 IIbullbulllli0 degiOo bull

(a) (b)

susceptibilities bull mo int-dio 0 mi

Fig 7 Variation in principal susceptibility orientations in meta-sandstones with a single tectonic fabric L indicates the grain elongation in the schistosity plane which is horizontal in these diagrams In some cases the maximum susceptibility is nearly parallel to the grain elongation (b) in others it is

perpendicular (a) (Borradai1e and Tarling 1984)

stylolitic cl~voge dOmOin

Fig 8 Where a tectonic fabric develops a domainal texture such as in stylolitic cleavage there may be distinct contribushytions of magnetic anisotropy from different parts of the rock Qeavage zones may contribute a tectonic susceptibility anishysotropy while inter-cleavage domains may still retain a sedimiddot mentary magnetic fabric The susceptibility determination for

the rock blends the two fabrics

metasediments with isoclinal sheath folds (Borshyradaile et al bull in press)

A third explanation similar to the previous one has been given for rocks that have been very weakly strained with pressure solution as the deshyformation mechanism lbis mechanism often proshyduces a regular domainal tectonic fabric of closely spaced laminae which concentrate insoluble material (including iron oxides and paramagnetic silicates) in thin sheets between rock that retains a sedimentary fabric Where laminae are more closely spaced than the width of the core used to determine susceptibility the net susceptibility is a combination of sedimentary and tectonic contrishybutions In this case the maximum susceptibility is often parallel to the intersection lineation of the domains (stylolitic cleavage) and bedding (Fig 8) Rochette and Vialon (1984) note that heterogeshyneous fabrics combining magnetic sub-fabrics of different ages prohibit any kind of quantitative correlation of strain and susceptibility

In mylonite zones (Goldstein 1980) and in major shear zones (Rathore 1985) magnetic fabrics have orientations that indicate maximum susceptshyibilities compatible with maximum extension dishyrections Similarly minimum susceptibilities are reported perpendicular to schistosities or foliashytions The relationship to boudinage directions and mineral stretching lineations has been cited to support the contention that there is a one-ta-one correspondence of strain axes and principal susshyceptibility directions in some cases Hrouda (1979 reported 1977) seems to have been the first person

9

to have considered the combining effects of magshynetic fabrics of different ages He described early susceptibility fabrics by a tensor P superimposed tectonic fabrics by a tensor D and suggested that they combine to form a resultant susceptibility tensor R by

D P = R or D = R p- 1

Goldstein (1980) applied the same approach to mylonitic fabrics Some authors have simply asshysumed that it is permissible to use the orientations of magnetic fabrics within shear zones rather like a schistosity to determine the amount and sense of shear Similar studies have been carried out subsequently on shear zones up to a regional scale in extent (eg Rathore 1985) However in experishymental shear zones the author has found that earlier magnetic fabrics are difficult to overprint and magnetic fabric maybe an unreliable kineshymatic indicator

Magnitudes ofsusceptibility and magnitudes ofstrain

The relationship between the shape of the magshynitude ellipsoid of susceptibility and the intensity of the tectonic fabric is more complex than the relationship between directions as discussed in the previous section Usually comparisons have been attempted between the shapes of the susceptshyibility and finite strain ellipsoids The latter is usually derived from some macroscopic straiI) marker such as pebbles concretions lappilli or rotated sand-dikes (eg Rathore 1979 Borradaile and Tarling 19811984 Rathore and Henry 1982 Clendenen et at 1988 Hirt et al 1988) Reducshytion spots have been used as strain markers from time to time however their pre-metamorphic origin is not always certain and in the Welsh examples some outcrops have susceptibilities that are too low to give reproducible magnetic fabrics

The susceptibility ellipsoid normally plots much nearer the origin of the Flinn-diagram than does the strain ellipsoid (Fig 9) In some cases logashyrithmic plots (Fig 10) help in their discrimination The relationships between strain and magnetic fabric are not straightforward The most strained samples in an outcrop do not necessarily have the most extreme magnetic anisotropies This is shown

a or L

20-1 AI IfIOOltfrc ItJtedtlDoloty 0IItN11tOy

JWUiOl2L1LL bull for QIdfl c~1 f~~

O for fktlPOf lCIStl ( ~ I

15

ol~~ ~bOrF 10 15 20 B

Fig 9 Strain ellipsoid data determined by de-straining analyshysis for quartz clasts and for feldspar clasts and the susceptibilshy

ity anisotropy in meta-sandstones a XY b - YZ where X lt Y lt Z L and F are the equivalent ratios for the magnetic susceptibility There is a single schistose tectonic fabric Data for the same hand-specimens are connected by tie-lines There is no simple relationship between the magnitude of strain and

intensity of magnetic fabric (Borradaile and Tarling 1984)

by the crossing tie-lines in Fig 9 Moreover there is always some question as to the validity of the comparison since the strain is commonly heterogeshyneous on the scale of a thin section whereas the homogeneously strained markers are much larger Susceptibility is usually measured from a sample about 10 cm3

so that the susceptibility tensor will be defined on a smaller scale than the strain tensor Another approach although less common in the literature is to compare the susceptibility

t log a (log l)

~ ~

~ +~ iii~iffl ~

0 lr b ~ C-_~~

0 ~J 04 ~tgt~J-~

~~~I ~~Q

0middot1

az

~ llZ I

o CH 02 0middot4 0middot6 08 1middot0 IZ

- log b (log F)

bull ST~AIN EItIPSOIO SHAPE SUSCEPTISILITY ELUPSOID SHAPE

Fig 10 Strain ellipsoid data and susceptibility data for four outcrops of slate (l to IV) with a single tectonic fabric connected by tie-lines and presented on a logarithmic Flinn-dishy

agram (From Borradaile and Tarling 1981)

bull bull bull bull

10

003

Mj maximum (i -I) values

006 I intermediate I

( i bull 2 l values 1 ~~---------~~------

- 003 -lmiddotmiddot - 006

bull bull III(L -middot00

II I

minimum (imiddot 3) values

I NmiddotI 000

Fig 11 Nonnalised measures of principal susceptibility magnishytudes (M) and o( principal strain magnitudes (Ni ) (or specishymens o( a metavolcanic rock with a single tectonic fabric There is no correlation between minimum values of susceptibilshyity and strain nor between intennediate values etc Nevertheshyless it would be possible to infer a correlation incorrectly by considering all the data laquo(or maximum intermediate and minimum susceptibilities) simultaneously (From Borradaile

and Mothersill 1984)

fabric with the petrofabric of a slightly smaller sample detennined by means of X-ray texture goniometry (eg Wood et al 1976 Hrouda et al 1985b) This overcomes the criticism that different scales will be sampled but there is the added complication of interpreting the texture goniomeshyter data in terms of finite strain (Oertel 1983)

One of the earliest attempts to relate the strain and susceptibility tensors was by Kneen (1976) She plotted ratios of principal strains against ratios of principal susceptibilities and inferred correlashytions Similar studies that compared strain ratios with susceptibility anisotropy used special loga-

M 02

rithmic parameters to normalise values (Wood et al 1976 Rathore 1979 1980 Rathore and Henry 1982 Kligfield et al 1982) These are termed IV (for strain) and M (for susceptibility) where i = 1 2 or 3 for the appropriate principal value The actual algebraic definition of N and M varies in the literature and care should be taken in comparshying data from one paper to another) Unforshytunately in most of these cases the authors plotted the data for all three principal directions on the same axes and generally established correlation coefficients for the maximum intermediate and minimum values simultaneously Strictly speaking this is invalid (Fig 11) and in one instance the correlation of anisotropies attempted in this manner has been disproved (Borradaile and Mothersill 1984)

This may give a discouraging view of the correshylations of strain and susceptibility but the data already published do give some indication that correlations may exist although weaker than origishynally claimed For example comparing data for just minimum (normalised) strains and minimum (normalised) susceptibilities it is possible to reshycognise modest correlations between susceptibility and strain in the case of the Welsh slates (eg Wood et al 1976) here in Fig 12 Clendenen et al (1988) have recently recognised that this kind of weaker correlation between the strain of conshycretions and susceptibility can be statistically sigshynificant

Thus although weak correlations of the kind

klk2 =(XY) may exist these must only be of local siginificance

I I I bullbullbullbullbullbullbull bull

I ttl bullbull~

ol------------r ------ shy bull V

~- fmiddot I maximum (i1) and -0middot2 r I intermediate (middot 2 ) values

minimum values (i 3) I

~~~____~____~I~____~ Nj -~ -~ 0 ~

Fig 12 Nonnalised measures of principal susceptibilities (M) and of principal strains (Ni ) for slates with a single tectonic fabric Note that a weak correlation exists between minimum strains and minimum susceptibilities (From Wood et al 1976)

11

Q Z p Marchian rofafion

S ~ b

t1- y p 0- Zr +y~

k X L oL

X SI bull bull S

Fig 13 a Theoretical outline of the March model as applied to the rotation and preferred orientation of phyUosilicate grains For strain axes X ~ Y ~ Z the rotation of a pole p of a platelet is shown schematically as is the rotation of the long axis of a rod-like element Such elements are considered to be dispersed and perfectly rigid b Schematic cross-section of a typical natural preferred orientation of phyllosilicate grains defining a schistosity Sl Grains with less favoured orientations are truncated and their volumetric contribution to the magnetic fabric may be reduced Usually the pattern of

preferred orientation can only be explained by the March model to a limited degree

and it seems unduly optimistic to consider them as universal relationships that may be extrapolated from one region to another Within a single reshygion with a limited range of deformation mechashynisms and lithological uniformity it might be posshysible to extrapolate some correlations of magnetic fabric with strain

The approaches reviewed so far in this section are essentially empirical and in most cases the susceptibility was attributed to disseminated magshynetite The studies of Coward and Whalley (1979) and of Henry and Daly (1983) were exceptions they recognised multiple sources of susceptibility and Kligfield et al (1982) also investigated the sources thoroughly The latter authors demonshystrated susceptibility anisotropy was due to iron oxides whose distributions and orientations were controlled mimetically by their position on the surfaces of the oolites used as strain markers The other studies mentioned adopt the premise or imply that magnetite grains were distributed throughout the rocks and were tectonically aligned to produce a magnetite shape-fabric which in turn dictated the magnetic fabric The underlying mechanistic model that appears to have influenced this train of thought is attributed to March (1932) This model (eg Wood et al 1976) outlines the situation in which platy elements that do not impinge upon oneanother and that are preferably randomly oriented in their initial configuration

become systematically re-oriented by homogeshyneous strain and are not impeded by the matrix (Fig 13a) Consequently the orientation-distribushytion of the poles to these platelets after constantshyvolume strain is directly related to the strain Thus for a given direction i the strain e is related to the normalised density (d) of platelet poles by

emiddot = d(-1j3 - 1 I bull

In the structural geology literature some considershyation has been given to the aspect ratios of the platelets as well as accompanying volume changes of tqe aggregate (Tullis 1976 Tullis and Wood 1975) However these modifications still fall short of reality The March model is difficult to adapt to three-dimensional grains and even more difficult to reconcile with the premises of passive beshyhaviour and non-impingement of the rotating grains on each other A worse shortcoming is the inherent assumption that the grains are spatially separated whereas in a typical metamorphic rock the variation in orientation imposes restrictions on the degree to which differently oriented crystals grow (Fig 13b) Nevertheless it has found applishycations in magnetic studies (eg Cogne and Gapais 1986) and studies of comparable mathematical models (Hrouda 1980) and is frequently cited in petrofabric studies (Oertel 1983)

Hrouda (1987) has extended these arguments to situations in which it is known that paramagnetic

12

sheet silicates such as chlorite and biotite0

dominate the anisotropy of susceptibility An inshyteresting development of this study is that in slates of the Carpathians in which the anisotropy is due to paramagnetic phyllosilicates the degree of anishysotropy is proportional to the bulk or mean susshyceptibility This has also been reported in Archean slates (Borradaile et aI in press)

Strain response models and multiple sources of susshy

ceptibility

Owens (1974) first drew attention to two imshyportant items that must be taken into account in any interpretation of susceptibility anisotropy in terms of strain Firstly the mineralogical source of the susceptibility should be defined If there are multiple sources of susceptibility the direct applishycation of the simple March model or any other model assuming a penetrative homogeneous magshynetic response is invalid Rochette and Vialon (1984) and Henry (1983) enforced this argument in different ways Slight variations in the proporshytions of minerals with different magnetic anishysotropies may under certain circumstances proshyduce changes in the bulk anisotropy that override any changes in anisotropy due to strain (Borshyradaile 1987b)

The second major point raised by Owens was that the actual strain response model has a major influence on the way in which the anisotropy accumulates from the pre-strain situation For simplicity he considered three models The first was a lineplane model that we can compare to the March model already referred to above (Fig 13a) The second was the viscous or Jeffery model in which the magnetic grain is likened to a rigid ellipsoid undergoing strain-induced motion in a viscous medium The third passive model likens the magnetic grains to passive strain markers Structural geologists may compare this to the model proposed by Ramsays school of structshyural geology to approximate the shape and conseshyquent orientation changes of for example a tectonically deforming passive ellipsoidal marker by the Rrcp equations see Fig 14 (Borradaile 1987a) Care should be taken with the term passhysive some geophysicists use the term to refer to

$e85 ~_068 fRo= 15 ~t=135

C)-shystrain ellipse (j) ~5middot Rs= 20 0_01409lt

Ro= 15 iff=15

original possive passive markers markers after strain

Fig 14 The R rlt1gt model Particles with the original orientashy J

tions (8) shown as a result of strain indicated by the strain ellipse take up new orientations (lt1raquo At the same time the ratios of the original shapes (R1f) change to final shapes (Ry2) The shape-ratio of the strain ellipse is 2 1 as indicated

the lineplane or March model and where they do not appear to imply any similarity to the Rrcp model (eg Cogne and Gapais 1986)

The mechanical response is usually neglected in the correlation of strains and susceptibility anishysotropies Indeed it is likely that many rocks and many types of deformation mechanisms are unsuishytable for establishing a correlation using the preshymises of simple mathematical models involving a single mode of deformation For example if there are relict components of sedimentary magnetic fabrics mixed with the tectonic fabrics or magshynetic fabrics of different tectonic ages a model assuming homogeneity will fail Similarly deforshymation structures that produce domainal fabrics that differently influence the magnetic fabric will cause complications if the magnetic fabric is samshypled on a scale that does not take this into account In particulate flow (Fig 15) the movement of grains may be poorly ordered Some grains move more than their neighbours rotate more or even exchange neighbours despite the fact that on a suitably large polygranular scale the strain may be approximately homogeneous Movement in polyshygranular units is also possible (Fig 16) as has been shown by experiments on analog materials (Means 1977) The scale on which magnetic susceptibility is defined will determine whether or not this preshysents a problem

The deformation mechanisms may be still more complicated The deformation may cause the rock

I bull

13

(01 (bl

Fig IS Particulate flow of a simulated (two-dimensional) aggregate Deformation proceeds from (a) through (c) The motions of particles is somewhat disordered whereas on a large scale the strain may appear to be approximately homogeneous as shown by the

strain ellipse defined by the black particles

J mm Fig 16 Experimentally produced particulate flow of groups of alum grains involving intergranular displacement surfaces

(From Means 1977)

et

deformation gt

bull00 bull

Fig 17 Possible deformation processes in metamorphic rocks that could be significant in the evolution of magnetic fabrics c -intergranular displacement surfaces (may be invisible) d-ductile (may be plastic) deformation of grains e-styloshylitie surfaces and grain-truncation f -penetration of grains g -microfaults (cleavage slip) h-rotation of blocks or groups of grains between faults or other discontinuities m-pressureshysolution material transfer (may be out of system) n-new

minerals crystallise

to be a discontinuum on various scales Lozenges of rock may rotate mass removal may occur loshycally or even to outside the system while grains plastically deform by intercrystalline processes and slide and roll past oneanother (Fig 16) At the same time new minerals may form with their crystallographic orientations controlled by the contemporary stress system Any of these factors could complicate the strain-response model of the rock and the development of its magnetic fabric While all of these processes are unlikely to occur at once the roles of several of these (or others not discussed) have to be assessed before the magnetic fabric can be correlated with the bulk strain Amongst these complications probably the most common one is the growth of new minerals as for example in phyllites schists and gneisses In these cases the explanation of schistosity may be bound up with the origin of the metamorphic texture more than with the strain of the rock (Fig 17) (Borradaile et at 1986)

Experimental studies

Although there has been some early interest in the effects of stress on magnetic susceptibility (eg Nagata 1966 1970 Kean et al 1976) this was associated with strains within the elastic limit Of interest here are the susceptibility changes that occur with large strains due to deformation that is macroscopically ductile if not actually plastic at the crystalline level The problem in the laboratory

bullbull bull bullbull bull bull

bullbull

14

environment is that even at the slowest strain rates that are practicable (10- 6 to 10-9 S-I) most rocks and minerals are not sufficiently ductile at room temperature to fail by the natural mechanisms of metamorphic rocks

Owens and Rutter (1978) first tackled this subshyject with a study of marbles and of calcite Alshythough the diamagnetic susceptibility of calcite is low the mineral is relatively easily deformed in a plastic manner at moderate confining pressures It is also stable at modest experimental temperatures so that Owens and Rutter were able to enhance the ductility by using temperatures up to 500 0 C in combination with pressures of 150 to 300 MPa (15 to 3 kbar) at strain-rates of approximately 10 - 4 to 10 - s s - 1 They achieved strains up to 50 axial-symmetrical (coaxial) shortening of the cylindrical specimens

The marbles they used had essentially isotropic magnetic and optical-crystallographic fabrics inishytially The magnetic anisotropy rapidly reached a plateau intensity at about 45 shortening The optical fabrics and the susceptibility fabric rapidly became axisymmetric to the shortening axis of the specimens This study didmiddot much to confirm the value of magnetic fabrics as indicators of strain and kinematics of deformation but most natural studies are based on ferrirnagnetic or parashymagnetic materials

Natural paramagnetic and ferrimagnetic matershyials are difficult to deform in a realistic manner without raising the temperature Heating will not normally be possible without inducing mineralogishycal changes that might mask susceptibility changes due to deformation Borradaile and Alford (1987) approached this problem by using a synthetic aggregate of sand enriched with magnetite that was cemented with commercial Portland cement The latter has a negligible (diamagnetic) susceptshyibility in comparison with the aggregate and pershymitted the aggregate to shorten by 35 in a ductile manner by axial symmetrical shortening The deshyformation did not involve cataclasis of the sand grains Rather the deformation was accommodshyated by the shearing of the cement gel This pershymitted a grain-shape alignment to develop by rollshying and sliding of the grains The magnetite grains were of the same grain-size as the matrix sand so

bulll1pl -04

bull 03

02 bull bull

01 bullbull01 02 03 04 In (XZ)

00 I I bull I I ~

11 12 13 14 15 (XI Z)

Fig 18 A correlation between the change in degree (fl) of susceptibility anisotropy and the strain ratio in some pure shear experiments on synthetic magnetite-bearing sandshy

stones (From Borradaile and Alford 1987)

that these experiments essentially addressed the problem of the rotational behaviour of the clasts (In most natural sandstones the iron oxide grains are much smaller than the sand clasts) The experiments were at carefully controlled strainshyrates of 5 x 10 - 6 S - 1 and confining pressures of 150 MPa (15 kbar) The maximum and intershymediate principal directions of susceptibility of these specimens rotated very rapidly towards the plane of flattening at rates exceeding the rate of rotation of a line undergoing homogeneous strain (cf the lineplane model) It was inferred that the magnetites rotated rigidly possibly with some plastic deformation The rotation was even more rapid when the matrix was composed of calcite instead of silicate mineral grains For initial susshyceptibility fabrics that were suitably oriented it was found that the change in the degree of anishysotropy was related to the strain by a power law (Fig 18) This serves to emphasise the importance of the initial magnetic fabric Relatively little can be deduced of the strain history from the final magnetic fabric alone Just as the initial ellipsoidal shape and orientation is of paramount importance in the strain analysis of ellipsoidal objects so is a knowledge of similar information for the initial magnetic fabric ellipsoid Although a power law relationship between the change in orientation of specially oriented magnetic fabrics exists in cershytain axial-symmetrical ( pure shear) experiments

15

In ( kmox kim J Calcite -cement - magnetite Q9g~gotes

at 150 MPo 05

04

XZHI XZmiddotH403 --

~ U-C3Z ~ AC -10 SHEAR ZOHEt ~ PURE SHEAR

02

t 01 XZ 20 XZ -115

In (kint kmln )

-0 02 03 04 -05 06 -07 os

bull Fig 19 The paths of incremental changes in magnetic anishysotropy are shown for the experimental deformation of syntheshysised calcite-cement-magnetite specimens The pure shear test produces little change in anisotropy even though the XZ strain ratio reaches 135 In contrast the changes produced in a shear zone (transpressive) are much greater despite the fact

that the ultimate XZ strain ratio for the zone is only 114

it is premature to make extrapolations to nature at the present state of knowledge

Recent work on experimental shear zones of synthetic materials at 150 MPa extends these conshyclusions to the case of transpressive deformation -a non-coaxial strain history (Borradaile and Alshyford in press) The susceptibility ellipsoids rotate rapidly toward stable orientations in which the minimum susceptibility is at a high angle to the shear zone boundaries The magnetic anisotropy changes very rapidly in the shear zones they produce a stronger magnetic fabric than axial symmetrical shortening at the same strain This is shown for two typical incremental- tests on the same synthetic calcite-matrix material at 150 Mpa in Fig 19 A further complication recognised in the experiments is that the magnetic fabrics may be planar (F gt L) whereas the mineral fabrics are constricted (a gt b) or plane strain (a = b) It is not known if these observations are transferable to natural shear zones

Conclusions

The interpretation of natural magnetic fabrics may be more complex than was initially recogshynised but progressive changes in magnetic anishysotropy do occur sympathetically with regional strain gradients despite accompanying regional

metamorphism (eg Hrouda and Janak 1976 Hrouda 1976 Coward and Whalley 1979) Indeed Rochette (1987) has shown that the metashymorphic production of pyrrhotite can enhance the susceptibility and produce a magnetically detectashyble isograd Also in certain rocks there are at least weak correlatiCfls between ratios of principal strains and the ratios of principal susceptibilities Numerous examples of the parallelism of principal susceptibility directions and structural directions (or even principal strain directions) support the contention that genetic relationships do exist beshytween strain and susceptibility in some cases Nevshyertheless these correlations are not universal and it is not possible to predict which natural situashytions will yield susceptibility data that _will faithshyfully represent principal strain directions or prinshycipal strain magnitudes or both For exampl~ magnetic fabrics do not always seem to be reliable kinematic indicators for shear zones and in the case of polyphase deformation later magnetic fabrics do not uniformly overprint earlier ones Magnetic fabrics should not be used for routine methods of strain analysis without further study A more profitable avenue is to determine how the susceptibility and strain tensors relate taking account of the actual strain-response model (deshyformation mechanisms) and the actual minerashylogical sources of susceptibility in that rock inshycluding phases produced by metamorphism A fruitful approach would be to consider the tensorial combination of coexisting magnetic subshyfabrics and successive episodes of magnetic fabric development along the lines initiated by Hrouda (1979)

Relationships between susceptibility and strain are in vogue However the earliest uses of magshynetic studies simply to investigate bulk petroshyfabrics are not yet been fully developed or inshytegrated with detailed petrofabric studies by optishycalor X-ray means Furthermore studies of remashynence and of susceptibility at different field strengths can yield information on magnetic subshyfabrics of different grain-sizes or different mineralogy This information is essential in the study of metamorphism of magnetic phases as well as their preferred orientation The anisotropy of remanence is also a profitable area of study

16 _

because only the ferrimagnetic traces contribute to that sub-fabric

Finally the nondestructive nature of magnetic fabric analysis provides a tool for investigating the progressive deformation or progressive metamorshyphism of a single specimen in laboratory experishyments Experiments on synthetii aggregates indishycate that the initial anisotropy of materials is not easily overprinted by small strains at low tempershyature They demonstrate also that the magnetic fabric ellipsoid spins very rapidly where the chief magnetic mineral is magnetite This is more noticeable when the matrix grains undergo crystal-plastic deformation Experimental shear zones produce greater changes in magnetic shape fabrics than axial-symmetrical shortening (pure shear) at the same strain they can also produce magnetic fabrics differing in symmetry from the grain fabric Such results develop an awareness for the greater complexities of natural structures

Acknowledgments

I wish to thank the Natural Sciences and Enshygineering Research Council of Canada for the continuing support of my work Frantisek Hrouda and Brian Bayly are thanked for constructive criticism of this article Karel Zapletal is thanked for some data on biotite Mel Friedman and Jan Tullis provided helpful reviews

Postscript

Since this paper was accepted for publication P Rochette has drawn attention to unusual inshyverse magnetic fabrics probably produced by single-domain magnetite (Thesis University of Grenoble 1988211 pp)

APPENDIX

Presentation of anisotropy of susceptibility

Magnetic susceptibility is a second rank tensor property conveniently envisaged as a magnitude ellipsoid (see Hrouda 1982 p 38) with three principal axes k max bull kim and k min or k ll bull kn k 33 The average or bulk susceptibility is comshy

monly defined as the arithmetic mean of the three principal values (Ellwood et al 1986-Symshyposium recommendations) but it is not clear why the arithmetic mean is a more appropriate represhysentation of bulk susceptibility than the geometric mean Susceptibility anisotropies for rocks are so low (Figs 9 and 10) that there is often little difference between these two expressions For exshyample seventeen specimens of strongly strained fine schist of the English Borrowdale Volcanic Series have principal susceptibilities in the ratio 104 102 0943 ~

Hrouda (1982) lists 25 different parameters that have been used at various times to represent anishysotropy The most useful are sometimes termed the magnetic lineation and the magnetic foliashytion

L = kmaxkint and F= kintkmin

Note that some authors chose alternative definishytions for Land F (eg Coward 1976) The parameters L and F are plotted vertically and horizontally respectively and compare directly with the ratios used to describe the strain ellipsoid on a Flinn-diagram

a=XY and b= YZ where X 2 Y ~ Z are the principal strains In some instances it is clearer if the natural logarithms of L F and of a and b are plotted

If the ratios of principal susceptibilities are listed individually it is helpful to normalise them so that their product is unity The normalised versions of the principal susceptibilities are related to their ratios by the following relations

kmax = L 2 3 bull pl3

kml

= L -13 F I 3

k = L -13 bull F- 23mm

It is advisable also to present a mean (bulk) susceptibility value This enables the reader to assess the significance of the results (Conference recommendations Ellwood et al 1986) Unforshytunately this has often not been done in the past Commonly one finds that anisotropies are poorly reproducible for rocks with susceptibility lt 10-4

SIjvol Providing cones of confidence about principal directions and standard errors for prinshycipal magnitudes is also useful in this regard

bull

30

2-5

20

-5

10 F=~ WI shy - middotmiddotV j Y

0 5 20 25 30 35

F =(klnkmin)

Fig AI The relationship between Jelineks (1981) P and T parameters and the conventional anisotropy parameters L and

F

The ratios L and F like their counterparts in strain (a and b) are very useful in describing the ellipsoids shape or sense of anisotropy However the distance of the point (L F) from the origin is also a measure of the degree of anisotropy that is to say its departure from sphericity Jelineks (1981) parameters pi and T overcome this T represents sense of anisotropy and ranges from -1 (prolate) to + 1 (oblate) pi (gt 1) expresses degree of anisotropy These are defined as

[ 2(In k -In k~]T= -1

In k itM - In k min 1

pi = exp [ 2( af + a ~ + a~ ) ] ~ where a1 = In(kmaxkb) etc and kb = (kmax k inl

kmin )(l3) The relationship of p and T to L and F is shown in Fig AI

References

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17

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5

T p bull B2 bull BI diSC -snoped

middotM C2

rod -shoped

-I 0 t~1 1~2 1~3 14 s 16 t~1 pi

Fig 2 Susceptibility anisotropies of metamorphic minerals separated from metamorphic rocks (from Borradaile et al 1987) and the field (stippled) of common metamorphic rocks (from Hrouda et al 1978) P and T are explained in the Appendix AI AZ-actinolite BI etc-biotite CI etc-chlorite CR-crocidolite G-g1aucophane H-bomblende M-muscovite

P-phJogopite Triangle-metamorphic magnetite partly crushed triangle in circle-detrital magnetite

for ore minerals (Uyeda et al 1963 Schwarz 1974 1975 Rochette 1988) hornblende (Parry reported in Wagner et al 1981) augite and calcite (Owens and Bamford 1976) and quartz (Hrouda 1986) However for many rock-forming metamorshyphic minerals large single crystals are unavailable or have unrepresentative compositions To overshycome this problem samples large enough for deshytermination can be synthesised by orienting small (c 1 mm) grains into an aggregate (Borradaile et al 1986) This technique can be applied to any markedly anisometric single-crystal grains that can be physically manipulated or magnetically arranged into a strong preferred crystallographic orientation (Fig 1) The technique yields a minishymum estimate of the anisotropy because it is not possible to produce a perfect alignment of crystalshylographic axes in this manner Nevertheless it is the only practical method at the present time for isolating the contribution of specific mineral grains with fme-grained habits to the susceptibility and anisotropy of susceptibility of a given rock

Anisotropy data for some important rock-forshyming minerals mainly from metamorphic rocks and some bulk anisoir~py data for other imshyportant minerals are given in Table 1 and Fig 2

Contributions to whole-rock susceptibility and its anisotropy

Initially most work on metamorphic or deshyformed rocks concentrated on examples in which the susceptibility was due to iron oxides However several workers have addressed the more general situation in which there may be paramagnetic

contributions also (Coward and Whalley 1979 Henry 1983 Rochette and Vialon 1984 Borshyradaile et al 1986 Lamarche and Rochette 1987) or even diamagnetic contributions (Hrouda 1986) Such effects become important where magnetite is present in small amounts usually less than 1 wt in a rock that has a matrix of moderately susceptishyble silicates Detailed magnetic studies have been undertaken involving magnetic susceptibility deshyterminations at different field strengths (Coward and Whalley 1979 Hrouda and Jelinek in press) at different temperatures (Rochette and Vialon 1984) and the effects of temperature on remanent magnetisation (KJigfield et al 1982) Such studies have identified the mineralogical source of the susceptibility However those techniques are not routine and it may be beneficial to physically separate the minerals in a few typical samples so that susceptibility measurements may be carried out on these individually

Henry (1983) and Henry and Daly (1983) inshyferred multiple sources of susceptibility from the measurements directly by using multiple specishymens of similar lithologies but different intensities of fabric The method uses a plot of principal susceptibilities of individual specimens against their mean or bulk susceptibility The data for each of the principal susceptibilities lie on straight lines that intersect at a point that has equal values on both graph axes This can be considered as a gradual transition in anisotropies from the most anisotropic case at the right of the graph through lesser anisotropies to a theoretically predictable equivalent isotropic case in which all principal susceptibilities equal the mean susceptibility (Fig

6

10-4

o

ki (i I 10 3) [ellsem ]

e~

~~T ~~I

eQ e ~ 0 v~ e~ - 1 ~~fFel e~ gt

$ ~~ I V( (shy~+ middot~eQ ~( e

(- bull v ( oJ ~ ~~e9 r ~ u 1 I I bull 1

+ 1 mosl anisolropic + specimen

leasl anisolropic specimen

i ( bull k [ellsem]

o 10-4

Fig 3 Diagram from Henry (1983) showing the variation in anisotropy of adjacent specimens or parts of a specimen The axes are individual principal susceptibilities (vertical) and the

mean or bulk susceptibility (horizontal)

3) This pattern was predicted by Henrys model of additive combinations of ferrimagnetic contrishybutions from traces of magnetite with contribushytions from paramagnetic silicates In a natural example the range in anisotropies on his special plot could be an indication of the degree to which mineralogical constitution affects the magnetic anshyisotropy of a rock Other influences cannot be ruled out however The variation in mineral comshyposition between different specimens or the variashytion in the degree to which the ferrimagnetic grains have similar preferred orientations to the other mineral grains could al~o playa role

Studies of susceptibility at low temperatures and of remanent and saturation magnetisation have confirmed that there are paramagnetic conshytributions from silicates and that these can swamp the ferrimagnetic contributions (Coward and Whalley 1979 Henry and Daly 1983 Rochette and Vialon 1984) These contributions cannot yet be attributed to a specific mineral without physishycally separating the grains (Hrouda and Jelinek in press)

The reverse procedure predicting whole-rock anisotropy from multiple mineralogical sources is easier Consider a rock with a perfect preferred crystallographic fabric of mica grains with their basal planes perfectly parallel and their long axes perfectly aligned in that plane In the simple case of a monomineralic rock with perfectly aligned

grains the mineral anisotropy is equal to the anisotropy of the rock If susceptibility contrishybutions from different mineral sources can be summed as Henry (1983) and Hrouda (1986) sugshygest the effect of adding a small proportion of magnetite to a paramagnetic matrix can be predicshyted For simplicity assume that the magnetite grains are dispersed and present as a small trace ( lt 1) with a perfect shape alignment coaxial with the preferred crystallographic fabric of the matrix Although magnetite has an enormous susshyceptibility magnitude its anisotropy (directly reshy

lated to its shape) is usually small especially if it is of detrital origin On the other hand metamorshyphic silicates have moderate susceptibility magnishytudes but very high anisotropies (Table 1) (Whether the susceptibility anisotropy is intrinsic or due to inclusions is immaterial here)

The magnetic anisotropies of metamorphic silicate grains are more extreme than those of most metamorphic rocks Thus a trace of magshynetite combined with much mica in a schist proshyduces an anisotropy intermediate between that of the minerals In Fig 4 this thought experiment is carried out using model rocks with 60 plagioclase (a diamagnetic matrix with almost negligible susceptibility) traces of magnetite in the proportions stated on the figure and about 40 of the named metamorphic silicate From Fig 4 it can be seen that the anisotropy of the rock is virtually equal to that of magnetite if the latter is present as gt 1 This is important for those intershypretations of magnetic fabrics in terms of March-type analysis (see below) in which disshyseminated markers are virtually solely responsible for the magnetic fabric But where the magnetite is present in smaller proportions the anisotropy of the rock may be influenced more by the composishytion of the rock than by its petrofabric or strain Thus compositional variation between specimens could produce differences in anisotropy even if the specimens had identical fabrics or strains

Recently a mathematical model has been inshyvestigated in which paramagnetic silicates are the only source of susceptibility (Hrouda 1987) With increasing preferred crystallographic orientation the anisotropy is shown to increase until it equals that of the crystal lattice Hrouda notes that this

14

13

1-2

I-I

t1-0 I-I -2 13 k2k3 Fig 4 Flinn-type diagram of susceptibility anisotropies for hypothetical rocks indicating the effects of variable proporshytions of magnetite and a paramagnetic mineral Each rook is represented by a tie-line and is composed of approximately 40$ of the named mineral plus magnetite (in the small fraction indicated by the numbers on the tie-line) and 60$ feldspar As the proportion of magnetite in the rock is increased (from 10-6

at the distal end of the tie-line in each case) the magnetic anisotropy of the rock decreases towards the anisotropy of magnetite The anisotropy of the particular magnetite chosen in these models is located near the convergence of the tie-lines

(From Borradaile 1987b)

relationship can be disturbed by the smallest traces of ferrimagnetic material and is difficult to calibrate in terms of strain Moreover a general difficulty of this type of mathematical model (both in magnetic fabrics and petrofabrics) is that it treats the grains as dispersed crystallites of no finite size which are free to develop their ideal crystal shape In nature grains are in contact and in the case of paramagnetic silicates in metamorshyphic tectonites their preferred orientations pose special problems For example grains with crystalshylographic orientations at high angles to the preshyferred orientation (schistosity) are restricted in growth Thus their reduced volumes will decrease their contribution to the rock anisotropy (see Fig 13b)

Magnetic anisotropy and finite strain

Principal susceptibility directions

In rocks with strong tectonic fabrics the prinshycipal magnetic susceptibility directions are often

7

parallel to prominent structural directions (Kligshyfield et al 1977) or related to fold geometry (Owens and Bamford 1976) For example the minimum susceptibili ty is usually perpendicular to a primary cleavage The maximum susceptibility may be parallel to the maximum extension in the rock (eg Fig 6b) contained in the cleavage and defined by stretched objects or mineral lineations (eg Singh et aI 1975 Kligfield et aI 1977 Coward and Whalley 1979 Rathore 1979 Goldshystein 1980) In contrast the maximum susceptibilshyity may be parallel to the intersection lineation of bedding and cleavage (eg Hrouda 1976 also Fig 5)

These two different patterns have been intershypreted in a number of ways One interpretation is that the maximum susceptibility is parallel always to the maximum extension It implies that the intersection lineation of bedding and cleavage is the maximum extension direction This appears to be unusual because an intersection lineation is the fortuitous interference of a tectonic fabric with the disturbed bedding surfaces In some areas the magnetic fabrics may be reasonably consistent in orientation while the (single-generation) fold hinges and intersection lineations may vary conshysiderably in orientation (Fig 6) There is no good reason for supposing that the intersection lineashytion must necessarily have some genetic relation to the strain ellipsoid

Another interpretation is that maximum susshyceptibilities occur parallel to intersection lineashytions because of heterogeneous combinations of sub fabrics If some portions of the rock retain a

bedding

cleole

bull maximum susceptibilify

intermediote susceptibility bull minimum sUKeptibihly

Fig 5 Principal susceptibility directions in Hercynian slates with a single tectonic fabric Note the maximum susceptibilishyties close to the intersection lineation of cleavage and bedding and the minimum susceptibility perpendicular to bedding

(From Borradaile and Tarling 1981)

8

bull -l-A~

~xL 0--~

~

b)0)

SUSCfptiblhtibullbull bull mcaimum in~rmtdIQt bull mntnlUtl

X IMOn fOld plunQl I inttotcon liMohon

Fig 6 Susceptibility orientations and major fold plunges in Archean slates with a single tectonic fabric Despite the varishyation in fold plunge ( sheath folds or periclinal folds) the metamorphic and magnetic fabrics are reasonably consistently

oriented in different adjacent parts of the area (From Borradaile and Brown 1987)

bedding parallel oblate magnetic fabric due to sedimentation then this may interfere with the fabric due to tectonic causes Under the right circumstances which are not too special this comshybination may produce maximum susceptibilities parallel to cleavage and bedding or perpendicular to the stretching direction (Fig 7) For this exshyplanation to be valid indeed for this arrangement of susceptibility axis to be detectable the interfershying subfabrics must be present on scales smaller than the sample size used in susceptibility deshyterminations (usually about 10 em3) Recently bedding-parallel fabrics have been detected in

L L

0 IIbullbulllli0 degiOo bull

(a) (b)

susceptibilities bull mo int-dio 0 mi

Fig 7 Variation in principal susceptibility orientations in meta-sandstones with a single tectonic fabric L indicates the grain elongation in the schistosity plane which is horizontal in these diagrams In some cases the maximum susceptibility is nearly parallel to the grain elongation (b) in others it is

perpendicular (a) (Borradai1e and Tarling 1984)

stylolitic cl~voge dOmOin

Fig 8 Where a tectonic fabric develops a domainal texture such as in stylolitic cleavage there may be distinct contribushytions of magnetic anisotropy from different parts of the rock Qeavage zones may contribute a tectonic susceptibility anishysotropy while inter-cleavage domains may still retain a sedimiddot mentary magnetic fabric The susceptibility determination for

the rock blends the two fabrics

metasediments with isoclinal sheath folds (Borshyradaile et al bull in press)

A third explanation similar to the previous one has been given for rocks that have been very weakly strained with pressure solution as the deshyformation mechanism lbis mechanism often proshyduces a regular domainal tectonic fabric of closely spaced laminae which concentrate insoluble material (including iron oxides and paramagnetic silicates) in thin sheets between rock that retains a sedimentary fabric Where laminae are more closely spaced than the width of the core used to determine susceptibility the net susceptibility is a combination of sedimentary and tectonic contrishybutions In this case the maximum susceptibility is often parallel to the intersection lineation of the domains (stylolitic cleavage) and bedding (Fig 8) Rochette and Vialon (1984) note that heterogeshyneous fabrics combining magnetic sub-fabrics of different ages prohibit any kind of quantitative correlation of strain and susceptibility

In mylonite zones (Goldstein 1980) and in major shear zones (Rathore 1985) magnetic fabrics have orientations that indicate maximum susceptshyibilities compatible with maximum extension dishyrections Similarly minimum susceptibilities are reported perpendicular to schistosities or foliashytions The relationship to boudinage directions and mineral stretching lineations has been cited to support the contention that there is a one-ta-one correspondence of strain axes and principal susshyceptibility directions in some cases Hrouda (1979 reported 1977) seems to have been the first person

9

to have considered the combining effects of magshynetic fabrics of different ages He described early susceptibility fabrics by a tensor P superimposed tectonic fabrics by a tensor D and suggested that they combine to form a resultant susceptibility tensor R by

D P = R or D = R p- 1

Goldstein (1980) applied the same approach to mylonitic fabrics Some authors have simply asshysumed that it is permissible to use the orientations of magnetic fabrics within shear zones rather like a schistosity to determine the amount and sense of shear Similar studies have been carried out subsequently on shear zones up to a regional scale in extent (eg Rathore 1985) However in experishymental shear zones the author has found that earlier magnetic fabrics are difficult to overprint and magnetic fabric maybe an unreliable kineshymatic indicator

Magnitudes ofsusceptibility and magnitudes ofstrain

The relationship between the shape of the magshynitude ellipsoid of susceptibility and the intensity of the tectonic fabric is more complex than the relationship between directions as discussed in the previous section Usually comparisons have been attempted between the shapes of the susceptshyibility and finite strain ellipsoids The latter is usually derived from some macroscopic straiI) marker such as pebbles concretions lappilli or rotated sand-dikes (eg Rathore 1979 Borradaile and Tarling 19811984 Rathore and Henry 1982 Clendenen et at 1988 Hirt et al 1988) Reducshytion spots have been used as strain markers from time to time however their pre-metamorphic origin is not always certain and in the Welsh examples some outcrops have susceptibilities that are too low to give reproducible magnetic fabrics

The susceptibility ellipsoid normally plots much nearer the origin of the Flinn-diagram than does the strain ellipsoid (Fig 9) In some cases logashyrithmic plots (Fig 10) help in their discrimination The relationships between strain and magnetic fabric are not straightforward The most strained samples in an outcrop do not necessarily have the most extreme magnetic anisotropies This is shown

a or L

20-1 AI IfIOOltfrc ItJtedtlDoloty 0IItN11tOy

JWUiOl2L1LL bull for QIdfl c~1 f~~

O for fktlPOf lCIStl ( ~ I

15

ol~~ ~bOrF 10 15 20 B

Fig 9 Strain ellipsoid data determined by de-straining analyshysis for quartz clasts and for feldspar clasts and the susceptibilshy

ity anisotropy in meta-sandstones a XY b - YZ where X lt Y lt Z L and F are the equivalent ratios for the magnetic susceptibility There is a single schistose tectonic fabric Data for the same hand-specimens are connected by tie-lines There is no simple relationship between the magnitude of strain and

intensity of magnetic fabric (Borradaile and Tarling 1984)

by the crossing tie-lines in Fig 9 Moreover there is always some question as to the validity of the comparison since the strain is commonly heterogeshyneous on the scale of a thin section whereas the homogeneously strained markers are much larger Susceptibility is usually measured from a sample about 10 cm3

so that the susceptibility tensor will be defined on a smaller scale than the strain tensor Another approach although less common in the literature is to compare the susceptibility

t log a (log l)

~ ~

~ +~ iii~iffl ~

0 lr b ~ C-_~~

0 ~J 04 ~tgt~J-~

~~~I ~~Q

0middot1

az

~ llZ I

o CH 02 0middot4 0middot6 08 1middot0 IZ

- log b (log F)

bull ST~AIN EItIPSOIO SHAPE SUSCEPTISILITY ELUPSOID SHAPE

Fig 10 Strain ellipsoid data and susceptibility data for four outcrops of slate (l to IV) with a single tectonic fabric connected by tie-lines and presented on a logarithmic Flinn-dishy

agram (From Borradaile and Tarling 1981)

bull bull bull bull

10

003

Mj maximum (i -I) values

006 I intermediate I

( i bull 2 l values 1 ~~---------~~------

- 003 -lmiddotmiddot - 006

bull bull III(L -middot00

II I

minimum (imiddot 3) values

I NmiddotI 000

Fig 11 Nonnalised measures of principal susceptibility magnishytudes (M) and o( principal strain magnitudes (Ni ) (or specishymens o( a metavolcanic rock with a single tectonic fabric There is no correlation between minimum values of susceptibilshyity and strain nor between intennediate values etc Nevertheshyless it would be possible to infer a correlation incorrectly by considering all the data laquo(or maximum intermediate and minimum susceptibilities) simultaneously (From Borradaile

and Mothersill 1984)

fabric with the petrofabric of a slightly smaller sample detennined by means of X-ray texture goniometry (eg Wood et al 1976 Hrouda et al 1985b) This overcomes the criticism that different scales will be sampled but there is the added complication of interpreting the texture goniomeshyter data in terms of finite strain (Oertel 1983)

One of the earliest attempts to relate the strain and susceptibility tensors was by Kneen (1976) She plotted ratios of principal strains against ratios of principal susceptibilities and inferred correlashytions Similar studies that compared strain ratios with susceptibility anisotropy used special loga-

M 02

rithmic parameters to normalise values (Wood et al 1976 Rathore 1979 1980 Rathore and Henry 1982 Kligfield et al 1982) These are termed IV (for strain) and M (for susceptibility) where i = 1 2 or 3 for the appropriate principal value The actual algebraic definition of N and M varies in the literature and care should be taken in comparshying data from one paper to another) Unforshytunately in most of these cases the authors plotted the data for all three principal directions on the same axes and generally established correlation coefficients for the maximum intermediate and minimum values simultaneously Strictly speaking this is invalid (Fig 11) and in one instance the correlation of anisotropies attempted in this manner has been disproved (Borradaile and Mothersill 1984)

This may give a discouraging view of the correshylations of strain and susceptibility but the data already published do give some indication that correlations may exist although weaker than origishynally claimed For example comparing data for just minimum (normalised) strains and minimum (normalised) susceptibilities it is possible to reshycognise modest correlations between susceptibility and strain in the case of the Welsh slates (eg Wood et al 1976) here in Fig 12 Clendenen et al (1988) have recently recognised that this kind of weaker correlation between the strain of conshycretions and susceptibility can be statistically sigshynificant

Thus although weak correlations of the kind

klk2 =(XY) may exist these must only be of local siginificance

I I I bullbullbullbullbullbullbull bull

I ttl bullbull~

ol------------r ------ shy bull V

~- fmiddot I maximum (i1) and -0middot2 r I intermediate (middot 2 ) values

minimum values (i 3) I

~~~____~____~I~____~ Nj -~ -~ 0 ~

Fig 12 Nonnalised measures of principal susceptibilities (M) and of principal strains (Ni ) for slates with a single tectonic fabric Note that a weak correlation exists between minimum strains and minimum susceptibilities (From Wood et al 1976)

11

Q Z p Marchian rofafion

S ~ b

t1- y p 0- Zr +y~

k X L oL

X SI bull bull S

Fig 13 a Theoretical outline of the March model as applied to the rotation and preferred orientation of phyUosilicate grains For strain axes X ~ Y ~ Z the rotation of a pole p of a platelet is shown schematically as is the rotation of the long axis of a rod-like element Such elements are considered to be dispersed and perfectly rigid b Schematic cross-section of a typical natural preferred orientation of phyllosilicate grains defining a schistosity Sl Grains with less favoured orientations are truncated and their volumetric contribution to the magnetic fabric may be reduced Usually the pattern of

preferred orientation can only be explained by the March model to a limited degree

and it seems unduly optimistic to consider them as universal relationships that may be extrapolated from one region to another Within a single reshygion with a limited range of deformation mechashynisms and lithological uniformity it might be posshysible to extrapolate some correlations of magnetic fabric with strain

The approaches reviewed so far in this section are essentially empirical and in most cases the susceptibility was attributed to disseminated magshynetite The studies of Coward and Whalley (1979) and of Henry and Daly (1983) were exceptions they recognised multiple sources of susceptibility and Kligfield et al (1982) also investigated the sources thoroughly The latter authors demonshystrated susceptibility anisotropy was due to iron oxides whose distributions and orientations were controlled mimetically by their position on the surfaces of the oolites used as strain markers The other studies mentioned adopt the premise or imply that magnetite grains were distributed throughout the rocks and were tectonically aligned to produce a magnetite shape-fabric which in turn dictated the magnetic fabric The underlying mechanistic model that appears to have influenced this train of thought is attributed to March (1932) This model (eg Wood et al 1976) outlines the situation in which platy elements that do not impinge upon oneanother and that are preferably randomly oriented in their initial configuration

become systematically re-oriented by homogeshyneous strain and are not impeded by the matrix (Fig 13a) Consequently the orientation-distribushytion of the poles to these platelets after constantshyvolume strain is directly related to the strain Thus for a given direction i the strain e is related to the normalised density (d) of platelet poles by

emiddot = d(-1j3 - 1 I bull

In the structural geology literature some considershyation has been given to the aspect ratios of the platelets as well as accompanying volume changes of tqe aggregate (Tullis 1976 Tullis and Wood 1975) However these modifications still fall short of reality The March model is difficult to adapt to three-dimensional grains and even more difficult to reconcile with the premises of passive beshyhaviour and non-impingement of the rotating grains on each other A worse shortcoming is the inherent assumption that the grains are spatially separated whereas in a typical metamorphic rock the variation in orientation imposes restrictions on the degree to which differently oriented crystals grow (Fig 13b) Nevertheless it has found applishycations in magnetic studies (eg Cogne and Gapais 1986) and studies of comparable mathematical models (Hrouda 1980) and is frequently cited in petrofabric studies (Oertel 1983)

Hrouda (1987) has extended these arguments to situations in which it is known that paramagnetic

12

sheet silicates such as chlorite and biotite0

dominate the anisotropy of susceptibility An inshyteresting development of this study is that in slates of the Carpathians in which the anisotropy is due to paramagnetic phyllosilicates the degree of anishysotropy is proportional to the bulk or mean susshyceptibility This has also been reported in Archean slates (Borradaile et aI in press)

Strain response models and multiple sources of susshy

ceptibility

Owens (1974) first drew attention to two imshyportant items that must be taken into account in any interpretation of susceptibility anisotropy in terms of strain Firstly the mineralogical source of the susceptibility should be defined If there are multiple sources of susceptibility the direct applishycation of the simple March model or any other model assuming a penetrative homogeneous magshynetic response is invalid Rochette and Vialon (1984) and Henry (1983) enforced this argument in different ways Slight variations in the proporshytions of minerals with different magnetic anishysotropies may under certain circumstances proshyduce changes in the bulk anisotropy that override any changes in anisotropy due to strain (Borshyradaile 1987b)

The second major point raised by Owens was that the actual strain response model has a major influence on the way in which the anisotropy accumulates from the pre-strain situation For simplicity he considered three models The first was a lineplane model that we can compare to the March model already referred to above (Fig 13a) The second was the viscous or Jeffery model in which the magnetic grain is likened to a rigid ellipsoid undergoing strain-induced motion in a viscous medium The third passive model likens the magnetic grains to passive strain markers Structural geologists may compare this to the model proposed by Ramsays school of structshyural geology to approximate the shape and conseshyquent orientation changes of for example a tectonically deforming passive ellipsoidal marker by the Rrcp equations see Fig 14 (Borradaile 1987a) Care should be taken with the term passhysive some geophysicists use the term to refer to

$e85 ~_068 fRo= 15 ~t=135

C)-shystrain ellipse (j) ~5middot Rs= 20 0_01409lt

Ro= 15 iff=15

original possive passive markers markers after strain

Fig 14 The R rlt1gt model Particles with the original orientashy J

tions (8) shown as a result of strain indicated by the strain ellipse take up new orientations (lt1raquo At the same time the ratios of the original shapes (R1f) change to final shapes (Ry2) The shape-ratio of the strain ellipse is 2 1 as indicated

the lineplane or March model and where they do not appear to imply any similarity to the Rrcp model (eg Cogne and Gapais 1986)

The mechanical response is usually neglected in the correlation of strains and susceptibility anishysotropies Indeed it is likely that many rocks and many types of deformation mechanisms are unsuishytable for establishing a correlation using the preshymises of simple mathematical models involving a single mode of deformation For example if there are relict components of sedimentary magnetic fabrics mixed with the tectonic fabrics or magshynetic fabrics of different tectonic ages a model assuming homogeneity will fail Similarly deforshymation structures that produce domainal fabrics that differently influence the magnetic fabric will cause complications if the magnetic fabric is samshypled on a scale that does not take this into account In particulate flow (Fig 15) the movement of grains may be poorly ordered Some grains move more than their neighbours rotate more or even exchange neighbours despite the fact that on a suitably large polygranular scale the strain may be approximately homogeneous Movement in polyshygranular units is also possible (Fig 16) as has been shown by experiments on analog materials (Means 1977) The scale on which magnetic susceptibility is defined will determine whether or not this preshysents a problem

The deformation mechanisms may be still more complicated The deformation may cause the rock

I bull

13

(01 (bl

Fig IS Particulate flow of a simulated (two-dimensional) aggregate Deformation proceeds from (a) through (c) The motions of particles is somewhat disordered whereas on a large scale the strain may appear to be approximately homogeneous as shown by the

strain ellipse defined by the black particles

J mm Fig 16 Experimentally produced particulate flow of groups of alum grains involving intergranular displacement surfaces

(From Means 1977)

et

deformation gt

bull00 bull

Fig 17 Possible deformation processes in metamorphic rocks that could be significant in the evolution of magnetic fabrics c -intergranular displacement surfaces (may be invisible) d-ductile (may be plastic) deformation of grains e-styloshylitie surfaces and grain-truncation f -penetration of grains g -microfaults (cleavage slip) h-rotation of blocks or groups of grains between faults or other discontinuities m-pressureshysolution material transfer (may be out of system) n-new

minerals crystallise

to be a discontinuum on various scales Lozenges of rock may rotate mass removal may occur loshycally or even to outside the system while grains plastically deform by intercrystalline processes and slide and roll past oneanother (Fig 16) At the same time new minerals may form with their crystallographic orientations controlled by the contemporary stress system Any of these factors could complicate the strain-response model of the rock and the development of its magnetic fabric While all of these processes are unlikely to occur at once the roles of several of these (or others not discussed) have to be assessed before the magnetic fabric can be correlated with the bulk strain Amongst these complications probably the most common one is the growth of new minerals as for example in phyllites schists and gneisses In these cases the explanation of schistosity may be bound up with the origin of the metamorphic texture more than with the strain of the rock (Fig 17) (Borradaile et at 1986)

Experimental studies

Although there has been some early interest in the effects of stress on magnetic susceptibility (eg Nagata 1966 1970 Kean et al 1976) this was associated with strains within the elastic limit Of interest here are the susceptibility changes that occur with large strains due to deformation that is macroscopically ductile if not actually plastic at the crystalline level The problem in the laboratory

bullbull bull bullbull bull bull

bullbull

14

environment is that even at the slowest strain rates that are practicable (10- 6 to 10-9 S-I) most rocks and minerals are not sufficiently ductile at room temperature to fail by the natural mechanisms of metamorphic rocks

Owens and Rutter (1978) first tackled this subshyject with a study of marbles and of calcite Alshythough the diamagnetic susceptibility of calcite is low the mineral is relatively easily deformed in a plastic manner at moderate confining pressures It is also stable at modest experimental temperatures so that Owens and Rutter were able to enhance the ductility by using temperatures up to 500 0 C in combination with pressures of 150 to 300 MPa (15 to 3 kbar) at strain-rates of approximately 10 - 4 to 10 - s s - 1 They achieved strains up to 50 axial-symmetrical (coaxial) shortening of the cylindrical specimens

The marbles they used had essentially isotropic magnetic and optical-crystallographic fabrics inishytially The magnetic anisotropy rapidly reached a plateau intensity at about 45 shortening The optical fabrics and the susceptibility fabric rapidly became axisymmetric to the shortening axis of the specimens This study didmiddot much to confirm the value of magnetic fabrics as indicators of strain and kinematics of deformation but most natural studies are based on ferrirnagnetic or parashymagnetic materials

Natural paramagnetic and ferrimagnetic matershyials are difficult to deform in a realistic manner without raising the temperature Heating will not normally be possible without inducing mineralogishycal changes that might mask susceptibility changes due to deformation Borradaile and Alford (1987) approached this problem by using a synthetic aggregate of sand enriched with magnetite that was cemented with commercial Portland cement The latter has a negligible (diamagnetic) susceptshyibility in comparison with the aggregate and pershymitted the aggregate to shorten by 35 in a ductile manner by axial symmetrical shortening The deshyformation did not involve cataclasis of the sand grains Rather the deformation was accommodshyated by the shearing of the cement gel This pershymitted a grain-shape alignment to develop by rollshying and sliding of the grains The magnetite grains were of the same grain-size as the matrix sand so

bulll1pl -04

bull 03

02 bull bull

01 bullbull01 02 03 04 In (XZ)

00 I I bull I I ~

11 12 13 14 15 (XI Z)

Fig 18 A correlation between the change in degree (fl) of susceptibility anisotropy and the strain ratio in some pure shear experiments on synthetic magnetite-bearing sandshy

stones (From Borradaile and Alford 1987)

that these experiments essentially addressed the problem of the rotational behaviour of the clasts (In most natural sandstones the iron oxide grains are much smaller than the sand clasts) The experiments were at carefully controlled strainshyrates of 5 x 10 - 6 S - 1 and confining pressures of 150 MPa (15 kbar) The maximum and intershymediate principal directions of susceptibility of these specimens rotated very rapidly towards the plane of flattening at rates exceeding the rate of rotation of a line undergoing homogeneous strain (cf the lineplane model) It was inferred that the magnetites rotated rigidly possibly with some plastic deformation The rotation was even more rapid when the matrix was composed of calcite instead of silicate mineral grains For initial susshyceptibility fabrics that were suitably oriented it was found that the change in the degree of anishysotropy was related to the strain by a power law (Fig 18) This serves to emphasise the importance of the initial magnetic fabric Relatively little can be deduced of the strain history from the final magnetic fabric alone Just as the initial ellipsoidal shape and orientation is of paramount importance in the strain analysis of ellipsoidal objects so is a knowledge of similar information for the initial magnetic fabric ellipsoid Although a power law relationship between the change in orientation of specially oriented magnetic fabrics exists in cershytain axial-symmetrical ( pure shear) experiments

15

In ( kmox kim J Calcite -cement - magnetite Q9g~gotes

at 150 MPo 05

04

XZHI XZmiddotH403 --

~ U-C3Z ~ AC -10 SHEAR ZOHEt ~ PURE SHEAR

02

t 01 XZ 20 XZ -115

In (kint kmln )

-0 02 03 04 -05 06 -07 os

bull Fig 19 The paths of incremental changes in magnetic anishysotropy are shown for the experimental deformation of syntheshysised calcite-cement-magnetite specimens The pure shear test produces little change in anisotropy even though the XZ strain ratio reaches 135 In contrast the changes produced in a shear zone (transpressive) are much greater despite the fact

that the ultimate XZ strain ratio for the zone is only 114

it is premature to make extrapolations to nature at the present state of knowledge

Recent work on experimental shear zones of synthetic materials at 150 MPa extends these conshyclusions to the case of transpressive deformation -a non-coaxial strain history (Borradaile and Alshyford in press) The susceptibility ellipsoids rotate rapidly toward stable orientations in which the minimum susceptibility is at a high angle to the shear zone boundaries The magnetic anisotropy changes very rapidly in the shear zones they produce a stronger magnetic fabric than axial symmetrical shortening at the same strain This is shown for two typical incremental- tests on the same synthetic calcite-matrix material at 150 Mpa in Fig 19 A further complication recognised in the experiments is that the magnetic fabrics may be planar (F gt L) whereas the mineral fabrics are constricted (a gt b) or plane strain (a = b) It is not known if these observations are transferable to natural shear zones

Conclusions

The interpretation of natural magnetic fabrics may be more complex than was initially recogshynised but progressive changes in magnetic anishysotropy do occur sympathetically with regional strain gradients despite accompanying regional

metamorphism (eg Hrouda and Janak 1976 Hrouda 1976 Coward and Whalley 1979) Indeed Rochette (1987) has shown that the metashymorphic production of pyrrhotite can enhance the susceptibility and produce a magnetically detectashyble isograd Also in certain rocks there are at least weak correlatiCfls between ratios of principal strains and the ratios of principal susceptibilities Numerous examples of the parallelism of principal susceptibility directions and structural directions (or even principal strain directions) support the contention that genetic relationships do exist beshytween strain and susceptibility in some cases Nevshyertheless these correlations are not universal and it is not possible to predict which natural situashytions will yield susceptibility data that _will faithshyfully represent principal strain directions or prinshycipal strain magnitudes or both For exampl~ magnetic fabrics do not always seem to be reliable kinematic indicators for shear zones and in the case of polyphase deformation later magnetic fabrics do not uniformly overprint earlier ones Magnetic fabrics should not be used for routine methods of strain analysis without further study A more profitable avenue is to determine how the susceptibility and strain tensors relate taking account of the actual strain-response model (deshyformation mechanisms) and the actual minerashylogical sources of susceptibility in that rock inshycluding phases produced by metamorphism A fruitful approach would be to consider the tensorial combination of coexisting magnetic subshyfabrics and successive episodes of magnetic fabric development along the lines initiated by Hrouda (1979)

Relationships between susceptibility and strain are in vogue However the earliest uses of magshynetic studies simply to investigate bulk petroshyfabrics are not yet been fully developed or inshytegrated with detailed petrofabric studies by optishycalor X-ray means Furthermore studies of remashynence and of susceptibility at different field strengths can yield information on magnetic subshyfabrics of different grain-sizes or different mineralogy This information is essential in the study of metamorphism of magnetic phases as well as their preferred orientation The anisotropy of remanence is also a profitable area of study

16 _

because only the ferrimagnetic traces contribute to that sub-fabric

Finally the nondestructive nature of magnetic fabric analysis provides a tool for investigating the progressive deformation or progressive metamorshyphism of a single specimen in laboratory experishyments Experiments on synthetii aggregates indishycate that the initial anisotropy of materials is not easily overprinted by small strains at low tempershyature They demonstrate also that the magnetic fabric ellipsoid spins very rapidly where the chief magnetic mineral is magnetite This is more noticeable when the matrix grains undergo crystal-plastic deformation Experimental shear zones produce greater changes in magnetic shape fabrics than axial-symmetrical shortening (pure shear) at the same strain they can also produce magnetic fabrics differing in symmetry from the grain fabric Such results develop an awareness for the greater complexities of natural structures

Acknowledgments

I wish to thank the Natural Sciences and Enshygineering Research Council of Canada for the continuing support of my work Frantisek Hrouda and Brian Bayly are thanked for constructive criticism of this article Karel Zapletal is thanked for some data on biotite Mel Friedman and Jan Tullis provided helpful reviews

Postscript

Since this paper was accepted for publication P Rochette has drawn attention to unusual inshyverse magnetic fabrics probably produced by single-domain magnetite (Thesis University of Grenoble 1988211 pp)

APPENDIX

Presentation of anisotropy of susceptibility

Magnetic susceptibility is a second rank tensor property conveniently envisaged as a magnitude ellipsoid (see Hrouda 1982 p 38) with three principal axes k max bull kim and k min or k ll bull kn k 33 The average or bulk susceptibility is comshy

monly defined as the arithmetic mean of the three principal values (Ellwood et al 1986-Symshyposium recommendations) but it is not clear why the arithmetic mean is a more appropriate represhysentation of bulk susceptibility than the geometric mean Susceptibility anisotropies for rocks are so low (Figs 9 and 10) that there is often little difference between these two expressions For exshyample seventeen specimens of strongly strained fine schist of the English Borrowdale Volcanic Series have principal susceptibilities in the ratio 104 102 0943 ~

Hrouda (1982) lists 25 different parameters that have been used at various times to represent anishysotropy The most useful are sometimes termed the magnetic lineation and the magnetic foliashytion

L = kmaxkint and F= kintkmin

Note that some authors chose alternative definishytions for Land F (eg Coward 1976) The parameters L and F are plotted vertically and horizontally respectively and compare directly with the ratios used to describe the strain ellipsoid on a Flinn-diagram

a=XY and b= YZ where X 2 Y ~ Z are the principal strains In some instances it is clearer if the natural logarithms of L F and of a and b are plotted

If the ratios of principal susceptibilities are listed individually it is helpful to normalise them so that their product is unity The normalised versions of the principal susceptibilities are related to their ratios by the following relations

kmax = L 2 3 bull pl3

kml

= L -13 F I 3

k = L -13 bull F- 23mm

It is advisable also to present a mean (bulk) susceptibility value This enables the reader to assess the significance of the results (Conference recommendations Ellwood et al 1986) Unforshytunately this has often not been done in the past Commonly one finds that anisotropies are poorly reproducible for rocks with susceptibility lt 10-4

SIjvol Providing cones of confidence about principal directions and standard errors for prinshycipal magnitudes is also useful in this regard

bull

30

2-5

20

-5

10 F=~ WI shy - middotmiddotV j Y

0 5 20 25 30 35

F =(klnkmin)

Fig AI The relationship between Jelineks (1981) P and T parameters and the conventional anisotropy parameters L and

F

The ratios L and F like their counterparts in strain (a and b) are very useful in describing the ellipsoids shape or sense of anisotropy However the distance of the point (L F) from the origin is also a measure of the degree of anisotropy that is to say its departure from sphericity Jelineks (1981) parameters pi and T overcome this T represents sense of anisotropy and ranges from -1 (prolate) to + 1 (oblate) pi (gt 1) expresses degree of anisotropy These are defined as

[ 2(In k -In k~]T= -1

In k itM - In k min 1

pi = exp [ 2( af + a ~ + a~ ) ] ~ where a1 = In(kmaxkb) etc and kb = (kmax k inl

kmin )(l3) The relationship of p and T to L and F is shown in Fig AI

References

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Borradaile GJ 1987a Analysis of strained sedimentary fabrics Can J Earth Sci 131 121-125

Borradaile GJ 1987b Anisotropy of magnetic susceptibility rock composition versus strain Tectonophysics 138 327-329

Borradaile GJ and Alford C 1987 Relationship between

17

magnetic susceptibility and strain in laboratory experishyments Tectonophysics 133 121-135

Borradaile GJ and Alford C in press Experimental shear zones and magnetic fabrics J Struct Geol

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Borradaile GJ and Mothersill JS bull 1984 Coaxial deformed and magnetic fabrics without simply correlated magnitudes of principal values Phys Earth Planet Inter 35 294-300

Borradaile GJ and Tarling D bull 1981 The influence of deforshymation mechanisms on magnetic fabrics in weakly deshyformed rocks Tectonophysics 77 151-168

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Borradaile GJ Mothersill JS Tarling D and Alford C 1986 Sources of magnetic susceptibility in a slate Earth Planet Sci Lett 76 336-340

Borradaile GJ Keeler W Alford C and Sarvas P 1987 Anisotropy of magnetic susceptibility of some metamorphic minerals Phys Earth Planet Inter 48 161-166

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Carmichael RS 1982 Magnetic properties of minerals and rocks In RC Weast and MJ Ashe (Editors) CRC Handbook of Physical Constants for Rocks CRC Press Roca Baton Fla pp 229-287

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18

II

Goldstein AG bull 1980 Magnetic susceptibility anisotropy of mylonites from the Lake Char Mylonite Zone SE New England Tectonophysics 66 197-211

Graham lW 1954 Magnetic susceptibility anisotropy an unexploited petrofabric element Bull Gool Soc Am 65 1257-1258

Graham lWbull 1966 Significance of magnetic anisotropy in Appalachian sedimentary rocks In lS Steinhard and Tl Smith (Editors) The Earth beneath the Continents Gooshyphys Monogr Am Geophys Union 10 627-648

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Henry B 1983 Interpretation quantitative de lanisotropie de susceptibilite magnetique Tectonophysics 91 165-177

Henry B and Daly L 1983 From qualitative to quantitative magnetic anisotropy analysis the prospect of finite strain calibration Tectonophysics 98 327-336

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Hrouda F 1976 The origin of cleavage in the light of magnetic anisotropy investigations Pbys Earth Planet Inshyter 13 132-142

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Hrouda F Jelinek V and Zapletal K 1985a Use of magshynetic propenies of rocks in ore and petroleum geophysics (in Czech) Res rep Goofyz Brno pp 54-75

Hrouda F Siemes H Herres N and Hennig-Micbaeli c 1985b The relationship between the magnetic anisotropy and the cmiddotaxis fabric in a massive hematite ore J Geophys bull 56 174-182

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Jelinek V 1981 Characterization of the magnetic fabrics of rocks Tectonophysics 79 T63-T67

Karlin R Lyle M and Heath GR 1987 Authigenic magmiddot netite formation in suboxic marine sediments Nature 326 490--493

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KJigfie1d R Lowrie W and Dalziel I 1977 Magnetic susshyceptibility anisotropy as a strain indicator in the Sudbury Basin Ontario Tectonophysics 40 287-308

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Kneen SJ 1976 The relationship between the magnetic and

19

strain fabrics of some hematite-bearing Welsh Slates Earth Planet Sci Lett 31 413-416

Lamarche G and Rochette P 1987 Microstructural analysis and origin of lineations in the magnetic fabric of some Alpine slates Tectonophysics 139 285-293

Lapointe P Morris WA and Harding KL 1986 Interpreshytation of magnetic susceptibility a new approach 10 geoshyphysical evaluation of the degree of rock alteration Can J

Earth Sci 23 393-401 March A 1932 Mathematische Theorie der Regelung nach

der Korngestait bei afrmer Deformation Z Kristallogrmiddot 81 285-297

Means WD 1977 A deformation experiment in transmitted light Earth Planet Sci Lett 35 169-179

Nagata T 1966 Magnetic susceptibility of compressed rocks J Goomag Geoelectr 18 73-80

Nagata T 1970 Anisotropic magnetic susceptibility of rocks under mechanical stresses Pure App Goophys 78

110-122 Nye JF 1957 The Physical Properties of Crystals Clarendon

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Owens WH and Bamford D 1976 Magnetic seismic and other anisotropic properties of rock fabrics Philos Trans R Soc London Ser A 283 55-68

Owens WH and Rutter EH 1978 The development of magnetic susceptibility anisotropy through crystallographic preferred orientation in a calcite rock Phys Earth Planet Inter 16 215-222

Park JKmiddot1983 Paleomagnetism for geologists Geosci Can 4 180-188

Rathore JS 1979 Magnetic susceptibility anisotropy in the Cambrian Slate Belt of North Wales and correlation with strain Tectonophysics 53 83-97

Rathore JS 1985 Some magnetic characteristics of sheared zones J Geodyn 2 291-301

Rathore JS and Henry B 1982 Comparison of strained magnetic fabrics in Dalradian rocks from the southwest Highlands of Scotland J Struc Geol 4 373-384

Rees AI 1965 The use of anisotropy of magnetic susceptshyibility in the estimation of sedimentary fabric Sedimentolshyogy 4 257-271

Rees AI 1968 The production of preferred orientation in a concentrated dispersion of elongated and flattened grains J Geol 76 457-465

Rochetle P 1987 Metamorphic control of the mineralogy of black shales in the Swiss Alps toward the use of magnetic isograds Eanh Planet Sci Lett 84 446-456

Rochette P 1988 Relation entre deformation et metamorshy

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bull

phisme Alpin dans les schistes noirs Helvetiques Iapport de la fabrique magnetique Geodin Acta 2 (in press)

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Schwartz EJ 1975 Magnetic properties of pyrrhotite and their use in applied geology and geophysics Geo Surv Can Pap 74-59 24 pp

Singh J (now Rathore J) Sanderson DJ and Tariing DH 1975 The magnetic susceptibility anisotropy of deformed rocks from North Cornwall England Tectonophysics 27 141-153

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Tullis TEbull 1976 Experiments on the origin of slaty cleavage and schistosity Geo Soc Am Bull 87 745-753

Tullis TE and Wood DS 1975 Correlation of finite strain from both reduction bodies and preferred orientation of mica in slate from Wales Geol Soc Am Bull 86 632-638

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Uyeda S Fuller MD Belshe JC and Girdler RW 1963 Anisotropy of magnetic susceptibility of rocks and minershyals J Geophys Res 68 279-291

Van den Ende C 1975 On the origin of anisotropy of magshynetic susceptibility in Permian Redbeds from the western part of the Dome de Barrot (S France) In GJ Borradaile et al (Editors) Progress in Geodynamics North-Holland Pub Co Amsterdam pp 176-189

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20

II

Wing-Fatt L and Stacey FD 1966 Magnetic anisotropy of laboratory materials in which magma flow is simulated Pure AppJ Geophys 6478-80

Wood DS Oertel G Singh J and Bennett HF 1976 Strain and anisotropy in rocks Philos Trans R Soc London Ser A 283 27-42

Zavoyskiy VN 1982 Use of magnetic susceptibility tensor for solving problems in structural geology Izv Akad Nauk SSSR Earth Phys Ser 18 217-223

6

10-4

o

ki (i I 10 3) [ellsem ]

e~

~~T ~~I

eQ e ~ 0 v~ e~ - 1 ~~fFel e~ gt

$ ~~ I V( (shy~+ middot~eQ ~( e

(- bull v ( oJ ~ ~~e9 r ~ u 1 I I bull 1

+ 1 mosl anisolropic + specimen

leasl anisolropic specimen

i ( bull k [ellsem]

o 10-4

Fig 3 Diagram from Henry (1983) showing the variation in anisotropy of adjacent specimens or parts of a specimen The axes are individual principal susceptibilities (vertical) and the

mean or bulk susceptibility (horizontal)

3) This pattern was predicted by Henrys model of additive combinations of ferrimagnetic contrishybutions from traces of magnetite with contribushytions from paramagnetic silicates In a natural example the range in anisotropies on his special plot could be an indication of the degree to which mineralogical constitution affects the magnetic anshyisotropy of a rock Other influences cannot be ruled out however The variation in mineral comshyposition between different specimens or the variashytion in the degree to which the ferrimagnetic grains have similar preferred orientations to the other mineral grains could al~o playa role

Studies of susceptibility at low temperatures and of remanent and saturation magnetisation have confirmed that there are paramagnetic conshytributions from silicates and that these can swamp the ferrimagnetic contributions (Coward and Whalley 1979 Henry and Daly 1983 Rochette and Vialon 1984) These contributions cannot yet be attributed to a specific mineral without physishycally separating the grains (Hrouda and Jelinek in press)

The reverse procedure predicting whole-rock anisotropy from multiple mineralogical sources is easier Consider a rock with a perfect preferred crystallographic fabric of mica grains with their basal planes perfectly parallel and their long axes perfectly aligned in that plane In the simple case of a monomineralic rock with perfectly aligned

grains the mineral anisotropy is equal to the anisotropy of the rock If susceptibility contrishybutions from different mineral sources can be summed as Henry (1983) and Hrouda (1986) sugshygest the effect of adding a small proportion of magnetite to a paramagnetic matrix can be predicshyted For simplicity assume that the magnetite grains are dispersed and present as a small trace ( lt 1) with a perfect shape alignment coaxial with the preferred crystallographic fabric of the matrix Although magnetite has an enormous susshyceptibility magnitude its anisotropy (directly reshy

lated to its shape) is usually small especially if it is of detrital origin On the other hand metamorshyphic silicates have moderate susceptibility magnishytudes but very high anisotropies (Table 1) (Whether the susceptibility anisotropy is intrinsic or due to inclusions is immaterial here)

The magnetic anisotropies of metamorphic silicate grains are more extreme than those of most metamorphic rocks Thus a trace of magshynetite combined with much mica in a schist proshyduces an anisotropy intermediate between that of the minerals In Fig 4 this thought experiment is carried out using model rocks with 60 plagioclase (a diamagnetic matrix with almost negligible susceptibility) traces of magnetite in the proportions stated on the figure and about 40 of the named metamorphic silicate From Fig 4 it can be seen that the anisotropy of the rock is virtually equal to that of magnetite if the latter is present as gt 1 This is important for those intershypretations of magnetic fabrics in terms of March-type analysis (see below) in which disshyseminated markers are virtually solely responsible for the magnetic fabric But where the magnetite is present in smaller proportions the anisotropy of the rock may be influenced more by the composishytion of the rock than by its petrofabric or strain Thus compositional variation between specimens could produce differences in anisotropy even if the specimens had identical fabrics or strains

Recently a mathematical model has been inshyvestigated in which paramagnetic silicates are the only source of susceptibility (Hrouda 1987) With increasing preferred crystallographic orientation the anisotropy is shown to increase until it equals that of the crystal lattice Hrouda notes that this

14

13

1-2

I-I

t1-0 I-I -2 13 k2k3 Fig 4 Flinn-type diagram of susceptibility anisotropies for hypothetical rocks indicating the effects of variable proporshytions of magnetite and a paramagnetic mineral Each rook is represented by a tie-line and is composed of approximately 40$ of the named mineral plus magnetite (in the small fraction indicated by the numbers on the tie-line) and 60$ feldspar As the proportion of magnetite in the rock is increased (from 10-6

at the distal end of the tie-line in each case) the magnetic anisotropy of the rock decreases towards the anisotropy of magnetite The anisotropy of the particular magnetite chosen in these models is located near the convergence of the tie-lines

(From Borradaile 1987b)

relationship can be disturbed by the smallest traces of ferrimagnetic material and is difficult to calibrate in terms of strain Moreover a general difficulty of this type of mathematical model (both in magnetic fabrics and petrofabrics) is that it treats the grains as dispersed crystallites of no finite size which are free to develop their ideal crystal shape In nature grains are in contact and in the case of paramagnetic silicates in metamorshyphic tectonites their preferred orientations pose special problems For example grains with crystalshylographic orientations at high angles to the preshyferred orientation (schistosity) are restricted in growth Thus their reduced volumes will decrease their contribution to the rock anisotropy (see Fig 13b)

Magnetic anisotropy and finite strain

Principal susceptibility directions

In rocks with strong tectonic fabrics the prinshycipal magnetic susceptibility directions are often

7

parallel to prominent structural directions (Kligshyfield et al 1977) or related to fold geometry (Owens and Bamford 1976) For example the minimum susceptibili ty is usually perpendicular to a primary cleavage The maximum susceptibility may be parallel to the maximum extension in the rock (eg Fig 6b) contained in the cleavage and defined by stretched objects or mineral lineations (eg Singh et aI 1975 Kligfield et aI 1977 Coward and Whalley 1979 Rathore 1979 Goldshystein 1980) In contrast the maximum susceptibilshyity may be parallel to the intersection lineation of bedding and cleavage (eg Hrouda 1976 also Fig 5)

These two different patterns have been intershypreted in a number of ways One interpretation is that the maximum susceptibility is parallel always to the maximum extension It implies that the intersection lineation of bedding and cleavage is the maximum extension direction This appears to be unusual because an intersection lineation is the fortuitous interference of a tectonic fabric with the disturbed bedding surfaces In some areas the magnetic fabrics may be reasonably consistent in orientation while the (single-generation) fold hinges and intersection lineations may vary conshysiderably in orientation (Fig 6) There is no good reason for supposing that the intersection lineashytion must necessarily have some genetic relation to the strain ellipsoid

Another interpretation is that maximum susshyceptibilities occur parallel to intersection lineashytions because of heterogeneous combinations of sub fabrics If some portions of the rock retain a

bedding

cleole

bull maximum susceptibilify

intermediote susceptibility bull minimum sUKeptibihly

Fig 5 Principal susceptibility directions in Hercynian slates with a single tectonic fabric Note the maximum susceptibilishyties close to the intersection lineation of cleavage and bedding and the minimum susceptibility perpendicular to bedding

(From Borradaile and Tarling 1981)

8

bull -l-A~

~xL 0--~

~

b)0)

SUSCfptiblhtibullbull bull mcaimum in~rmtdIQt bull mntnlUtl

X IMOn fOld plunQl I inttotcon liMohon

Fig 6 Susceptibility orientations and major fold plunges in Archean slates with a single tectonic fabric Despite the varishyation in fold plunge ( sheath folds or periclinal folds) the metamorphic and magnetic fabrics are reasonably consistently

oriented in different adjacent parts of the area (From Borradaile and Brown 1987)

bedding parallel oblate magnetic fabric due to sedimentation then this may interfere with the fabric due to tectonic causes Under the right circumstances which are not too special this comshybination may produce maximum susceptibilities parallel to cleavage and bedding or perpendicular to the stretching direction (Fig 7) For this exshyplanation to be valid indeed for this arrangement of susceptibility axis to be detectable the interfershying subfabrics must be present on scales smaller than the sample size used in susceptibility deshyterminations (usually about 10 em3) Recently bedding-parallel fabrics have been detected in

L L

0 IIbullbulllli0 degiOo bull

(a) (b)

susceptibilities bull mo int-dio 0 mi

Fig 7 Variation in principal susceptibility orientations in meta-sandstones with a single tectonic fabric L indicates the grain elongation in the schistosity plane which is horizontal in these diagrams In some cases the maximum susceptibility is nearly parallel to the grain elongation (b) in others it is

perpendicular (a) (Borradai1e and Tarling 1984)

stylolitic cl~voge dOmOin

Fig 8 Where a tectonic fabric develops a domainal texture such as in stylolitic cleavage there may be distinct contribushytions of magnetic anisotropy from different parts of the rock Qeavage zones may contribute a tectonic susceptibility anishysotropy while inter-cleavage domains may still retain a sedimiddot mentary magnetic fabric The susceptibility determination for

the rock blends the two fabrics

metasediments with isoclinal sheath folds (Borshyradaile et al bull in press)

A third explanation similar to the previous one has been given for rocks that have been very weakly strained with pressure solution as the deshyformation mechanism lbis mechanism often proshyduces a regular domainal tectonic fabric of closely spaced laminae which concentrate insoluble material (including iron oxides and paramagnetic silicates) in thin sheets between rock that retains a sedimentary fabric Where laminae are more closely spaced than the width of the core used to determine susceptibility the net susceptibility is a combination of sedimentary and tectonic contrishybutions In this case the maximum susceptibility is often parallel to the intersection lineation of the domains (stylolitic cleavage) and bedding (Fig 8) Rochette and Vialon (1984) note that heterogeshyneous fabrics combining magnetic sub-fabrics of different ages prohibit any kind of quantitative correlation of strain and susceptibility

In mylonite zones (Goldstein 1980) and in major shear zones (Rathore 1985) magnetic fabrics have orientations that indicate maximum susceptshyibilities compatible with maximum extension dishyrections Similarly minimum susceptibilities are reported perpendicular to schistosities or foliashytions The relationship to boudinage directions and mineral stretching lineations has been cited to support the contention that there is a one-ta-one correspondence of strain axes and principal susshyceptibility directions in some cases Hrouda (1979 reported 1977) seems to have been the first person

9

to have considered the combining effects of magshynetic fabrics of different ages He described early susceptibility fabrics by a tensor P superimposed tectonic fabrics by a tensor D and suggested that they combine to form a resultant susceptibility tensor R by

D P = R or D = R p- 1

Goldstein (1980) applied the same approach to mylonitic fabrics Some authors have simply asshysumed that it is permissible to use the orientations of magnetic fabrics within shear zones rather like a schistosity to determine the amount and sense of shear Similar studies have been carried out subsequently on shear zones up to a regional scale in extent (eg Rathore 1985) However in experishymental shear zones the author has found that earlier magnetic fabrics are difficult to overprint and magnetic fabric maybe an unreliable kineshymatic indicator

Magnitudes ofsusceptibility and magnitudes ofstrain

The relationship between the shape of the magshynitude ellipsoid of susceptibility and the intensity of the tectonic fabric is more complex than the relationship between directions as discussed in the previous section Usually comparisons have been attempted between the shapes of the susceptshyibility and finite strain ellipsoids The latter is usually derived from some macroscopic straiI) marker such as pebbles concretions lappilli or rotated sand-dikes (eg Rathore 1979 Borradaile and Tarling 19811984 Rathore and Henry 1982 Clendenen et at 1988 Hirt et al 1988) Reducshytion spots have been used as strain markers from time to time however their pre-metamorphic origin is not always certain and in the Welsh examples some outcrops have susceptibilities that are too low to give reproducible magnetic fabrics

The susceptibility ellipsoid normally plots much nearer the origin of the Flinn-diagram than does the strain ellipsoid (Fig 9) In some cases logashyrithmic plots (Fig 10) help in their discrimination The relationships between strain and magnetic fabric are not straightforward The most strained samples in an outcrop do not necessarily have the most extreme magnetic anisotropies This is shown

a or L

20-1 AI IfIOOltfrc ItJtedtlDoloty 0IItN11tOy

JWUiOl2L1LL bull for QIdfl c~1 f~~

O for fktlPOf lCIStl ( ~ I

15

ol~~ ~bOrF 10 15 20 B

Fig 9 Strain ellipsoid data determined by de-straining analyshysis for quartz clasts and for feldspar clasts and the susceptibilshy

ity anisotropy in meta-sandstones a XY b - YZ where X lt Y lt Z L and F are the equivalent ratios for the magnetic susceptibility There is a single schistose tectonic fabric Data for the same hand-specimens are connected by tie-lines There is no simple relationship between the magnitude of strain and

intensity of magnetic fabric (Borradaile and Tarling 1984)

by the crossing tie-lines in Fig 9 Moreover there is always some question as to the validity of the comparison since the strain is commonly heterogeshyneous on the scale of a thin section whereas the homogeneously strained markers are much larger Susceptibility is usually measured from a sample about 10 cm3

so that the susceptibility tensor will be defined on a smaller scale than the strain tensor Another approach although less common in the literature is to compare the susceptibility

t log a (log l)

~ ~

~ +~ iii~iffl ~

0 lr b ~ C-_~~

0 ~J 04 ~tgt~J-~

~~~I ~~Q

0middot1

az

~ llZ I

o CH 02 0middot4 0middot6 08 1middot0 IZ

- log b (log F)

bull ST~AIN EItIPSOIO SHAPE SUSCEPTISILITY ELUPSOID SHAPE

Fig 10 Strain ellipsoid data and susceptibility data for four outcrops of slate (l to IV) with a single tectonic fabric connected by tie-lines and presented on a logarithmic Flinn-dishy

agram (From Borradaile and Tarling 1981)

bull bull bull bull

10

003

Mj maximum (i -I) values

006 I intermediate I

( i bull 2 l values 1 ~~---------~~------

- 003 -lmiddotmiddot - 006

bull bull III(L -middot00

II I

minimum (imiddot 3) values

I NmiddotI 000

Fig 11 Nonnalised measures of principal susceptibility magnishytudes (M) and o( principal strain magnitudes (Ni ) (or specishymens o( a metavolcanic rock with a single tectonic fabric There is no correlation between minimum values of susceptibilshyity and strain nor between intennediate values etc Nevertheshyless it would be possible to infer a correlation incorrectly by considering all the data laquo(or maximum intermediate and minimum susceptibilities) simultaneously (From Borradaile

and Mothersill 1984)

fabric with the petrofabric of a slightly smaller sample detennined by means of X-ray texture goniometry (eg Wood et al 1976 Hrouda et al 1985b) This overcomes the criticism that different scales will be sampled but there is the added complication of interpreting the texture goniomeshyter data in terms of finite strain (Oertel 1983)

One of the earliest attempts to relate the strain and susceptibility tensors was by Kneen (1976) She plotted ratios of principal strains against ratios of principal susceptibilities and inferred correlashytions Similar studies that compared strain ratios with susceptibility anisotropy used special loga-

M 02

rithmic parameters to normalise values (Wood et al 1976 Rathore 1979 1980 Rathore and Henry 1982 Kligfield et al 1982) These are termed IV (for strain) and M (for susceptibility) where i = 1 2 or 3 for the appropriate principal value The actual algebraic definition of N and M varies in the literature and care should be taken in comparshying data from one paper to another) Unforshytunately in most of these cases the authors plotted the data for all three principal directions on the same axes and generally established correlation coefficients for the maximum intermediate and minimum values simultaneously Strictly speaking this is invalid (Fig 11) and in one instance the correlation of anisotropies attempted in this manner has been disproved (Borradaile and Mothersill 1984)

This may give a discouraging view of the correshylations of strain and susceptibility but the data already published do give some indication that correlations may exist although weaker than origishynally claimed For example comparing data for just minimum (normalised) strains and minimum (normalised) susceptibilities it is possible to reshycognise modest correlations between susceptibility and strain in the case of the Welsh slates (eg Wood et al 1976) here in Fig 12 Clendenen et al (1988) have recently recognised that this kind of weaker correlation between the strain of conshycretions and susceptibility can be statistically sigshynificant

Thus although weak correlations of the kind

klk2 =(XY) may exist these must only be of local siginificance

I I I bullbullbullbullbullbullbull bull

I ttl bullbull~

ol------------r ------ shy bull V

~- fmiddot I maximum (i1) and -0middot2 r I intermediate (middot 2 ) values

minimum values (i 3) I

~~~____~____~I~____~ Nj -~ -~ 0 ~

Fig 12 Nonnalised measures of principal susceptibilities (M) and of principal strains (Ni ) for slates with a single tectonic fabric Note that a weak correlation exists between minimum strains and minimum susceptibilities (From Wood et al 1976)

11

Q Z p Marchian rofafion

S ~ b

t1- y p 0- Zr +y~

k X L oL

X SI bull bull S

Fig 13 a Theoretical outline of the March model as applied to the rotation and preferred orientation of phyUosilicate grains For strain axes X ~ Y ~ Z the rotation of a pole p of a platelet is shown schematically as is the rotation of the long axis of a rod-like element Such elements are considered to be dispersed and perfectly rigid b Schematic cross-section of a typical natural preferred orientation of phyllosilicate grains defining a schistosity Sl Grains with less favoured orientations are truncated and their volumetric contribution to the magnetic fabric may be reduced Usually the pattern of

preferred orientation can only be explained by the March model to a limited degree

and it seems unduly optimistic to consider them as universal relationships that may be extrapolated from one region to another Within a single reshygion with a limited range of deformation mechashynisms and lithological uniformity it might be posshysible to extrapolate some correlations of magnetic fabric with strain

The approaches reviewed so far in this section are essentially empirical and in most cases the susceptibility was attributed to disseminated magshynetite The studies of Coward and Whalley (1979) and of Henry and Daly (1983) were exceptions they recognised multiple sources of susceptibility and Kligfield et al (1982) also investigated the sources thoroughly The latter authors demonshystrated susceptibility anisotropy was due to iron oxides whose distributions and orientations were controlled mimetically by their position on the surfaces of the oolites used as strain markers The other studies mentioned adopt the premise or imply that magnetite grains were distributed throughout the rocks and were tectonically aligned to produce a magnetite shape-fabric which in turn dictated the magnetic fabric The underlying mechanistic model that appears to have influenced this train of thought is attributed to March (1932) This model (eg Wood et al 1976) outlines the situation in which platy elements that do not impinge upon oneanother and that are preferably randomly oriented in their initial configuration

become systematically re-oriented by homogeshyneous strain and are not impeded by the matrix (Fig 13a) Consequently the orientation-distribushytion of the poles to these platelets after constantshyvolume strain is directly related to the strain Thus for a given direction i the strain e is related to the normalised density (d) of platelet poles by

emiddot = d(-1j3 - 1 I bull

In the structural geology literature some considershyation has been given to the aspect ratios of the platelets as well as accompanying volume changes of tqe aggregate (Tullis 1976 Tullis and Wood 1975) However these modifications still fall short of reality The March model is difficult to adapt to three-dimensional grains and even more difficult to reconcile with the premises of passive beshyhaviour and non-impingement of the rotating grains on each other A worse shortcoming is the inherent assumption that the grains are spatially separated whereas in a typical metamorphic rock the variation in orientation imposes restrictions on the degree to which differently oriented crystals grow (Fig 13b) Nevertheless it has found applishycations in magnetic studies (eg Cogne and Gapais 1986) and studies of comparable mathematical models (Hrouda 1980) and is frequently cited in petrofabric studies (Oertel 1983)

Hrouda (1987) has extended these arguments to situations in which it is known that paramagnetic

12

sheet silicates such as chlorite and biotite0

dominate the anisotropy of susceptibility An inshyteresting development of this study is that in slates of the Carpathians in which the anisotropy is due to paramagnetic phyllosilicates the degree of anishysotropy is proportional to the bulk or mean susshyceptibility This has also been reported in Archean slates (Borradaile et aI in press)

Strain response models and multiple sources of susshy

ceptibility

Owens (1974) first drew attention to two imshyportant items that must be taken into account in any interpretation of susceptibility anisotropy in terms of strain Firstly the mineralogical source of the susceptibility should be defined If there are multiple sources of susceptibility the direct applishycation of the simple March model or any other model assuming a penetrative homogeneous magshynetic response is invalid Rochette and Vialon (1984) and Henry (1983) enforced this argument in different ways Slight variations in the proporshytions of minerals with different magnetic anishysotropies may under certain circumstances proshyduce changes in the bulk anisotropy that override any changes in anisotropy due to strain (Borshyradaile 1987b)

The second major point raised by Owens was that the actual strain response model has a major influence on the way in which the anisotropy accumulates from the pre-strain situation For simplicity he considered three models The first was a lineplane model that we can compare to the March model already referred to above (Fig 13a) The second was the viscous or Jeffery model in which the magnetic grain is likened to a rigid ellipsoid undergoing strain-induced motion in a viscous medium The third passive model likens the magnetic grains to passive strain markers Structural geologists may compare this to the model proposed by Ramsays school of structshyural geology to approximate the shape and conseshyquent orientation changes of for example a tectonically deforming passive ellipsoidal marker by the Rrcp equations see Fig 14 (Borradaile 1987a) Care should be taken with the term passhysive some geophysicists use the term to refer to

$e85 ~_068 fRo= 15 ~t=135

C)-shystrain ellipse (j) ~5middot Rs= 20 0_01409lt

Ro= 15 iff=15

original possive passive markers markers after strain

Fig 14 The R rlt1gt model Particles with the original orientashy J

tions (8) shown as a result of strain indicated by the strain ellipse take up new orientations (lt1raquo At the same time the ratios of the original shapes (R1f) change to final shapes (Ry2) The shape-ratio of the strain ellipse is 2 1 as indicated

the lineplane or March model and where they do not appear to imply any similarity to the Rrcp model (eg Cogne and Gapais 1986)

The mechanical response is usually neglected in the correlation of strains and susceptibility anishysotropies Indeed it is likely that many rocks and many types of deformation mechanisms are unsuishytable for establishing a correlation using the preshymises of simple mathematical models involving a single mode of deformation For example if there are relict components of sedimentary magnetic fabrics mixed with the tectonic fabrics or magshynetic fabrics of different tectonic ages a model assuming homogeneity will fail Similarly deforshymation structures that produce domainal fabrics that differently influence the magnetic fabric will cause complications if the magnetic fabric is samshypled on a scale that does not take this into account In particulate flow (Fig 15) the movement of grains may be poorly ordered Some grains move more than their neighbours rotate more or even exchange neighbours despite the fact that on a suitably large polygranular scale the strain may be approximately homogeneous Movement in polyshygranular units is also possible (Fig 16) as has been shown by experiments on analog materials (Means 1977) The scale on which magnetic susceptibility is defined will determine whether or not this preshysents a problem

The deformation mechanisms may be still more complicated The deformation may cause the rock

I bull

13

(01 (bl

Fig IS Particulate flow of a simulated (two-dimensional) aggregate Deformation proceeds from (a) through (c) The motions of particles is somewhat disordered whereas on a large scale the strain may appear to be approximately homogeneous as shown by the

strain ellipse defined by the black particles

J mm Fig 16 Experimentally produced particulate flow of groups of alum grains involving intergranular displacement surfaces

(From Means 1977)

et

deformation gt

bull00 bull

Fig 17 Possible deformation processes in metamorphic rocks that could be significant in the evolution of magnetic fabrics c -intergranular displacement surfaces (may be invisible) d-ductile (may be plastic) deformation of grains e-styloshylitie surfaces and grain-truncation f -penetration of grains g -microfaults (cleavage slip) h-rotation of blocks or groups of grains between faults or other discontinuities m-pressureshysolution material transfer (may be out of system) n-new

minerals crystallise

to be a discontinuum on various scales Lozenges of rock may rotate mass removal may occur loshycally or even to outside the system while grains plastically deform by intercrystalline processes and slide and roll past oneanother (Fig 16) At the same time new minerals may form with their crystallographic orientations controlled by the contemporary stress system Any of these factors could complicate the strain-response model of the rock and the development of its magnetic fabric While all of these processes are unlikely to occur at once the roles of several of these (or others not discussed) have to be assessed before the magnetic fabric can be correlated with the bulk strain Amongst these complications probably the most common one is the growth of new minerals as for example in phyllites schists and gneisses In these cases the explanation of schistosity may be bound up with the origin of the metamorphic texture more than with the strain of the rock (Fig 17) (Borradaile et at 1986)

Experimental studies

Although there has been some early interest in the effects of stress on magnetic susceptibility (eg Nagata 1966 1970 Kean et al 1976) this was associated with strains within the elastic limit Of interest here are the susceptibility changes that occur with large strains due to deformation that is macroscopically ductile if not actually plastic at the crystalline level The problem in the laboratory

bullbull bull bullbull bull bull

bullbull

14

environment is that even at the slowest strain rates that are practicable (10- 6 to 10-9 S-I) most rocks and minerals are not sufficiently ductile at room temperature to fail by the natural mechanisms of metamorphic rocks

Owens and Rutter (1978) first tackled this subshyject with a study of marbles and of calcite Alshythough the diamagnetic susceptibility of calcite is low the mineral is relatively easily deformed in a plastic manner at moderate confining pressures It is also stable at modest experimental temperatures so that Owens and Rutter were able to enhance the ductility by using temperatures up to 500 0 C in combination with pressures of 150 to 300 MPa (15 to 3 kbar) at strain-rates of approximately 10 - 4 to 10 - s s - 1 They achieved strains up to 50 axial-symmetrical (coaxial) shortening of the cylindrical specimens

The marbles they used had essentially isotropic magnetic and optical-crystallographic fabrics inishytially The magnetic anisotropy rapidly reached a plateau intensity at about 45 shortening The optical fabrics and the susceptibility fabric rapidly became axisymmetric to the shortening axis of the specimens This study didmiddot much to confirm the value of magnetic fabrics as indicators of strain and kinematics of deformation but most natural studies are based on ferrirnagnetic or parashymagnetic materials

Natural paramagnetic and ferrimagnetic matershyials are difficult to deform in a realistic manner without raising the temperature Heating will not normally be possible without inducing mineralogishycal changes that might mask susceptibility changes due to deformation Borradaile and Alford (1987) approached this problem by using a synthetic aggregate of sand enriched with magnetite that was cemented with commercial Portland cement The latter has a negligible (diamagnetic) susceptshyibility in comparison with the aggregate and pershymitted the aggregate to shorten by 35 in a ductile manner by axial symmetrical shortening The deshyformation did not involve cataclasis of the sand grains Rather the deformation was accommodshyated by the shearing of the cement gel This pershymitted a grain-shape alignment to develop by rollshying and sliding of the grains The magnetite grains were of the same grain-size as the matrix sand so

bulll1pl -04

bull 03

02 bull bull

01 bullbull01 02 03 04 In (XZ)

00 I I bull I I ~

11 12 13 14 15 (XI Z)

Fig 18 A correlation between the change in degree (fl) of susceptibility anisotropy and the strain ratio in some pure shear experiments on synthetic magnetite-bearing sandshy

stones (From Borradaile and Alford 1987)

that these experiments essentially addressed the problem of the rotational behaviour of the clasts (In most natural sandstones the iron oxide grains are much smaller than the sand clasts) The experiments were at carefully controlled strainshyrates of 5 x 10 - 6 S - 1 and confining pressures of 150 MPa (15 kbar) The maximum and intershymediate principal directions of susceptibility of these specimens rotated very rapidly towards the plane of flattening at rates exceeding the rate of rotation of a line undergoing homogeneous strain (cf the lineplane model) It was inferred that the magnetites rotated rigidly possibly with some plastic deformation The rotation was even more rapid when the matrix was composed of calcite instead of silicate mineral grains For initial susshyceptibility fabrics that were suitably oriented it was found that the change in the degree of anishysotropy was related to the strain by a power law (Fig 18) This serves to emphasise the importance of the initial magnetic fabric Relatively little can be deduced of the strain history from the final magnetic fabric alone Just as the initial ellipsoidal shape and orientation is of paramount importance in the strain analysis of ellipsoidal objects so is a knowledge of similar information for the initial magnetic fabric ellipsoid Although a power law relationship between the change in orientation of specially oriented magnetic fabrics exists in cershytain axial-symmetrical ( pure shear) experiments

15

In ( kmox kim J Calcite -cement - magnetite Q9g~gotes

at 150 MPo 05

04

XZHI XZmiddotH403 --

~ U-C3Z ~ AC -10 SHEAR ZOHEt ~ PURE SHEAR

02

t 01 XZ 20 XZ -115

In (kint kmln )

-0 02 03 04 -05 06 -07 os

bull Fig 19 The paths of incremental changes in magnetic anishysotropy are shown for the experimental deformation of syntheshysised calcite-cement-magnetite specimens The pure shear test produces little change in anisotropy even though the XZ strain ratio reaches 135 In contrast the changes produced in a shear zone (transpressive) are much greater despite the fact

that the ultimate XZ strain ratio for the zone is only 114

it is premature to make extrapolations to nature at the present state of knowledge

Recent work on experimental shear zones of synthetic materials at 150 MPa extends these conshyclusions to the case of transpressive deformation -a non-coaxial strain history (Borradaile and Alshyford in press) The susceptibility ellipsoids rotate rapidly toward stable orientations in which the minimum susceptibility is at a high angle to the shear zone boundaries The magnetic anisotropy changes very rapidly in the shear zones they produce a stronger magnetic fabric than axial symmetrical shortening at the same strain This is shown for two typical incremental- tests on the same synthetic calcite-matrix material at 150 Mpa in Fig 19 A further complication recognised in the experiments is that the magnetic fabrics may be planar (F gt L) whereas the mineral fabrics are constricted (a gt b) or plane strain (a = b) It is not known if these observations are transferable to natural shear zones

Conclusions

The interpretation of natural magnetic fabrics may be more complex than was initially recogshynised but progressive changes in magnetic anishysotropy do occur sympathetically with regional strain gradients despite accompanying regional

metamorphism (eg Hrouda and Janak 1976 Hrouda 1976 Coward and Whalley 1979) Indeed Rochette (1987) has shown that the metashymorphic production of pyrrhotite can enhance the susceptibility and produce a magnetically detectashyble isograd Also in certain rocks there are at least weak correlatiCfls between ratios of principal strains and the ratios of principal susceptibilities Numerous examples of the parallelism of principal susceptibility directions and structural directions (or even principal strain directions) support the contention that genetic relationships do exist beshytween strain and susceptibility in some cases Nevshyertheless these correlations are not universal and it is not possible to predict which natural situashytions will yield susceptibility data that _will faithshyfully represent principal strain directions or prinshycipal strain magnitudes or both For exampl~ magnetic fabrics do not always seem to be reliable kinematic indicators for shear zones and in the case of polyphase deformation later magnetic fabrics do not uniformly overprint earlier ones Magnetic fabrics should not be used for routine methods of strain analysis without further study A more profitable avenue is to determine how the susceptibility and strain tensors relate taking account of the actual strain-response model (deshyformation mechanisms) and the actual minerashylogical sources of susceptibility in that rock inshycluding phases produced by metamorphism A fruitful approach would be to consider the tensorial combination of coexisting magnetic subshyfabrics and successive episodes of magnetic fabric development along the lines initiated by Hrouda (1979)

Relationships between susceptibility and strain are in vogue However the earliest uses of magshynetic studies simply to investigate bulk petroshyfabrics are not yet been fully developed or inshytegrated with detailed petrofabric studies by optishycalor X-ray means Furthermore studies of remashynence and of susceptibility at different field strengths can yield information on magnetic subshyfabrics of different grain-sizes or different mineralogy This information is essential in the study of metamorphism of magnetic phases as well as their preferred orientation The anisotropy of remanence is also a profitable area of study

16 _

because only the ferrimagnetic traces contribute to that sub-fabric

Finally the nondestructive nature of magnetic fabric analysis provides a tool for investigating the progressive deformation or progressive metamorshyphism of a single specimen in laboratory experishyments Experiments on synthetii aggregates indishycate that the initial anisotropy of materials is not easily overprinted by small strains at low tempershyature They demonstrate also that the magnetic fabric ellipsoid spins very rapidly where the chief magnetic mineral is magnetite This is more noticeable when the matrix grains undergo crystal-plastic deformation Experimental shear zones produce greater changes in magnetic shape fabrics than axial-symmetrical shortening (pure shear) at the same strain they can also produce magnetic fabrics differing in symmetry from the grain fabric Such results develop an awareness for the greater complexities of natural structures

Acknowledgments

I wish to thank the Natural Sciences and Enshygineering Research Council of Canada for the continuing support of my work Frantisek Hrouda and Brian Bayly are thanked for constructive criticism of this article Karel Zapletal is thanked for some data on biotite Mel Friedman and Jan Tullis provided helpful reviews

Postscript

Since this paper was accepted for publication P Rochette has drawn attention to unusual inshyverse magnetic fabrics probably produced by single-domain magnetite (Thesis University of Grenoble 1988211 pp)

APPENDIX

Presentation of anisotropy of susceptibility

Magnetic susceptibility is a second rank tensor property conveniently envisaged as a magnitude ellipsoid (see Hrouda 1982 p 38) with three principal axes k max bull kim and k min or k ll bull kn k 33 The average or bulk susceptibility is comshy

monly defined as the arithmetic mean of the three principal values (Ellwood et al 1986-Symshyposium recommendations) but it is not clear why the arithmetic mean is a more appropriate represhysentation of bulk susceptibility than the geometric mean Susceptibility anisotropies for rocks are so low (Figs 9 and 10) that there is often little difference between these two expressions For exshyample seventeen specimens of strongly strained fine schist of the English Borrowdale Volcanic Series have principal susceptibilities in the ratio 104 102 0943 ~

Hrouda (1982) lists 25 different parameters that have been used at various times to represent anishysotropy The most useful are sometimes termed the magnetic lineation and the magnetic foliashytion

L = kmaxkint and F= kintkmin

Note that some authors chose alternative definishytions for Land F (eg Coward 1976) The parameters L and F are plotted vertically and horizontally respectively and compare directly with the ratios used to describe the strain ellipsoid on a Flinn-diagram

a=XY and b= YZ where X 2 Y ~ Z are the principal strains In some instances it is clearer if the natural logarithms of L F and of a and b are plotted

If the ratios of principal susceptibilities are listed individually it is helpful to normalise them so that their product is unity The normalised versions of the principal susceptibilities are related to their ratios by the following relations

kmax = L 2 3 bull pl3

kml

= L -13 F I 3

k = L -13 bull F- 23mm

It is advisable also to present a mean (bulk) susceptibility value This enables the reader to assess the significance of the results (Conference recommendations Ellwood et al 1986) Unforshytunately this has often not been done in the past Commonly one finds that anisotropies are poorly reproducible for rocks with susceptibility lt 10-4

SIjvol Providing cones of confidence about principal directions and standard errors for prinshycipal magnitudes is also useful in this regard

bull

30

2-5

20

-5

10 F=~ WI shy - middotmiddotV j Y

0 5 20 25 30 35

F =(klnkmin)

Fig AI The relationship between Jelineks (1981) P and T parameters and the conventional anisotropy parameters L and

F

The ratios L and F like their counterparts in strain (a and b) are very useful in describing the ellipsoids shape or sense of anisotropy However the distance of the point (L F) from the origin is also a measure of the degree of anisotropy that is to say its departure from sphericity Jelineks (1981) parameters pi and T overcome this T represents sense of anisotropy and ranges from -1 (prolate) to + 1 (oblate) pi (gt 1) expresses degree of anisotropy These are defined as

[ 2(In k -In k~]T= -1

In k itM - In k min 1

pi = exp [ 2( af + a ~ + a~ ) ] ~ where a1 = In(kmaxkb) etc and kb = (kmax k inl

kmin )(l3) The relationship of p and T to L and F is shown in Fig AI

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17

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Uyeda S Fuller MD Belshe JC and Girdler RW 1963 Anisotropy of magnetic susceptibility of rocks and minershyals J Geophys Res 68 279-291

Van den Ende C 1975 On the origin of anisotropy of magshynetic susceptibility in Permian Redbeds from the western part of the Dome de Barrot (S France) In GJ Borradaile et al (Editors) Progress in Geodynamics North-Holland Pub Co Amsterdam pp 176-189

Voight W and Kinoshita S 1907 Bestimmung absoluler Wene von Magnelisierungszahlen insbesondere fUr Krisshytalle Ann Phys 24 492-514

Wagner JJ Hedley FG Steen D Tinkler C and Vaugnat M 1981 Magnetic anisotropy and fabric of some progresshysively deformed ophiolitic gabbros J Geophys Res 86 307-315

Weast RC and Astle MJ (Editors) 1978 CRC handbook of Chemistry and Physics 59th edn CRC Press Palm Beach Fla

20

II

Wing-Fatt L and Stacey FD 1966 Magnetic anisotropy of laboratory materials in which magma flow is simulated Pure AppJ Geophys 6478-80

Wood DS Oertel G Singh J and Bennett HF 1976 Strain and anisotropy in rocks Philos Trans R Soc London Ser A 283 27-42

Zavoyskiy VN 1982 Use of magnetic susceptibility tensor for solving problems in structural geology Izv Akad Nauk SSSR Earth Phys Ser 18 217-223

14

13

1-2

I-I

t1-0 I-I -2 13 k2k3 Fig 4 Flinn-type diagram of susceptibility anisotropies for hypothetical rocks indicating the effects of variable proporshytions of magnetite and a paramagnetic mineral Each rook is represented by a tie-line and is composed of approximately 40$ of the named mineral plus magnetite (in the small fraction indicated by the numbers on the tie-line) and 60$ feldspar As the proportion of magnetite in the rock is increased (from 10-6

at the distal end of the tie-line in each case) the magnetic anisotropy of the rock decreases towards the anisotropy of magnetite The anisotropy of the particular magnetite chosen in these models is located near the convergence of the tie-lines

(From Borradaile 1987b)

relationship can be disturbed by the smallest traces of ferrimagnetic material and is difficult to calibrate in terms of strain Moreover a general difficulty of this type of mathematical model (both in magnetic fabrics and petrofabrics) is that it treats the grains as dispersed crystallites of no finite size which are free to develop their ideal crystal shape In nature grains are in contact and in the case of paramagnetic silicates in metamorshyphic tectonites their preferred orientations pose special problems For example grains with crystalshylographic orientations at high angles to the preshyferred orientation (schistosity) are restricted in growth Thus their reduced volumes will decrease their contribution to the rock anisotropy (see Fig 13b)

Magnetic anisotropy and finite strain

Principal susceptibility directions

In rocks with strong tectonic fabrics the prinshycipal magnetic susceptibility directions are often

7

parallel to prominent structural directions (Kligshyfield et al 1977) or related to fold geometry (Owens and Bamford 1976) For example the minimum susceptibili ty is usually perpendicular to a primary cleavage The maximum susceptibility may be parallel to the maximum extension in the rock (eg Fig 6b) contained in the cleavage and defined by stretched objects or mineral lineations (eg Singh et aI 1975 Kligfield et aI 1977 Coward and Whalley 1979 Rathore 1979 Goldshystein 1980) In contrast the maximum susceptibilshyity may be parallel to the intersection lineation of bedding and cleavage (eg Hrouda 1976 also Fig 5)

These two different patterns have been intershypreted in a number of ways One interpretation is that the maximum susceptibility is parallel always to the maximum extension It implies that the intersection lineation of bedding and cleavage is the maximum extension direction This appears to be unusual because an intersection lineation is the fortuitous interference of a tectonic fabric with the disturbed bedding surfaces In some areas the magnetic fabrics may be reasonably consistent in orientation while the (single-generation) fold hinges and intersection lineations may vary conshysiderably in orientation (Fig 6) There is no good reason for supposing that the intersection lineashytion must necessarily have some genetic relation to the strain ellipsoid

Another interpretation is that maximum susshyceptibilities occur parallel to intersection lineashytions because of heterogeneous combinations of sub fabrics If some portions of the rock retain a

bedding

cleole

bull maximum susceptibilify

intermediote susceptibility bull minimum sUKeptibihly

Fig 5 Principal susceptibility directions in Hercynian slates with a single tectonic fabric Note the maximum susceptibilishyties close to the intersection lineation of cleavage and bedding and the minimum susceptibility perpendicular to bedding

(From Borradaile and Tarling 1981)

8

bull -l-A~

~xL 0--~

~

b)0)

SUSCfptiblhtibullbull bull mcaimum in~rmtdIQt bull mntnlUtl

X IMOn fOld plunQl I inttotcon liMohon

Fig 6 Susceptibility orientations and major fold plunges in Archean slates with a single tectonic fabric Despite the varishyation in fold plunge ( sheath folds or periclinal folds) the metamorphic and magnetic fabrics are reasonably consistently

oriented in different adjacent parts of the area (From Borradaile and Brown 1987)

bedding parallel oblate magnetic fabric due to sedimentation then this may interfere with the fabric due to tectonic causes Under the right circumstances which are not too special this comshybination may produce maximum susceptibilities parallel to cleavage and bedding or perpendicular to the stretching direction (Fig 7) For this exshyplanation to be valid indeed for this arrangement of susceptibility axis to be detectable the interfershying subfabrics must be present on scales smaller than the sample size used in susceptibility deshyterminations (usually about 10 em3) Recently bedding-parallel fabrics have been detected in

L L

0 IIbullbulllli0 degiOo bull

(a) (b)

susceptibilities bull mo int-dio 0 mi

Fig 7 Variation in principal susceptibility orientations in meta-sandstones with a single tectonic fabric L indicates the grain elongation in the schistosity plane which is horizontal in these diagrams In some cases the maximum susceptibility is nearly parallel to the grain elongation (b) in others it is

perpendicular (a) (Borradai1e and Tarling 1984)

stylolitic cl~voge dOmOin

Fig 8 Where a tectonic fabric develops a domainal texture such as in stylolitic cleavage there may be distinct contribushytions of magnetic anisotropy from different parts of the rock Qeavage zones may contribute a tectonic susceptibility anishysotropy while inter-cleavage domains may still retain a sedimiddot mentary magnetic fabric The susceptibility determination for

the rock blends the two fabrics

metasediments with isoclinal sheath folds (Borshyradaile et al bull in press)

A third explanation similar to the previous one has been given for rocks that have been very weakly strained with pressure solution as the deshyformation mechanism lbis mechanism often proshyduces a regular domainal tectonic fabric of closely spaced laminae which concentrate insoluble material (including iron oxides and paramagnetic silicates) in thin sheets between rock that retains a sedimentary fabric Where laminae are more closely spaced than the width of the core used to determine susceptibility the net susceptibility is a combination of sedimentary and tectonic contrishybutions In this case the maximum susceptibility is often parallel to the intersection lineation of the domains (stylolitic cleavage) and bedding (Fig 8) Rochette and Vialon (1984) note that heterogeshyneous fabrics combining magnetic sub-fabrics of different ages prohibit any kind of quantitative correlation of strain and susceptibility

In mylonite zones (Goldstein 1980) and in major shear zones (Rathore 1985) magnetic fabrics have orientations that indicate maximum susceptshyibilities compatible with maximum extension dishyrections Similarly minimum susceptibilities are reported perpendicular to schistosities or foliashytions The relationship to boudinage directions and mineral stretching lineations has been cited to support the contention that there is a one-ta-one correspondence of strain axes and principal susshyceptibility directions in some cases Hrouda (1979 reported 1977) seems to have been the first person

9

to have considered the combining effects of magshynetic fabrics of different ages He described early susceptibility fabrics by a tensor P superimposed tectonic fabrics by a tensor D and suggested that they combine to form a resultant susceptibility tensor R by

D P = R or D = R p- 1

Goldstein (1980) applied the same approach to mylonitic fabrics Some authors have simply asshysumed that it is permissible to use the orientations of magnetic fabrics within shear zones rather like a schistosity to determine the amount and sense of shear Similar studies have been carried out subsequently on shear zones up to a regional scale in extent (eg Rathore 1985) However in experishymental shear zones the author has found that earlier magnetic fabrics are difficult to overprint and magnetic fabric maybe an unreliable kineshymatic indicator

Magnitudes ofsusceptibility and magnitudes ofstrain

The relationship between the shape of the magshynitude ellipsoid of susceptibility and the intensity of the tectonic fabric is more complex than the relationship between directions as discussed in the previous section Usually comparisons have been attempted between the shapes of the susceptshyibility and finite strain ellipsoids The latter is usually derived from some macroscopic straiI) marker such as pebbles concretions lappilli or rotated sand-dikes (eg Rathore 1979 Borradaile and Tarling 19811984 Rathore and Henry 1982 Clendenen et at 1988 Hirt et al 1988) Reducshytion spots have been used as strain markers from time to time however their pre-metamorphic origin is not always certain and in the Welsh examples some outcrops have susceptibilities that are too low to give reproducible magnetic fabrics

The susceptibility ellipsoid normally plots much nearer the origin of the Flinn-diagram than does the strain ellipsoid (Fig 9) In some cases logashyrithmic plots (Fig 10) help in their discrimination The relationships between strain and magnetic fabric are not straightforward The most strained samples in an outcrop do not necessarily have the most extreme magnetic anisotropies This is shown

a or L

20-1 AI IfIOOltfrc ItJtedtlDoloty 0IItN11tOy

JWUiOl2L1LL bull for QIdfl c~1 f~~

O for fktlPOf lCIStl ( ~ I

15

ol~~ ~bOrF 10 15 20 B

Fig 9 Strain ellipsoid data determined by de-straining analyshysis for quartz clasts and for feldspar clasts and the susceptibilshy

ity anisotropy in meta-sandstones a XY b - YZ where X lt Y lt Z L and F are the equivalent ratios for the magnetic susceptibility There is a single schistose tectonic fabric Data for the same hand-specimens are connected by tie-lines There is no simple relationship between the magnitude of strain and

intensity of magnetic fabric (Borradaile and Tarling 1984)

by the crossing tie-lines in Fig 9 Moreover there is always some question as to the validity of the comparison since the strain is commonly heterogeshyneous on the scale of a thin section whereas the homogeneously strained markers are much larger Susceptibility is usually measured from a sample about 10 cm3

so that the susceptibility tensor will be defined on a smaller scale than the strain tensor Another approach although less common in the literature is to compare the susceptibility

t log a (log l)

~ ~

~ +~ iii~iffl ~

0 lr b ~ C-_~~

0 ~J 04 ~tgt~J-~

~~~I ~~Q

0middot1

az

~ llZ I

o CH 02 0middot4 0middot6 08 1middot0 IZ

- log b (log F)

bull ST~AIN EItIPSOIO SHAPE SUSCEPTISILITY ELUPSOID SHAPE

Fig 10 Strain ellipsoid data and susceptibility data for four outcrops of slate (l to IV) with a single tectonic fabric connected by tie-lines and presented on a logarithmic Flinn-dishy

agram (From Borradaile and Tarling 1981)

bull bull bull bull

10

003

Mj maximum (i -I) values

006 I intermediate I

( i bull 2 l values 1 ~~---------~~------

- 003 -lmiddotmiddot - 006

bull bull III(L -middot00

II I

minimum (imiddot 3) values

I NmiddotI 000

Fig 11 Nonnalised measures of principal susceptibility magnishytudes (M) and o( principal strain magnitudes (Ni ) (or specishymens o( a metavolcanic rock with a single tectonic fabric There is no correlation between minimum values of susceptibilshyity and strain nor between intennediate values etc Nevertheshyless it would be possible to infer a correlation incorrectly by considering all the data laquo(or maximum intermediate and minimum susceptibilities) simultaneously (From Borradaile

and Mothersill 1984)

fabric with the petrofabric of a slightly smaller sample detennined by means of X-ray texture goniometry (eg Wood et al 1976 Hrouda et al 1985b) This overcomes the criticism that different scales will be sampled but there is the added complication of interpreting the texture goniomeshyter data in terms of finite strain (Oertel 1983)

One of the earliest attempts to relate the strain and susceptibility tensors was by Kneen (1976) She plotted ratios of principal strains against ratios of principal susceptibilities and inferred correlashytions Similar studies that compared strain ratios with susceptibility anisotropy used special loga-

M 02

rithmic parameters to normalise values (Wood et al 1976 Rathore 1979 1980 Rathore and Henry 1982 Kligfield et al 1982) These are termed IV (for strain) and M (for susceptibility) where i = 1 2 or 3 for the appropriate principal value The actual algebraic definition of N and M varies in the literature and care should be taken in comparshying data from one paper to another) Unforshytunately in most of these cases the authors plotted the data for all three principal directions on the same axes and generally established correlation coefficients for the maximum intermediate and minimum values simultaneously Strictly speaking this is invalid (Fig 11) and in one instance the correlation of anisotropies attempted in this manner has been disproved (Borradaile and Mothersill 1984)

This may give a discouraging view of the correshylations of strain and susceptibility but the data already published do give some indication that correlations may exist although weaker than origishynally claimed For example comparing data for just minimum (normalised) strains and minimum (normalised) susceptibilities it is possible to reshycognise modest correlations between susceptibility and strain in the case of the Welsh slates (eg Wood et al 1976) here in Fig 12 Clendenen et al (1988) have recently recognised that this kind of weaker correlation between the strain of conshycretions and susceptibility can be statistically sigshynificant

Thus although weak correlations of the kind

klk2 =(XY) may exist these must only be of local siginificance

I I I bullbullbullbullbullbullbull bull

I ttl bullbull~

ol------------r ------ shy bull V

~- fmiddot I maximum (i1) and -0middot2 r I intermediate (middot 2 ) values

minimum values (i 3) I

~~~____~____~I~____~ Nj -~ -~ 0 ~

Fig 12 Nonnalised measures of principal susceptibilities (M) and of principal strains (Ni ) for slates with a single tectonic fabric Note that a weak correlation exists between minimum strains and minimum susceptibilities (From Wood et al 1976)

11

Q Z p Marchian rofafion

S ~ b

t1- y p 0- Zr +y~

k X L oL

X SI bull bull S

Fig 13 a Theoretical outline of the March model as applied to the rotation and preferred orientation of phyUosilicate grains For strain axes X ~ Y ~ Z the rotation of a pole p of a platelet is shown schematically as is the rotation of the long axis of a rod-like element Such elements are considered to be dispersed and perfectly rigid b Schematic cross-section of a typical natural preferred orientation of phyllosilicate grains defining a schistosity Sl Grains with less favoured orientations are truncated and their volumetric contribution to the magnetic fabric may be reduced Usually the pattern of

preferred orientation can only be explained by the March model to a limited degree

and it seems unduly optimistic to consider them as universal relationships that may be extrapolated from one region to another Within a single reshygion with a limited range of deformation mechashynisms and lithological uniformity it might be posshysible to extrapolate some correlations of magnetic fabric with strain

The approaches reviewed so far in this section are essentially empirical and in most cases the susceptibility was attributed to disseminated magshynetite The studies of Coward and Whalley (1979) and of Henry and Daly (1983) were exceptions they recognised multiple sources of susceptibility and Kligfield et al (1982) also investigated the sources thoroughly The latter authors demonshystrated susceptibility anisotropy was due to iron oxides whose distributions and orientations were controlled mimetically by their position on the surfaces of the oolites used as strain markers The other studies mentioned adopt the premise or imply that magnetite grains were distributed throughout the rocks and were tectonically aligned to produce a magnetite shape-fabric which in turn dictated the magnetic fabric The underlying mechanistic model that appears to have influenced this train of thought is attributed to March (1932) This model (eg Wood et al 1976) outlines the situation in which platy elements that do not impinge upon oneanother and that are preferably randomly oriented in their initial configuration

become systematically re-oriented by homogeshyneous strain and are not impeded by the matrix (Fig 13a) Consequently the orientation-distribushytion of the poles to these platelets after constantshyvolume strain is directly related to the strain Thus for a given direction i the strain e is related to the normalised density (d) of platelet poles by

emiddot = d(-1j3 - 1 I bull

In the structural geology literature some considershyation has been given to the aspect ratios of the platelets as well as accompanying volume changes of tqe aggregate (Tullis 1976 Tullis and Wood 1975) However these modifications still fall short of reality The March model is difficult to adapt to three-dimensional grains and even more difficult to reconcile with the premises of passive beshyhaviour and non-impingement of the rotating grains on each other A worse shortcoming is the inherent assumption that the grains are spatially separated whereas in a typical metamorphic rock the variation in orientation imposes restrictions on the degree to which differently oriented crystals grow (Fig 13b) Nevertheless it has found applishycations in magnetic studies (eg Cogne and Gapais 1986) and studies of comparable mathematical models (Hrouda 1980) and is frequently cited in petrofabric studies (Oertel 1983)

Hrouda (1987) has extended these arguments to situations in which it is known that paramagnetic

12

sheet silicates such as chlorite and biotite0

dominate the anisotropy of susceptibility An inshyteresting development of this study is that in slates of the Carpathians in which the anisotropy is due to paramagnetic phyllosilicates the degree of anishysotropy is proportional to the bulk or mean susshyceptibility This has also been reported in Archean slates (Borradaile et aI in press)

Strain response models and multiple sources of susshy

ceptibility

Owens (1974) first drew attention to two imshyportant items that must be taken into account in any interpretation of susceptibility anisotropy in terms of strain Firstly the mineralogical source of the susceptibility should be defined If there are multiple sources of susceptibility the direct applishycation of the simple March model or any other model assuming a penetrative homogeneous magshynetic response is invalid Rochette and Vialon (1984) and Henry (1983) enforced this argument in different ways Slight variations in the proporshytions of minerals with different magnetic anishysotropies may under certain circumstances proshyduce changes in the bulk anisotropy that override any changes in anisotropy due to strain (Borshyradaile 1987b)

The second major point raised by Owens was that the actual strain response model has a major influence on the way in which the anisotropy accumulates from the pre-strain situation For simplicity he considered three models The first was a lineplane model that we can compare to the March model already referred to above (Fig 13a) The second was the viscous or Jeffery model in which the magnetic grain is likened to a rigid ellipsoid undergoing strain-induced motion in a viscous medium The third passive model likens the magnetic grains to passive strain markers Structural geologists may compare this to the model proposed by Ramsays school of structshyural geology to approximate the shape and conseshyquent orientation changes of for example a tectonically deforming passive ellipsoidal marker by the Rrcp equations see Fig 14 (Borradaile 1987a) Care should be taken with the term passhysive some geophysicists use the term to refer to

$e85 ~_068 fRo= 15 ~t=135

C)-shystrain ellipse (j) ~5middot Rs= 20 0_01409lt

Ro= 15 iff=15

original possive passive markers markers after strain

Fig 14 The R rlt1gt model Particles with the original orientashy J

tions (8) shown as a result of strain indicated by the strain ellipse take up new orientations (lt1raquo At the same time the ratios of the original shapes (R1f) change to final shapes (Ry2) The shape-ratio of the strain ellipse is 2 1 as indicated

the lineplane or March model and where they do not appear to imply any similarity to the Rrcp model (eg Cogne and Gapais 1986)

The mechanical response is usually neglected in the correlation of strains and susceptibility anishysotropies Indeed it is likely that many rocks and many types of deformation mechanisms are unsuishytable for establishing a correlation using the preshymises of simple mathematical models involving a single mode of deformation For example if there are relict components of sedimentary magnetic fabrics mixed with the tectonic fabrics or magshynetic fabrics of different tectonic ages a model assuming homogeneity will fail Similarly deforshymation structures that produce domainal fabrics that differently influence the magnetic fabric will cause complications if the magnetic fabric is samshypled on a scale that does not take this into account In particulate flow (Fig 15) the movement of grains may be poorly ordered Some grains move more than their neighbours rotate more or even exchange neighbours despite the fact that on a suitably large polygranular scale the strain may be approximately homogeneous Movement in polyshygranular units is also possible (Fig 16) as has been shown by experiments on analog materials (Means 1977) The scale on which magnetic susceptibility is defined will determine whether or not this preshysents a problem

The deformation mechanisms may be still more complicated The deformation may cause the rock

I bull

13

(01 (bl

Fig IS Particulate flow of a simulated (two-dimensional) aggregate Deformation proceeds from (a) through (c) The motions of particles is somewhat disordered whereas on a large scale the strain may appear to be approximately homogeneous as shown by the

strain ellipse defined by the black particles

J mm Fig 16 Experimentally produced particulate flow of groups of alum grains involving intergranular displacement surfaces

(From Means 1977)

et

deformation gt

bull00 bull

Fig 17 Possible deformation processes in metamorphic rocks that could be significant in the evolution of magnetic fabrics c -intergranular displacement surfaces (may be invisible) d-ductile (may be plastic) deformation of grains e-styloshylitie surfaces and grain-truncation f -penetration of grains g -microfaults (cleavage slip) h-rotation of blocks or groups of grains between faults or other discontinuities m-pressureshysolution material transfer (may be out of system) n-new

minerals crystallise

to be a discontinuum on various scales Lozenges of rock may rotate mass removal may occur loshycally or even to outside the system while grains plastically deform by intercrystalline processes and slide and roll past oneanother (Fig 16) At the same time new minerals may form with their crystallographic orientations controlled by the contemporary stress system Any of these factors could complicate the strain-response model of the rock and the development of its magnetic fabric While all of these processes are unlikely to occur at once the roles of several of these (or others not discussed) have to be assessed before the magnetic fabric can be correlated with the bulk strain Amongst these complications probably the most common one is the growth of new minerals as for example in phyllites schists and gneisses In these cases the explanation of schistosity may be bound up with the origin of the metamorphic texture more than with the strain of the rock (Fig 17) (Borradaile et at 1986)

Experimental studies

Although there has been some early interest in the effects of stress on magnetic susceptibility (eg Nagata 1966 1970 Kean et al 1976) this was associated with strains within the elastic limit Of interest here are the susceptibility changes that occur with large strains due to deformation that is macroscopically ductile if not actually plastic at the crystalline level The problem in the laboratory

bullbull bull bullbull bull bull

bullbull

14

environment is that even at the slowest strain rates that are practicable (10- 6 to 10-9 S-I) most rocks and minerals are not sufficiently ductile at room temperature to fail by the natural mechanisms of metamorphic rocks

Owens and Rutter (1978) first tackled this subshyject with a study of marbles and of calcite Alshythough the diamagnetic susceptibility of calcite is low the mineral is relatively easily deformed in a plastic manner at moderate confining pressures It is also stable at modest experimental temperatures so that Owens and Rutter were able to enhance the ductility by using temperatures up to 500 0 C in combination with pressures of 150 to 300 MPa (15 to 3 kbar) at strain-rates of approximately 10 - 4 to 10 - s s - 1 They achieved strains up to 50 axial-symmetrical (coaxial) shortening of the cylindrical specimens

The marbles they used had essentially isotropic magnetic and optical-crystallographic fabrics inishytially The magnetic anisotropy rapidly reached a plateau intensity at about 45 shortening The optical fabrics and the susceptibility fabric rapidly became axisymmetric to the shortening axis of the specimens This study didmiddot much to confirm the value of magnetic fabrics as indicators of strain and kinematics of deformation but most natural studies are based on ferrirnagnetic or parashymagnetic materials

Natural paramagnetic and ferrimagnetic matershyials are difficult to deform in a realistic manner without raising the temperature Heating will not normally be possible without inducing mineralogishycal changes that might mask susceptibility changes due to deformation Borradaile and Alford (1987) approached this problem by using a synthetic aggregate of sand enriched with magnetite that was cemented with commercial Portland cement The latter has a negligible (diamagnetic) susceptshyibility in comparison with the aggregate and pershymitted the aggregate to shorten by 35 in a ductile manner by axial symmetrical shortening The deshyformation did not involve cataclasis of the sand grains Rather the deformation was accommodshyated by the shearing of the cement gel This pershymitted a grain-shape alignment to develop by rollshying and sliding of the grains The magnetite grains were of the same grain-size as the matrix sand so

bulll1pl -04

bull 03

02 bull bull

01 bullbull01 02 03 04 In (XZ)

00 I I bull I I ~

11 12 13 14 15 (XI Z)

Fig 18 A correlation between the change in degree (fl) of susceptibility anisotropy and the strain ratio in some pure shear experiments on synthetic magnetite-bearing sandshy

stones (From Borradaile and Alford 1987)

that these experiments essentially addressed the problem of the rotational behaviour of the clasts (In most natural sandstones the iron oxide grains are much smaller than the sand clasts) The experiments were at carefully controlled strainshyrates of 5 x 10 - 6 S - 1 and confining pressures of 150 MPa (15 kbar) The maximum and intershymediate principal directions of susceptibility of these specimens rotated very rapidly towards the plane of flattening at rates exceeding the rate of rotation of a line undergoing homogeneous strain (cf the lineplane model) It was inferred that the magnetites rotated rigidly possibly with some plastic deformation The rotation was even more rapid when the matrix was composed of calcite instead of silicate mineral grains For initial susshyceptibility fabrics that were suitably oriented it was found that the change in the degree of anishysotropy was related to the strain by a power law (Fig 18) This serves to emphasise the importance of the initial magnetic fabric Relatively little can be deduced of the strain history from the final magnetic fabric alone Just as the initial ellipsoidal shape and orientation is of paramount importance in the strain analysis of ellipsoidal objects so is a knowledge of similar information for the initial magnetic fabric ellipsoid Although a power law relationship between the change in orientation of specially oriented magnetic fabrics exists in cershytain axial-symmetrical ( pure shear) experiments

15

In ( kmox kim J Calcite -cement - magnetite Q9g~gotes

at 150 MPo 05

04

XZHI XZmiddotH403 --

~ U-C3Z ~ AC -10 SHEAR ZOHEt ~ PURE SHEAR

02

t 01 XZ 20 XZ -115

In (kint kmln )

-0 02 03 04 -05 06 -07 os

bull Fig 19 The paths of incremental changes in magnetic anishysotropy are shown for the experimental deformation of syntheshysised calcite-cement-magnetite specimens The pure shear test produces little change in anisotropy even though the XZ strain ratio reaches 135 In contrast the changes produced in a shear zone (transpressive) are much greater despite the fact

that the ultimate XZ strain ratio for the zone is only 114

it is premature to make extrapolations to nature at the present state of knowledge

Recent work on experimental shear zones of synthetic materials at 150 MPa extends these conshyclusions to the case of transpressive deformation -a non-coaxial strain history (Borradaile and Alshyford in press) The susceptibility ellipsoids rotate rapidly toward stable orientations in which the minimum susceptibility is at a high angle to the shear zone boundaries The magnetic anisotropy changes very rapidly in the shear zones they produce a stronger magnetic fabric than axial symmetrical shortening at the same strain This is shown for two typical incremental- tests on the same synthetic calcite-matrix material at 150 Mpa in Fig 19 A further complication recognised in the experiments is that the magnetic fabrics may be planar (F gt L) whereas the mineral fabrics are constricted (a gt b) or plane strain (a = b) It is not known if these observations are transferable to natural shear zones

Conclusions

The interpretation of natural magnetic fabrics may be more complex than was initially recogshynised but progressive changes in magnetic anishysotropy do occur sympathetically with regional strain gradients despite accompanying regional

metamorphism (eg Hrouda and Janak 1976 Hrouda 1976 Coward and Whalley 1979) Indeed Rochette (1987) has shown that the metashymorphic production of pyrrhotite can enhance the susceptibility and produce a magnetically detectashyble isograd Also in certain rocks there are at least weak correlatiCfls between ratios of principal strains and the ratios of principal susceptibilities Numerous examples of the parallelism of principal susceptibility directions and structural directions (or even principal strain directions) support the contention that genetic relationships do exist beshytween strain and susceptibility in some cases Nevshyertheless these correlations are not universal and it is not possible to predict which natural situashytions will yield susceptibility data that _will faithshyfully represent principal strain directions or prinshycipal strain magnitudes or both For exampl~ magnetic fabrics do not always seem to be reliable kinematic indicators for shear zones and in the case of polyphase deformation later magnetic fabrics do not uniformly overprint earlier ones Magnetic fabrics should not be used for routine methods of strain analysis without further study A more profitable avenue is to determine how the susceptibility and strain tensors relate taking account of the actual strain-response model (deshyformation mechanisms) and the actual minerashylogical sources of susceptibility in that rock inshycluding phases produced by metamorphism A fruitful approach would be to consider the tensorial combination of coexisting magnetic subshyfabrics and successive episodes of magnetic fabric development along the lines initiated by Hrouda (1979)

Relationships between susceptibility and strain are in vogue However the earliest uses of magshynetic studies simply to investigate bulk petroshyfabrics are not yet been fully developed or inshytegrated with detailed petrofabric studies by optishycalor X-ray means Furthermore studies of remashynence and of susceptibility at different field strengths can yield information on magnetic subshyfabrics of different grain-sizes or different mineralogy This information is essential in the study of metamorphism of magnetic phases as well as their preferred orientation The anisotropy of remanence is also a profitable area of study

16 _

because only the ferrimagnetic traces contribute to that sub-fabric

Finally the nondestructive nature of magnetic fabric analysis provides a tool for investigating the progressive deformation or progressive metamorshyphism of a single specimen in laboratory experishyments Experiments on synthetii aggregates indishycate that the initial anisotropy of materials is not easily overprinted by small strains at low tempershyature They demonstrate also that the magnetic fabric ellipsoid spins very rapidly where the chief magnetic mineral is magnetite This is more noticeable when the matrix grains undergo crystal-plastic deformation Experimental shear zones produce greater changes in magnetic shape fabrics than axial-symmetrical shortening (pure shear) at the same strain they can also produce magnetic fabrics differing in symmetry from the grain fabric Such results develop an awareness for the greater complexities of natural structures

Acknowledgments

I wish to thank the Natural Sciences and Enshygineering Research Council of Canada for the continuing support of my work Frantisek Hrouda and Brian Bayly are thanked for constructive criticism of this article Karel Zapletal is thanked for some data on biotite Mel Friedman and Jan Tullis provided helpful reviews

Postscript

Since this paper was accepted for publication P Rochette has drawn attention to unusual inshyverse magnetic fabrics probably produced by single-domain magnetite (Thesis University of Grenoble 1988211 pp)

APPENDIX

Presentation of anisotropy of susceptibility

Magnetic susceptibility is a second rank tensor property conveniently envisaged as a magnitude ellipsoid (see Hrouda 1982 p 38) with three principal axes k max bull kim and k min or k ll bull kn k 33 The average or bulk susceptibility is comshy

monly defined as the arithmetic mean of the three principal values (Ellwood et al 1986-Symshyposium recommendations) but it is not clear why the arithmetic mean is a more appropriate represhysentation of bulk susceptibility than the geometric mean Susceptibility anisotropies for rocks are so low (Figs 9 and 10) that there is often little difference between these two expressions For exshyample seventeen specimens of strongly strained fine schist of the English Borrowdale Volcanic Series have principal susceptibilities in the ratio 104 102 0943 ~

Hrouda (1982) lists 25 different parameters that have been used at various times to represent anishysotropy The most useful are sometimes termed the magnetic lineation and the magnetic foliashytion

L = kmaxkint and F= kintkmin

Note that some authors chose alternative definishytions for Land F (eg Coward 1976) The parameters L and F are plotted vertically and horizontally respectively and compare directly with the ratios used to describe the strain ellipsoid on a Flinn-diagram

a=XY and b= YZ where X 2 Y ~ Z are the principal strains In some instances it is clearer if the natural logarithms of L F and of a and b are plotted

If the ratios of principal susceptibilities are listed individually it is helpful to normalise them so that their product is unity The normalised versions of the principal susceptibilities are related to their ratios by the following relations

kmax = L 2 3 bull pl3

kml

= L -13 F I 3

k = L -13 bull F- 23mm

It is advisable also to present a mean (bulk) susceptibility value This enables the reader to assess the significance of the results (Conference recommendations Ellwood et al 1986) Unforshytunately this has often not been done in the past Commonly one finds that anisotropies are poorly reproducible for rocks with susceptibility lt 10-4

SIjvol Providing cones of confidence about principal directions and standard errors for prinshycipal magnitudes is also useful in this regard

bull

30

2-5

20

-5

10 F=~ WI shy - middotmiddotV j Y

0 5 20 25 30 35

F =(klnkmin)

Fig AI The relationship between Jelineks (1981) P and T parameters and the conventional anisotropy parameters L and

F

The ratios L and F like their counterparts in strain (a and b) are very useful in describing the ellipsoids shape or sense of anisotropy However the distance of the point (L F) from the origin is also a measure of the degree of anisotropy that is to say its departure from sphericity Jelineks (1981) parameters pi and T overcome this T represents sense of anisotropy and ranges from -1 (prolate) to + 1 (oblate) pi (gt 1) expresses degree of anisotropy These are defined as

[ 2(In k -In k~]T= -1

In k itM - In k min 1

pi = exp [ 2( af + a ~ + a~ ) ] ~ where a1 = In(kmaxkb) etc and kb = (kmax k inl

kmin )(l3) The relationship of p and T to L and F is shown in Fig AI

References

Borradaile GJ 1981 Particulate flow of rock and the formashytion of rock cleavage Tectonophysics 24 442-455

Borradaile GJ 1987a Analysis of strained sedimentary fabrics Can J Earth Sci 131 121-125

Borradaile GJ 1987b Anisotropy of magnetic susceptibility rock composition versus strain Tectonophysics 138 327-329

Borradaile GJ and Alford C 1987 Relationship between

17

magnetic susceptibility and strain in laboratory experishyments Tectonophysics 133 121-135

Borradaile GJ and Alford C in press Experimental shear zones and magnetic fabrics J Struct Geol

Borradaile GJ and Brown HG 1987 The Shebandowan Group Timiskaming-like Archean rocks in northwestern Ontario Can J Earth Sci 24 185-188

Borradaile GJ and Mothersill JS bull 1984 Coaxial deformed and magnetic fabrics without simply correlated magnitudes of principal values Phys Earth Planet Inter 35 294-300

Borradaile GJ and Tarling D bull 1981 The influence of deforshymation mechanisms on magnetic fabrics in weakly deshyformed rocks Tectonophysics 77 151-168

Borradaile GJ and Tarling D bull 1984 Strain partitioning and magnetic fabrics in particulate flow Can J Earth Sci 21 694-697

Borradaile GJ Mothersill JS Tarling D and Alford C 1986 Sources of magnetic susceptibility in a slate Earth Planet Sci Lett 76 336-340

Borradaile GJ Keeler W Alford C and Sarvas P 1987 Anisotropy of magnetic susceptibility of some metamorphic minerals Phys Earth Planet Inter 48 161-166

Borradaile G Sarvas P Dutka R Stewart R and Stubley M in press Dextral transpression of the northern margin of the Quetico subprovince-magnetic fabrics and microshyfabrics Can J Earth Sci

Carmichael RS 1982 Magnetic properties of minerals and rocks In RC Weast and MJ Ashe (Editors) CRC Handbook of Physical Constants for Rocks CRC Press Roca Baton Fla pp 229-287

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Clendenen WS Kligfield R Hirt AM and Lowrie W 1988 Strain studies of cleavage development in the Chelmsford Formation Sudbury Basin Ontario Tectonophysics 145 191-211

Cognc JP and Gapais D bull 1986 Passive rotation of hematite during deformation a comparison of simulated and natural redbeds fabrics Tectonophysics 121 365-372

Collinson DW 1983 Methods in Paleomagnetism and Rock Magnetism Chapman and Hall London 500 pp

Coward MP 1976 Strain within ductile shear wnes Tectonophysics 34 181-197

Coward MP and Whalley 1S 1979 Texture and fabric studies across the Kishorn Nappe near Kyle of Lochalsh Western Scotland J Struct Geol 1 259-273

Crimes TP and Oldershaw MA 1967 Paleocurrent demiddot terminations by magnetic fabri measurement on the Cambrian rocks of St Tudwals peninsula North Wales Geol J 5 217-232

Ellwood BBbull Hrouda F and Wagner J-J 1988 Symposia on magnetic fabrics Introductory comments Phys Earth Planet Inter 51 249-252

Fuller MDbull 1964 On the magnetic fabrics of certain rocks 1 Geol 72 368-376

18

II

Goldstein AG bull 1980 Magnetic susceptibility anisotropy of mylonites from the Lake Char Mylonite Zone SE New England Tectonophysics 66 197-211

Graham lW 1954 Magnetic susceptibility anisotropy an unexploited petrofabric element Bull Gool Soc Am 65 1257-1258

Graham lWbull 1966 Significance of magnetic anisotropy in Appalachian sedimentary rocks In lS Steinhard and Tl Smith (Editors) The Earth beneath the Continents Gooshyphys Monogr Am Geophys Union 10 627-648

Hamano Y and Yom ida K 1982 Magnetic anisotropy and porosity of Antarctic chondrites Mem Natl Inst Polar Res Tokyo 25 281-290

Hamilton N 1963 Susceptibility anisotropy measurements on some Silurian siltstones Nature 197 170-171

Hamilton N and Rees AI 1970 The use of magnetic fabric in paleocurrent estimation In SK Runcorn (Editor) Paleogeophysics Academic Press New York NY pp 445-464

Hamilton N and Rees AI 1971 The anisotropy of magnetic susceptibility of the Franciscan Rocks of the Diablo Range Central California Geo Rundsch 60 1103-1124

Hamilton N Owens WH and Rees AI 1968 Laboratory experiments on the production of grain orientation in shearing sand l Goo 76 465-472

Hargraves RB 1959 Magnetic anisotropy and remanent magnetism in hemo-ilmenite from ore deposits at Allard Lake Quebec l Goophys Res 68 293-309

Heider Fbull Dunlop DJ and Sugiura N 1987 Magnetic properties oC hydrothermally recrystallized magnetite crystals Science 236 1287-1290

Henry B 1983 Interpretation quantitative de lanisotropie de susceptibilite magnetique Tectonophysics 91 165-177

Henry B and Daly L 1983 From qualitative to quantitative magnetic anisotropy analysis the prospect of finite strain calibration Tectonophysics 98 327-336

Hirt AM Lowrie W bull Clendenen WS and Kligfield R 1988 The correlation of magnetic anisotropy with strain in the Chelmsford Formation of the Sudbury Basin Ontario Tectonophysics 145 177-189

Hrouda F 1976 The origin of cleavage in the light of magnetic anisotropy investigations Pbys Earth Planet Inshyter 13 132-142

Hrouda F 1979 (reponed 1977) The strain interpretation of magnetic anisotropy in rocks of the Nizky lesenik Mounmiddot tains (Czechoslovakia) Sb Gool Ved (Uzit Geofyz) 16 27-62

Hrouda F 1980 Magnetocrystalline anisotropy of rocks and massive ores a mathematical model study and its fabric implications l Struct Geo1bull 2 459-462

Hrouda F 1982 Magnetic anisotropy of rocks and its apmiddot plication in geology and geophysics Geophys Surv 5 37-82

Hrouda F 1986 The effect of quanz on the magnetic ani sotropy of quartzite Studia Geophys Geod 30 39-45

Hrouda F bull 1987 Mathematical model relationships between

the paramagnetic anisotropy and strain in slates Tectonophysics 142 323-327

Hrouda F and Chlupacova M bull 1980 The magnetic fabric in the Nasavrky massif Cas Mineral Goo 25 17-27

Hrouda F and lanak F 1971 A study of the hematite fabric of some red sediments on the basis of their magnetic susceptibility anisotropy Sediment Geol 6 187-199

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Hrouda F and Jelinek V in prep Resolution of ferromagmiddot netic and paramagnetic components of magnetic anishysotropy using combined low-field and high-field anishysotropy measurements I

Hrouda F Chlupacova M and Rejl L 1971 The mimetic fabric of magnetite in some foliated granodiorites as indio cated by magnetic anisotropy Earth Planet Sci Leu 11 381-384

Hrouda F Chlupacova M and Rejl L bull 1972 Changes in magnetite content and magnetite fabric during Cenitization as investigated by petromagnetic methods Neues Jahrb Mineral Abh 117 61-72

Hrouda F Janalc F and Rejl L 1978 Magnetic fabric and ductile deformation of rocks in zones of progressive reshygional metamorphism Ger Beitr Goophys 87 126-134

Hrouda F Jelinek V and Zapletal K 1985a Use of magshynetic propenies of rocks in ore and petroleum geophysics (in Czech) Res rep Goofyz Brno pp 54-75

Hrouda F Siemes H Herres N and Hennig-Micbaeli c 1985b The relationship between the magnetic anisotropy and the cmiddotaxis fabric in a massive hematite ore J Geophys bull 56 174-182

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Jelinek V 1981 Characterization of the magnetic fabrics of rocks Tectonophysics 79 T63-T67

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Kean WF Day R Fuller M and Schmidt VA 1976 The effect of uniaxial compression on the initial susceptibility of rocks as a function of grain-size and composition of their constituent titanomagnetites J Geophys Res 81 861-874

Khan MA 1962 Anisotropy of magnetic susceptibility of some igneous and metamorphic rocks J Geophys Res 67 2873-2885

KJigfie1d R Lowrie W and Dalziel I 1977 Magnetic susshyceptibility anisotropy as a strain indicator in the Sudbury Basin Ontario Tectonophysics 40 287-308

KJigfield R Lowrie W and Pfiffner OA 1982 Magnetic propenies of deformed oolitic limestones from the Swiss Alps the correlation of magnetic anisotropy and strain Eclogae Geo He1v 75 127-157

Kneen SJ 1976 The relationship between the magnetic and

19

strain fabrics of some hematite-bearing Welsh Slates Earth Planet Sci Lett 31 413-416

Lamarche G and Rochette P 1987 Microstructural analysis and origin of lineations in the magnetic fabric of some Alpine slates Tectonophysics 139 285-293

Lapointe P Morris WA and Harding KL 1986 Interpreshytation of magnetic susceptibility a new approach 10 geoshyphysical evaluation of the degree of rock alteration Can J

Earth Sci 23 393-401 March A 1932 Mathematische Theorie der Regelung nach

der Korngestait bei afrmer Deformation Z Kristallogrmiddot 81 285-297

Means WD 1977 A deformation experiment in transmitted light Earth Planet Sci Lett 35 169-179

Nagata T 1966 Magnetic susceptibility of compressed rocks J Goomag Geoelectr 18 73-80

Nagata T 1970 Anisotropic magnetic susceptibility of rocks under mechanical stresses Pure App Goophys 78

110-122 Nye JF 1957 The Physical Properties of Crystals Clarendon

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orientation of phyllosilicale grains in rocks-a review Tectonophysics 100 413-447

Owens WH 1974 Mathematical model studies on factors affecting the magnetic anisotropy of deformed rocks Tectonophysics 24 115-131

Owens WH and Bamford D 1976 Magnetic seismic and other anisotropic properties of rock fabrics Philos Trans R Soc London Ser A 283 55-68

Owens WH and Rutter EH 1978 The development of magnetic susceptibility anisotropy through crystallographic preferred orientation in a calcite rock Phys Earth Planet Inter 16 215-222

Park JKmiddot1983 Paleomagnetism for geologists Geosci Can 4 180-188

Rathore JS 1979 Magnetic susceptibility anisotropy in the Cambrian Slate Belt of North Wales and correlation with strain Tectonophysics 53 83-97

Rathore JS 1985 Some magnetic characteristics of sheared zones J Geodyn 2 291-301

Rathore JS and Henry B 1982 Comparison of strained magnetic fabrics in Dalradian rocks from the southwest Highlands of Scotland J Struc Geol 4 373-384

Rees AI 1965 The use of anisotropy of magnetic susceptshyibility in the estimation of sedimentary fabric Sedimentolshyogy 4 257-271

Rees AI 1968 The production of preferred orientation in a concentrated dispersion of elongated and flattened grains J Geol 76 457-465

Rochetle P 1987 Metamorphic control of the mineralogy of black shales in the Swiss Alps toward the use of magnetic isograds Eanh Planet Sci Lett 84 446-456

Rochette P 1988 Relation entre deformation et metamorshy

f

bull

phisme Alpin dans les schistes noirs Helvetiques Iapport de la fabrique magnetique Geodin Acta 2 (in press)

Rochette P and Vialon P 1984 Development of planar and linear fabrics in Dauphinois shales and slates (French Alps) studied by magnetic anisotropy and its mineralogical conshytrol J Struct Geo 6 33-38

Schwarz E 1974 Magnetic fabrics in massive sulfide deposits Can J Earth Sci 11 1669-1675

Schwartz EJ 1975 Magnetic properties of pyrrhotite and their use in applied geology and geophysics Geo Surv Can Pap 74-59 24 pp

Singh J (now Rathore J) Sanderson DJ and Tariing DH 1975 The magnetic susceptibility anisotropy of deformed rocks from North Cornwall England Tectonophysics 27 141-153

Smith GM and Banetjee SK bull 1987 The dependence of weak field susceptibility on applied magnetic field Phys Earth Planet Inter 46 71-76

Stott GM and Schwerdtner WM 1981 A structural analyshysis of the central part of the Shebandowan metavolcanicshymetasedimentary belt Ontario Dep Mines Toronto Final Repbull Onto Geosci Res Rep No 5349 44 pp

Strangway DW 1970 History of the Earths Magnetic Field McGraw-Hili New York NY 168 pp

Tarling DH 1983 Paleomagnetism Chapman and Hall London 379 pp

Tullis TEbull 1976 Experiments on the origin of slaty cleavage and schistosity Geo Soc Am Bull 87 745-753

Tullis TE and Wood DS 1975 Correlation of finite strain from both reduction bodies and preferred orientation of mica in slate from Wales Geol Soc Am Bull 86 632-638

Urrutia-Fucugauchi J and Odabachian Y 1982 A Bibiograshyphy of Magnetic Susceptibility Anisotropy of Rocks Inshystituto de Geofisica Universidad Nacional Autonoma de Mexico Mexico 42 pp

Uyeda S Fuller MD Belshe JC and Girdler RW 1963 Anisotropy of magnetic susceptibility of rocks and minershyals J Geophys Res 68 279-291

Van den Ende C 1975 On the origin of anisotropy of magshynetic susceptibility in Permian Redbeds from the western part of the Dome de Barrot (S France) In GJ Borradaile et al (Editors) Progress in Geodynamics North-Holland Pub Co Amsterdam pp 176-189

Voight W and Kinoshita S 1907 Bestimmung absoluler Wene von Magnelisierungszahlen insbesondere fUr Krisshytalle Ann Phys 24 492-514

Wagner JJ Hedley FG Steen D Tinkler C and Vaugnat M 1981 Magnetic anisotropy and fabric of some progresshysively deformed ophiolitic gabbros J Geophys Res 86 307-315

Weast RC and Astle MJ (Editors) 1978 CRC handbook of Chemistry and Physics 59th edn CRC Press Palm Beach Fla

20

II

Wing-Fatt L and Stacey FD 1966 Magnetic anisotropy of laboratory materials in which magma flow is simulated Pure AppJ Geophys 6478-80

Wood DS Oertel G Singh J and Bennett HF 1976 Strain and anisotropy in rocks Philos Trans R Soc London Ser A 283 27-42

Zavoyskiy VN 1982 Use of magnetic susceptibility tensor for solving problems in structural geology Izv Akad Nauk SSSR Earth Phys Ser 18 217-223

8

bull -l-A~

~xL 0--~

~

b)0)

SUSCfptiblhtibullbull bull mcaimum in~rmtdIQt bull mntnlUtl

X IMOn fOld plunQl I inttotcon liMohon

Fig 6 Susceptibility orientations and major fold plunges in Archean slates with a single tectonic fabric Despite the varishyation in fold plunge ( sheath folds or periclinal folds) the metamorphic and magnetic fabrics are reasonably consistently

oriented in different adjacent parts of the area (From Borradaile and Brown 1987)

bedding parallel oblate magnetic fabric due to sedimentation then this may interfere with the fabric due to tectonic causes Under the right circumstances which are not too special this comshybination may produce maximum susceptibilities parallel to cleavage and bedding or perpendicular to the stretching direction (Fig 7) For this exshyplanation to be valid indeed for this arrangement of susceptibility axis to be detectable the interfershying subfabrics must be present on scales smaller than the sample size used in susceptibility deshyterminations (usually about 10 em3) Recently bedding-parallel fabrics have been detected in

L L

0 IIbullbulllli0 degiOo bull

(a) (b)

susceptibilities bull mo int-dio 0 mi

Fig 7 Variation in principal susceptibility orientations in meta-sandstones with a single tectonic fabric L indicates the grain elongation in the schistosity plane which is horizontal in these diagrams In some cases the maximum susceptibility is nearly parallel to the grain elongation (b) in others it is

perpendicular (a) (Borradai1e and Tarling 1984)

stylolitic cl~voge dOmOin

Fig 8 Where a tectonic fabric develops a domainal texture such as in stylolitic cleavage there may be distinct contribushytions of magnetic anisotropy from different parts of the rock Qeavage zones may contribute a tectonic susceptibility anishysotropy while inter-cleavage domains may still retain a sedimiddot mentary magnetic fabric The susceptibility determination for

the rock blends the two fabrics

metasediments with isoclinal sheath folds (Borshyradaile et al bull in press)

A third explanation similar to the previous one has been given for rocks that have been very weakly strained with pressure solution as the deshyformation mechanism lbis mechanism often proshyduces a regular domainal tectonic fabric of closely spaced laminae which concentrate insoluble material (including iron oxides and paramagnetic silicates) in thin sheets between rock that retains a sedimentary fabric Where laminae are more closely spaced than the width of the core used to determine susceptibility the net susceptibility is a combination of sedimentary and tectonic contrishybutions In this case the maximum susceptibility is often parallel to the intersection lineation of the domains (stylolitic cleavage) and bedding (Fig 8) Rochette and Vialon (1984) note that heterogeshyneous fabrics combining magnetic sub-fabrics of different ages prohibit any kind of quantitative correlation of strain and susceptibility

In mylonite zones (Goldstein 1980) and in major shear zones (Rathore 1985) magnetic fabrics have orientations that indicate maximum susceptshyibilities compatible with maximum extension dishyrections Similarly minimum susceptibilities are reported perpendicular to schistosities or foliashytions The relationship to boudinage directions and mineral stretching lineations has been cited to support the contention that there is a one-ta-one correspondence of strain axes and principal susshyceptibility directions in some cases Hrouda (1979 reported 1977) seems to have been the first person

9

to have considered the combining effects of magshynetic fabrics of different ages He described early susceptibility fabrics by a tensor P superimposed tectonic fabrics by a tensor D and suggested that they combine to form a resultant susceptibility tensor R by

D P = R or D = R p- 1

Goldstein (1980) applied the same approach to mylonitic fabrics Some authors have simply asshysumed that it is permissible to use the orientations of magnetic fabrics within shear zones rather like a schistosity to determine the amount and sense of shear Similar studies have been carried out subsequently on shear zones up to a regional scale in extent (eg Rathore 1985) However in experishymental shear zones the author has found that earlier magnetic fabrics are difficult to overprint and magnetic fabric maybe an unreliable kineshymatic indicator

Magnitudes ofsusceptibility and magnitudes ofstrain

The relationship between the shape of the magshynitude ellipsoid of susceptibility and the intensity of the tectonic fabric is more complex than the relationship between directions as discussed in the previous section Usually comparisons have been attempted between the shapes of the susceptshyibility and finite strain ellipsoids The latter is usually derived from some macroscopic straiI) marker such as pebbles concretions lappilli or rotated sand-dikes (eg Rathore 1979 Borradaile and Tarling 19811984 Rathore and Henry 1982 Clendenen et at 1988 Hirt et al 1988) Reducshytion spots have been used as strain markers from time to time however their pre-metamorphic origin is not always certain and in the Welsh examples some outcrops have susceptibilities that are too low to give reproducible magnetic fabrics

The susceptibility ellipsoid normally plots much nearer the origin of the Flinn-diagram than does the strain ellipsoid (Fig 9) In some cases logashyrithmic plots (Fig 10) help in their discrimination The relationships between strain and magnetic fabric are not straightforward The most strained samples in an outcrop do not necessarily have the most extreme magnetic anisotropies This is shown

a or L

20-1 AI IfIOOltfrc ItJtedtlDoloty 0IItN11tOy

JWUiOl2L1LL bull for QIdfl c~1 f~~

O for fktlPOf lCIStl ( ~ I

15

ol~~ ~bOrF 10 15 20 B

Fig 9 Strain ellipsoid data determined by de-straining analyshysis for quartz clasts and for feldspar clasts and the susceptibilshy

ity anisotropy in meta-sandstones a XY b - YZ where X lt Y lt Z L and F are the equivalent ratios for the magnetic susceptibility There is a single schistose tectonic fabric Data for the same hand-specimens are connected by tie-lines There is no simple relationship between the magnitude of strain and

intensity of magnetic fabric (Borradaile and Tarling 1984)

by the crossing tie-lines in Fig 9 Moreover there is always some question as to the validity of the comparison since the strain is commonly heterogeshyneous on the scale of a thin section whereas the homogeneously strained markers are much larger Susceptibility is usually measured from a sample about 10 cm3

so that the susceptibility tensor will be defined on a smaller scale than the strain tensor Another approach although less common in the literature is to compare the susceptibility

t log a (log l)

~ ~

~ +~ iii~iffl ~

0 lr b ~ C-_~~

0 ~J 04 ~tgt~J-~

~~~I ~~Q

0middot1

az

~ llZ I

o CH 02 0middot4 0middot6 08 1middot0 IZ

- log b (log F)

bull ST~AIN EItIPSOIO SHAPE SUSCEPTISILITY ELUPSOID SHAPE

Fig 10 Strain ellipsoid data and susceptibility data for four outcrops of slate (l to IV) with a single tectonic fabric connected by tie-lines and presented on a logarithmic Flinn-dishy

agram (From Borradaile and Tarling 1981)

bull bull bull bull

10

003

Mj maximum (i -I) values

006 I intermediate I

( i bull 2 l values 1 ~~---------~~------

- 003 -lmiddotmiddot - 006

bull bull III(L -middot00

II I

minimum (imiddot 3) values

I NmiddotI 000

Fig 11 Nonnalised measures of principal susceptibility magnishytudes (M) and o( principal strain magnitudes (Ni ) (or specishymens o( a metavolcanic rock with a single tectonic fabric There is no correlation between minimum values of susceptibilshyity and strain nor between intennediate values etc Nevertheshyless it would be possible to infer a correlation incorrectly by considering all the data laquo(or maximum intermediate and minimum susceptibilities) simultaneously (From Borradaile

and Mothersill 1984)

fabric with the petrofabric of a slightly smaller sample detennined by means of X-ray texture goniometry (eg Wood et al 1976 Hrouda et al 1985b) This overcomes the criticism that different scales will be sampled but there is the added complication of interpreting the texture goniomeshyter data in terms of finite strain (Oertel 1983)

One of the earliest attempts to relate the strain and susceptibility tensors was by Kneen (1976) She plotted ratios of principal strains against ratios of principal susceptibilities and inferred correlashytions Similar studies that compared strain ratios with susceptibility anisotropy used special loga-

M 02

rithmic parameters to normalise values (Wood et al 1976 Rathore 1979 1980 Rathore and Henry 1982 Kligfield et al 1982) These are termed IV (for strain) and M (for susceptibility) where i = 1 2 or 3 for the appropriate principal value The actual algebraic definition of N and M varies in the literature and care should be taken in comparshying data from one paper to another) Unforshytunately in most of these cases the authors plotted the data for all three principal directions on the same axes and generally established correlation coefficients for the maximum intermediate and minimum values simultaneously Strictly speaking this is invalid (Fig 11) and in one instance the correlation of anisotropies attempted in this manner has been disproved (Borradaile and Mothersill 1984)

This may give a discouraging view of the correshylations of strain and susceptibility but the data already published do give some indication that correlations may exist although weaker than origishynally claimed For example comparing data for just minimum (normalised) strains and minimum (normalised) susceptibilities it is possible to reshycognise modest correlations between susceptibility and strain in the case of the Welsh slates (eg Wood et al 1976) here in Fig 12 Clendenen et al (1988) have recently recognised that this kind of weaker correlation between the strain of conshycretions and susceptibility can be statistically sigshynificant

Thus although weak correlations of the kind

klk2 =(XY) may exist these must only be of local siginificance

I I I bullbullbullbullbullbullbull bull

I ttl bullbull~

ol------------r ------ shy bull V

~- fmiddot I maximum (i1) and -0middot2 r I intermediate (middot 2 ) values

minimum values (i 3) I

~~~____~____~I~____~ Nj -~ -~ 0 ~

Fig 12 Nonnalised measures of principal susceptibilities (M) and of principal strains (Ni ) for slates with a single tectonic fabric Note that a weak correlation exists between minimum strains and minimum susceptibilities (From Wood et al 1976)

11

Q Z p Marchian rofafion

S ~ b

t1- y p 0- Zr +y~

k X L oL

X SI bull bull S

Fig 13 a Theoretical outline of the March model as applied to the rotation and preferred orientation of phyUosilicate grains For strain axes X ~ Y ~ Z the rotation of a pole p of a platelet is shown schematically as is the rotation of the long axis of a rod-like element Such elements are considered to be dispersed and perfectly rigid b Schematic cross-section of a typical natural preferred orientation of phyllosilicate grains defining a schistosity Sl Grains with less favoured orientations are truncated and their volumetric contribution to the magnetic fabric may be reduced Usually the pattern of

preferred orientation can only be explained by the March model to a limited degree

and it seems unduly optimistic to consider them as universal relationships that may be extrapolated from one region to another Within a single reshygion with a limited range of deformation mechashynisms and lithological uniformity it might be posshysible to extrapolate some correlations of magnetic fabric with strain

The approaches reviewed so far in this section are essentially empirical and in most cases the susceptibility was attributed to disseminated magshynetite The studies of Coward and Whalley (1979) and of Henry and Daly (1983) were exceptions they recognised multiple sources of susceptibility and Kligfield et al (1982) also investigated the sources thoroughly The latter authors demonshystrated susceptibility anisotropy was due to iron oxides whose distributions and orientations were controlled mimetically by their position on the surfaces of the oolites used as strain markers The other studies mentioned adopt the premise or imply that magnetite grains were distributed throughout the rocks and were tectonically aligned to produce a magnetite shape-fabric which in turn dictated the magnetic fabric The underlying mechanistic model that appears to have influenced this train of thought is attributed to March (1932) This model (eg Wood et al 1976) outlines the situation in which platy elements that do not impinge upon oneanother and that are preferably randomly oriented in their initial configuration

become systematically re-oriented by homogeshyneous strain and are not impeded by the matrix (Fig 13a) Consequently the orientation-distribushytion of the poles to these platelets after constantshyvolume strain is directly related to the strain Thus for a given direction i the strain e is related to the normalised density (d) of platelet poles by

emiddot = d(-1j3 - 1 I bull

In the structural geology literature some considershyation has been given to the aspect ratios of the platelets as well as accompanying volume changes of tqe aggregate (Tullis 1976 Tullis and Wood 1975) However these modifications still fall short of reality The March model is difficult to adapt to three-dimensional grains and even more difficult to reconcile with the premises of passive beshyhaviour and non-impingement of the rotating grains on each other A worse shortcoming is the inherent assumption that the grains are spatially separated whereas in a typical metamorphic rock the variation in orientation imposes restrictions on the degree to which differently oriented crystals grow (Fig 13b) Nevertheless it has found applishycations in magnetic studies (eg Cogne and Gapais 1986) and studies of comparable mathematical models (Hrouda 1980) and is frequently cited in petrofabric studies (Oertel 1983)

Hrouda (1987) has extended these arguments to situations in which it is known that paramagnetic

12

sheet silicates such as chlorite and biotite0

dominate the anisotropy of susceptibility An inshyteresting development of this study is that in slates of the Carpathians in which the anisotropy is due to paramagnetic phyllosilicates the degree of anishysotropy is proportional to the bulk or mean susshyceptibility This has also been reported in Archean slates (Borradaile et aI in press)

Strain response models and multiple sources of susshy

ceptibility

Owens (1974) first drew attention to two imshyportant items that must be taken into account in any interpretation of susceptibility anisotropy in terms of strain Firstly the mineralogical source of the susceptibility should be defined If there are multiple sources of susceptibility the direct applishycation of the simple March model or any other model assuming a penetrative homogeneous magshynetic response is invalid Rochette and Vialon (1984) and Henry (1983) enforced this argument in different ways Slight variations in the proporshytions of minerals with different magnetic anishysotropies may under certain circumstances proshyduce changes in the bulk anisotropy that override any changes in anisotropy due to strain (Borshyradaile 1987b)

The second major point raised by Owens was that the actual strain response model has a major influence on the way in which the anisotropy accumulates from the pre-strain situation For simplicity he considered three models The first was a lineplane model that we can compare to the March model already referred to above (Fig 13a) The second was the viscous or Jeffery model in which the magnetic grain is likened to a rigid ellipsoid undergoing strain-induced motion in a viscous medium The third passive model likens the magnetic grains to passive strain markers Structural geologists may compare this to the model proposed by Ramsays school of structshyural geology to approximate the shape and conseshyquent orientation changes of for example a tectonically deforming passive ellipsoidal marker by the Rrcp equations see Fig 14 (Borradaile 1987a) Care should be taken with the term passhysive some geophysicists use the term to refer to

$e85 ~_068 fRo= 15 ~t=135

C)-shystrain ellipse (j) ~5middot Rs= 20 0_01409lt

Ro= 15 iff=15

original possive passive markers markers after strain

Fig 14 The R rlt1gt model Particles with the original orientashy J

tions (8) shown as a result of strain indicated by the strain ellipse take up new orientations (lt1raquo At the same time the ratios of the original shapes (R1f) change to final shapes (Ry2) The shape-ratio of the strain ellipse is 2 1 as indicated

the lineplane or March model and where they do not appear to imply any similarity to the Rrcp model (eg Cogne and Gapais 1986)

The mechanical response is usually neglected in the correlation of strains and susceptibility anishysotropies Indeed it is likely that many rocks and many types of deformation mechanisms are unsuishytable for establishing a correlation using the preshymises of simple mathematical models involving a single mode of deformation For example if there are relict components of sedimentary magnetic fabrics mixed with the tectonic fabrics or magshynetic fabrics of different tectonic ages a model assuming homogeneity will fail Similarly deforshymation structures that produce domainal fabrics that differently influence the magnetic fabric will cause complications if the magnetic fabric is samshypled on a scale that does not take this into account In particulate flow (Fig 15) the movement of grains may be poorly ordered Some grains move more than their neighbours rotate more or even exchange neighbours despite the fact that on a suitably large polygranular scale the strain may be approximately homogeneous Movement in polyshygranular units is also possible (Fig 16) as has been shown by experiments on analog materials (Means 1977) The scale on which magnetic susceptibility is defined will determine whether or not this preshysents a problem

The deformation mechanisms may be still more complicated The deformation may cause the rock

I bull

13

(01 (bl

Fig IS Particulate flow of a simulated (two-dimensional) aggregate Deformation proceeds from (a) through (c) The motions of particles is somewhat disordered whereas on a large scale the strain may appear to be approximately homogeneous as shown by the

strain ellipse defined by the black particles

J mm Fig 16 Experimentally produced particulate flow of groups of alum grains involving intergranular displacement surfaces

(From Means 1977)

et

deformation gt

bull00 bull

Fig 17 Possible deformation processes in metamorphic rocks that could be significant in the evolution of magnetic fabrics c -intergranular displacement surfaces (may be invisible) d-ductile (may be plastic) deformation of grains e-styloshylitie surfaces and grain-truncation f -penetration of grains g -microfaults (cleavage slip) h-rotation of blocks or groups of grains between faults or other discontinuities m-pressureshysolution material transfer (may be out of system) n-new

minerals crystallise

to be a discontinuum on various scales Lozenges of rock may rotate mass removal may occur loshycally or even to outside the system while grains plastically deform by intercrystalline processes and slide and roll past oneanother (Fig 16) At the same time new minerals may form with their crystallographic orientations controlled by the contemporary stress system Any of these factors could complicate the strain-response model of the rock and the development of its magnetic fabric While all of these processes are unlikely to occur at once the roles of several of these (or others not discussed) have to be assessed before the magnetic fabric can be correlated with the bulk strain Amongst these complications probably the most common one is the growth of new minerals as for example in phyllites schists and gneisses In these cases the explanation of schistosity may be bound up with the origin of the metamorphic texture more than with the strain of the rock (Fig 17) (Borradaile et at 1986)

Experimental studies

Although there has been some early interest in the effects of stress on magnetic susceptibility (eg Nagata 1966 1970 Kean et al 1976) this was associated with strains within the elastic limit Of interest here are the susceptibility changes that occur with large strains due to deformation that is macroscopically ductile if not actually plastic at the crystalline level The problem in the laboratory

bullbull bull bullbull bull bull

bullbull

14

environment is that even at the slowest strain rates that are practicable (10- 6 to 10-9 S-I) most rocks and minerals are not sufficiently ductile at room temperature to fail by the natural mechanisms of metamorphic rocks

Owens and Rutter (1978) first tackled this subshyject with a study of marbles and of calcite Alshythough the diamagnetic susceptibility of calcite is low the mineral is relatively easily deformed in a plastic manner at moderate confining pressures It is also stable at modest experimental temperatures so that Owens and Rutter were able to enhance the ductility by using temperatures up to 500 0 C in combination with pressures of 150 to 300 MPa (15 to 3 kbar) at strain-rates of approximately 10 - 4 to 10 - s s - 1 They achieved strains up to 50 axial-symmetrical (coaxial) shortening of the cylindrical specimens

The marbles they used had essentially isotropic magnetic and optical-crystallographic fabrics inishytially The magnetic anisotropy rapidly reached a plateau intensity at about 45 shortening The optical fabrics and the susceptibility fabric rapidly became axisymmetric to the shortening axis of the specimens This study didmiddot much to confirm the value of magnetic fabrics as indicators of strain and kinematics of deformation but most natural studies are based on ferrirnagnetic or parashymagnetic materials

Natural paramagnetic and ferrimagnetic matershyials are difficult to deform in a realistic manner without raising the temperature Heating will not normally be possible without inducing mineralogishycal changes that might mask susceptibility changes due to deformation Borradaile and Alford (1987) approached this problem by using a synthetic aggregate of sand enriched with magnetite that was cemented with commercial Portland cement The latter has a negligible (diamagnetic) susceptshyibility in comparison with the aggregate and pershymitted the aggregate to shorten by 35 in a ductile manner by axial symmetrical shortening The deshyformation did not involve cataclasis of the sand grains Rather the deformation was accommodshyated by the shearing of the cement gel This pershymitted a grain-shape alignment to develop by rollshying and sliding of the grains The magnetite grains were of the same grain-size as the matrix sand so

bulll1pl -04

bull 03

02 bull bull

01 bullbull01 02 03 04 In (XZ)

00 I I bull I I ~

11 12 13 14 15 (XI Z)

Fig 18 A correlation between the change in degree (fl) of susceptibility anisotropy and the strain ratio in some pure shear experiments on synthetic magnetite-bearing sandshy

stones (From Borradaile and Alford 1987)

that these experiments essentially addressed the problem of the rotational behaviour of the clasts (In most natural sandstones the iron oxide grains are much smaller than the sand clasts) The experiments were at carefully controlled strainshyrates of 5 x 10 - 6 S - 1 and confining pressures of 150 MPa (15 kbar) The maximum and intershymediate principal directions of susceptibility of these specimens rotated very rapidly towards the plane of flattening at rates exceeding the rate of rotation of a line undergoing homogeneous strain (cf the lineplane model) It was inferred that the magnetites rotated rigidly possibly with some plastic deformation The rotation was even more rapid when the matrix was composed of calcite instead of silicate mineral grains For initial susshyceptibility fabrics that were suitably oriented it was found that the change in the degree of anishysotropy was related to the strain by a power law (Fig 18) This serves to emphasise the importance of the initial magnetic fabric Relatively little can be deduced of the strain history from the final magnetic fabric alone Just as the initial ellipsoidal shape and orientation is of paramount importance in the strain analysis of ellipsoidal objects so is a knowledge of similar information for the initial magnetic fabric ellipsoid Although a power law relationship between the change in orientation of specially oriented magnetic fabrics exists in cershytain axial-symmetrical ( pure shear) experiments

15

In ( kmox kim J Calcite -cement - magnetite Q9g~gotes

at 150 MPo 05

04

XZHI XZmiddotH403 --

~ U-C3Z ~ AC -10 SHEAR ZOHEt ~ PURE SHEAR

02

t 01 XZ 20 XZ -115

In (kint kmln )

-0 02 03 04 -05 06 -07 os

bull Fig 19 The paths of incremental changes in magnetic anishysotropy are shown for the experimental deformation of syntheshysised calcite-cement-magnetite specimens The pure shear test produces little change in anisotropy even though the XZ strain ratio reaches 135 In contrast the changes produced in a shear zone (transpressive) are much greater despite the fact

that the ultimate XZ strain ratio for the zone is only 114

it is premature to make extrapolations to nature at the present state of knowledge

Recent work on experimental shear zones of synthetic materials at 150 MPa extends these conshyclusions to the case of transpressive deformation -a non-coaxial strain history (Borradaile and Alshyford in press) The susceptibility ellipsoids rotate rapidly toward stable orientations in which the minimum susceptibility is at a high angle to the shear zone boundaries The magnetic anisotropy changes very rapidly in the shear zones they produce a stronger magnetic fabric than axial symmetrical shortening at the same strain This is shown for two typical incremental- tests on the same synthetic calcite-matrix material at 150 Mpa in Fig 19 A further complication recognised in the experiments is that the magnetic fabrics may be planar (F gt L) whereas the mineral fabrics are constricted (a gt b) or plane strain (a = b) It is not known if these observations are transferable to natural shear zones

Conclusions

The interpretation of natural magnetic fabrics may be more complex than was initially recogshynised but progressive changes in magnetic anishysotropy do occur sympathetically with regional strain gradients despite accompanying regional

metamorphism (eg Hrouda and Janak 1976 Hrouda 1976 Coward and Whalley 1979) Indeed Rochette (1987) has shown that the metashymorphic production of pyrrhotite can enhance the susceptibility and produce a magnetically detectashyble isograd Also in certain rocks there are at least weak correlatiCfls between ratios of principal strains and the ratios of principal susceptibilities Numerous examples of the parallelism of principal susceptibility directions and structural directions (or even principal strain directions) support the contention that genetic relationships do exist beshytween strain and susceptibility in some cases Nevshyertheless these correlations are not universal and it is not possible to predict which natural situashytions will yield susceptibility data that _will faithshyfully represent principal strain directions or prinshycipal strain magnitudes or both For exampl~ magnetic fabrics do not always seem to be reliable kinematic indicators for shear zones and in the case of polyphase deformation later magnetic fabrics do not uniformly overprint earlier ones Magnetic fabrics should not be used for routine methods of strain analysis without further study A more profitable avenue is to determine how the susceptibility and strain tensors relate taking account of the actual strain-response model (deshyformation mechanisms) and the actual minerashylogical sources of susceptibility in that rock inshycluding phases produced by metamorphism A fruitful approach would be to consider the tensorial combination of coexisting magnetic subshyfabrics and successive episodes of magnetic fabric development along the lines initiated by Hrouda (1979)

Relationships between susceptibility and strain are in vogue However the earliest uses of magshynetic studies simply to investigate bulk petroshyfabrics are not yet been fully developed or inshytegrated with detailed petrofabric studies by optishycalor X-ray means Furthermore studies of remashynence and of susceptibility at different field strengths can yield information on magnetic subshyfabrics of different grain-sizes or different mineralogy This information is essential in the study of metamorphism of magnetic phases as well as their preferred orientation The anisotropy of remanence is also a profitable area of study

16 _

because only the ferrimagnetic traces contribute to that sub-fabric

Finally the nondestructive nature of magnetic fabric analysis provides a tool for investigating the progressive deformation or progressive metamorshyphism of a single specimen in laboratory experishyments Experiments on synthetii aggregates indishycate that the initial anisotropy of materials is not easily overprinted by small strains at low tempershyature They demonstrate also that the magnetic fabric ellipsoid spins very rapidly where the chief magnetic mineral is magnetite This is more noticeable when the matrix grains undergo crystal-plastic deformation Experimental shear zones produce greater changes in magnetic shape fabrics than axial-symmetrical shortening (pure shear) at the same strain they can also produce magnetic fabrics differing in symmetry from the grain fabric Such results develop an awareness for the greater complexities of natural structures

Acknowledgments

I wish to thank the Natural Sciences and Enshygineering Research Council of Canada for the continuing support of my work Frantisek Hrouda and Brian Bayly are thanked for constructive criticism of this article Karel Zapletal is thanked for some data on biotite Mel Friedman and Jan Tullis provided helpful reviews

Postscript

Since this paper was accepted for publication P Rochette has drawn attention to unusual inshyverse magnetic fabrics probably produced by single-domain magnetite (Thesis University of Grenoble 1988211 pp)

APPENDIX

Presentation of anisotropy of susceptibility

Magnetic susceptibility is a second rank tensor property conveniently envisaged as a magnitude ellipsoid (see Hrouda 1982 p 38) with three principal axes k max bull kim and k min or k ll bull kn k 33 The average or bulk susceptibility is comshy

monly defined as the arithmetic mean of the three principal values (Ellwood et al 1986-Symshyposium recommendations) but it is not clear why the arithmetic mean is a more appropriate represhysentation of bulk susceptibility than the geometric mean Susceptibility anisotropies for rocks are so low (Figs 9 and 10) that there is often little difference between these two expressions For exshyample seventeen specimens of strongly strained fine schist of the English Borrowdale Volcanic Series have principal susceptibilities in the ratio 104 102 0943 ~

Hrouda (1982) lists 25 different parameters that have been used at various times to represent anishysotropy The most useful are sometimes termed the magnetic lineation and the magnetic foliashytion

L = kmaxkint and F= kintkmin

Note that some authors chose alternative definishytions for Land F (eg Coward 1976) The parameters L and F are plotted vertically and horizontally respectively and compare directly with the ratios used to describe the strain ellipsoid on a Flinn-diagram

a=XY and b= YZ where X 2 Y ~ Z are the principal strains In some instances it is clearer if the natural logarithms of L F and of a and b are plotted

If the ratios of principal susceptibilities are listed individually it is helpful to normalise them so that their product is unity The normalised versions of the principal susceptibilities are related to their ratios by the following relations

kmax = L 2 3 bull pl3

kml

= L -13 F I 3

k = L -13 bull F- 23mm

It is advisable also to present a mean (bulk) susceptibility value This enables the reader to assess the significance of the results (Conference recommendations Ellwood et al 1986) Unforshytunately this has often not been done in the past Commonly one finds that anisotropies are poorly reproducible for rocks with susceptibility lt 10-4

SIjvol Providing cones of confidence about principal directions and standard errors for prinshycipal magnitudes is also useful in this regard

bull

30

2-5

20

-5

10 F=~ WI shy - middotmiddotV j Y

0 5 20 25 30 35

F =(klnkmin)

Fig AI The relationship between Jelineks (1981) P and T parameters and the conventional anisotropy parameters L and

F

The ratios L and F like their counterparts in strain (a and b) are very useful in describing the ellipsoids shape or sense of anisotropy However the distance of the point (L F) from the origin is also a measure of the degree of anisotropy that is to say its departure from sphericity Jelineks (1981) parameters pi and T overcome this T represents sense of anisotropy and ranges from -1 (prolate) to + 1 (oblate) pi (gt 1) expresses degree of anisotropy These are defined as

[ 2(In k -In k~]T= -1

In k itM - In k min 1

pi = exp [ 2( af + a ~ + a~ ) ] ~ where a1 = In(kmaxkb) etc and kb = (kmax k inl

kmin )(l3) The relationship of p and T to L and F is shown in Fig AI

References

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17

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19

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9

to have considered the combining effects of magshynetic fabrics of different ages He described early susceptibility fabrics by a tensor P superimposed tectonic fabrics by a tensor D and suggested that they combine to form a resultant susceptibility tensor R by

D P = R or D = R p- 1

Goldstein (1980) applied the same approach to mylonitic fabrics Some authors have simply asshysumed that it is permissible to use the orientations of magnetic fabrics within shear zones rather like a schistosity to determine the amount and sense of shear Similar studies have been carried out subsequently on shear zones up to a regional scale in extent (eg Rathore 1985) However in experishymental shear zones the author has found that earlier magnetic fabrics are difficult to overprint and magnetic fabric maybe an unreliable kineshymatic indicator

Magnitudes ofsusceptibility and magnitudes ofstrain

The relationship between the shape of the magshynitude ellipsoid of susceptibility and the intensity of the tectonic fabric is more complex than the relationship between directions as discussed in the previous section Usually comparisons have been attempted between the shapes of the susceptshyibility and finite strain ellipsoids The latter is usually derived from some macroscopic straiI) marker such as pebbles concretions lappilli or rotated sand-dikes (eg Rathore 1979 Borradaile and Tarling 19811984 Rathore and Henry 1982 Clendenen et at 1988 Hirt et al 1988) Reducshytion spots have been used as strain markers from time to time however their pre-metamorphic origin is not always certain and in the Welsh examples some outcrops have susceptibilities that are too low to give reproducible magnetic fabrics

The susceptibility ellipsoid normally plots much nearer the origin of the Flinn-diagram than does the strain ellipsoid (Fig 9) In some cases logashyrithmic plots (Fig 10) help in their discrimination The relationships between strain and magnetic fabric are not straightforward The most strained samples in an outcrop do not necessarily have the most extreme magnetic anisotropies This is shown

a or L

20-1 AI IfIOOltfrc ItJtedtlDoloty 0IItN11tOy

JWUiOl2L1LL bull for QIdfl c~1 f~~

O for fktlPOf lCIStl ( ~ I

15

ol~~ ~bOrF 10 15 20 B

Fig 9 Strain ellipsoid data determined by de-straining analyshysis for quartz clasts and for feldspar clasts and the susceptibilshy

ity anisotropy in meta-sandstones a XY b - YZ where X lt Y lt Z L and F are the equivalent ratios for the magnetic susceptibility There is a single schistose tectonic fabric Data for the same hand-specimens are connected by tie-lines There is no simple relationship between the magnitude of strain and

intensity of magnetic fabric (Borradaile and Tarling 1984)

by the crossing tie-lines in Fig 9 Moreover there is always some question as to the validity of the comparison since the strain is commonly heterogeshyneous on the scale of a thin section whereas the homogeneously strained markers are much larger Susceptibility is usually measured from a sample about 10 cm3

so that the susceptibility tensor will be defined on a smaller scale than the strain tensor Another approach although less common in the literature is to compare the susceptibility

t log a (log l)

~ ~

~ +~ iii~iffl ~

0 lr b ~ C-_~~

0 ~J 04 ~tgt~J-~

~~~I ~~Q

0middot1

az

~ llZ I

o CH 02 0middot4 0middot6 08 1middot0 IZ

- log b (log F)

bull ST~AIN EItIPSOIO SHAPE SUSCEPTISILITY ELUPSOID SHAPE

Fig 10 Strain ellipsoid data and susceptibility data for four outcrops of slate (l to IV) with a single tectonic fabric connected by tie-lines and presented on a logarithmic Flinn-dishy

agram (From Borradaile and Tarling 1981)

bull bull bull bull

10

003

Mj maximum (i -I) values

006 I intermediate I

( i bull 2 l values 1 ~~---------~~------

- 003 -lmiddotmiddot - 006

bull bull III(L -middot00

II I

minimum (imiddot 3) values

I NmiddotI 000

Fig 11 Nonnalised measures of principal susceptibility magnishytudes (M) and o( principal strain magnitudes (Ni ) (or specishymens o( a metavolcanic rock with a single tectonic fabric There is no correlation between minimum values of susceptibilshyity and strain nor between intennediate values etc Nevertheshyless it would be possible to infer a correlation incorrectly by considering all the data laquo(or maximum intermediate and minimum susceptibilities) simultaneously (From Borradaile

and Mothersill 1984)

fabric with the petrofabric of a slightly smaller sample detennined by means of X-ray texture goniometry (eg Wood et al 1976 Hrouda et al 1985b) This overcomes the criticism that different scales will be sampled but there is the added complication of interpreting the texture goniomeshyter data in terms of finite strain (Oertel 1983)

One of the earliest attempts to relate the strain and susceptibility tensors was by Kneen (1976) She plotted ratios of principal strains against ratios of principal susceptibilities and inferred correlashytions Similar studies that compared strain ratios with susceptibility anisotropy used special loga-

M 02

rithmic parameters to normalise values (Wood et al 1976 Rathore 1979 1980 Rathore and Henry 1982 Kligfield et al 1982) These are termed IV (for strain) and M (for susceptibility) where i = 1 2 or 3 for the appropriate principal value The actual algebraic definition of N and M varies in the literature and care should be taken in comparshying data from one paper to another) Unforshytunately in most of these cases the authors plotted the data for all three principal directions on the same axes and generally established correlation coefficients for the maximum intermediate and minimum values simultaneously Strictly speaking this is invalid (Fig 11) and in one instance the correlation of anisotropies attempted in this manner has been disproved (Borradaile and Mothersill 1984)

This may give a discouraging view of the correshylations of strain and susceptibility but the data already published do give some indication that correlations may exist although weaker than origishynally claimed For example comparing data for just minimum (normalised) strains and minimum (normalised) susceptibilities it is possible to reshycognise modest correlations between susceptibility and strain in the case of the Welsh slates (eg Wood et al 1976) here in Fig 12 Clendenen et al (1988) have recently recognised that this kind of weaker correlation between the strain of conshycretions and susceptibility can be statistically sigshynificant

Thus although weak correlations of the kind

klk2 =(XY) may exist these must only be of local siginificance

I I I bullbullbullbullbullbullbull bull

I ttl bullbull~

ol------------r ------ shy bull V

~- fmiddot I maximum (i1) and -0middot2 r I intermediate (middot 2 ) values

minimum values (i 3) I

~~~____~____~I~____~ Nj -~ -~ 0 ~

Fig 12 Nonnalised measures of principal susceptibilities (M) and of principal strains (Ni ) for slates with a single tectonic fabric Note that a weak correlation exists between minimum strains and minimum susceptibilities (From Wood et al 1976)

11

Q Z p Marchian rofafion

S ~ b

t1- y p 0- Zr +y~

k X L oL

X SI bull bull S

Fig 13 a Theoretical outline of the March model as applied to the rotation and preferred orientation of phyUosilicate grains For strain axes X ~ Y ~ Z the rotation of a pole p of a platelet is shown schematically as is the rotation of the long axis of a rod-like element Such elements are considered to be dispersed and perfectly rigid b Schematic cross-section of a typical natural preferred orientation of phyllosilicate grains defining a schistosity Sl Grains with less favoured orientations are truncated and their volumetric contribution to the magnetic fabric may be reduced Usually the pattern of

preferred orientation can only be explained by the March model to a limited degree

and it seems unduly optimistic to consider them as universal relationships that may be extrapolated from one region to another Within a single reshygion with a limited range of deformation mechashynisms and lithological uniformity it might be posshysible to extrapolate some correlations of magnetic fabric with strain

The approaches reviewed so far in this section are essentially empirical and in most cases the susceptibility was attributed to disseminated magshynetite The studies of Coward and Whalley (1979) and of Henry and Daly (1983) were exceptions they recognised multiple sources of susceptibility and Kligfield et al (1982) also investigated the sources thoroughly The latter authors demonshystrated susceptibility anisotropy was due to iron oxides whose distributions and orientations were controlled mimetically by their position on the surfaces of the oolites used as strain markers The other studies mentioned adopt the premise or imply that magnetite grains were distributed throughout the rocks and were tectonically aligned to produce a magnetite shape-fabric which in turn dictated the magnetic fabric The underlying mechanistic model that appears to have influenced this train of thought is attributed to March (1932) This model (eg Wood et al 1976) outlines the situation in which platy elements that do not impinge upon oneanother and that are preferably randomly oriented in their initial configuration

become systematically re-oriented by homogeshyneous strain and are not impeded by the matrix (Fig 13a) Consequently the orientation-distribushytion of the poles to these platelets after constantshyvolume strain is directly related to the strain Thus for a given direction i the strain e is related to the normalised density (d) of platelet poles by

emiddot = d(-1j3 - 1 I bull

In the structural geology literature some considershyation has been given to the aspect ratios of the platelets as well as accompanying volume changes of tqe aggregate (Tullis 1976 Tullis and Wood 1975) However these modifications still fall short of reality The March model is difficult to adapt to three-dimensional grains and even more difficult to reconcile with the premises of passive beshyhaviour and non-impingement of the rotating grains on each other A worse shortcoming is the inherent assumption that the grains are spatially separated whereas in a typical metamorphic rock the variation in orientation imposes restrictions on the degree to which differently oriented crystals grow (Fig 13b) Nevertheless it has found applishycations in magnetic studies (eg Cogne and Gapais 1986) and studies of comparable mathematical models (Hrouda 1980) and is frequently cited in petrofabric studies (Oertel 1983)

Hrouda (1987) has extended these arguments to situations in which it is known that paramagnetic

12

sheet silicates such as chlorite and biotite0

dominate the anisotropy of susceptibility An inshyteresting development of this study is that in slates of the Carpathians in which the anisotropy is due to paramagnetic phyllosilicates the degree of anishysotropy is proportional to the bulk or mean susshyceptibility This has also been reported in Archean slates (Borradaile et aI in press)

Strain response models and multiple sources of susshy

ceptibility

Owens (1974) first drew attention to two imshyportant items that must be taken into account in any interpretation of susceptibility anisotropy in terms of strain Firstly the mineralogical source of the susceptibility should be defined If there are multiple sources of susceptibility the direct applishycation of the simple March model or any other model assuming a penetrative homogeneous magshynetic response is invalid Rochette and Vialon (1984) and Henry (1983) enforced this argument in different ways Slight variations in the proporshytions of minerals with different magnetic anishysotropies may under certain circumstances proshyduce changes in the bulk anisotropy that override any changes in anisotropy due to strain (Borshyradaile 1987b)

The second major point raised by Owens was that the actual strain response model has a major influence on the way in which the anisotropy accumulates from the pre-strain situation For simplicity he considered three models The first was a lineplane model that we can compare to the March model already referred to above (Fig 13a) The second was the viscous or Jeffery model in which the magnetic grain is likened to a rigid ellipsoid undergoing strain-induced motion in a viscous medium The third passive model likens the magnetic grains to passive strain markers Structural geologists may compare this to the model proposed by Ramsays school of structshyural geology to approximate the shape and conseshyquent orientation changes of for example a tectonically deforming passive ellipsoidal marker by the Rrcp equations see Fig 14 (Borradaile 1987a) Care should be taken with the term passhysive some geophysicists use the term to refer to

$e85 ~_068 fRo= 15 ~t=135

C)-shystrain ellipse (j) ~5middot Rs= 20 0_01409lt

Ro= 15 iff=15

original possive passive markers markers after strain

Fig 14 The R rlt1gt model Particles with the original orientashy J

tions (8) shown as a result of strain indicated by the strain ellipse take up new orientations (lt1raquo At the same time the ratios of the original shapes (R1f) change to final shapes (Ry2) The shape-ratio of the strain ellipse is 2 1 as indicated

the lineplane or March model and where they do not appear to imply any similarity to the Rrcp model (eg Cogne and Gapais 1986)

The mechanical response is usually neglected in the correlation of strains and susceptibility anishysotropies Indeed it is likely that many rocks and many types of deformation mechanisms are unsuishytable for establishing a correlation using the preshymises of simple mathematical models involving a single mode of deformation For example if there are relict components of sedimentary magnetic fabrics mixed with the tectonic fabrics or magshynetic fabrics of different tectonic ages a model assuming homogeneity will fail Similarly deforshymation structures that produce domainal fabrics that differently influence the magnetic fabric will cause complications if the magnetic fabric is samshypled on a scale that does not take this into account In particulate flow (Fig 15) the movement of grains may be poorly ordered Some grains move more than their neighbours rotate more or even exchange neighbours despite the fact that on a suitably large polygranular scale the strain may be approximately homogeneous Movement in polyshygranular units is also possible (Fig 16) as has been shown by experiments on analog materials (Means 1977) The scale on which magnetic susceptibility is defined will determine whether or not this preshysents a problem

The deformation mechanisms may be still more complicated The deformation may cause the rock

I bull

13

(01 (bl

Fig IS Particulate flow of a simulated (two-dimensional) aggregate Deformation proceeds from (a) through (c) The motions of particles is somewhat disordered whereas on a large scale the strain may appear to be approximately homogeneous as shown by the

strain ellipse defined by the black particles

J mm Fig 16 Experimentally produced particulate flow of groups of alum grains involving intergranular displacement surfaces

(From Means 1977)

et

deformation gt

bull00 bull

Fig 17 Possible deformation processes in metamorphic rocks that could be significant in the evolution of magnetic fabrics c -intergranular displacement surfaces (may be invisible) d-ductile (may be plastic) deformation of grains e-styloshylitie surfaces and grain-truncation f -penetration of grains g -microfaults (cleavage slip) h-rotation of blocks or groups of grains between faults or other discontinuities m-pressureshysolution material transfer (may be out of system) n-new

minerals crystallise

to be a discontinuum on various scales Lozenges of rock may rotate mass removal may occur loshycally or even to outside the system while grains plastically deform by intercrystalline processes and slide and roll past oneanother (Fig 16) At the same time new minerals may form with their crystallographic orientations controlled by the contemporary stress system Any of these factors could complicate the strain-response model of the rock and the development of its magnetic fabric While all of these processes are unlikely to occur at once the roles of several of these (or others not discussed) have to be assessed before the magnetic fabric can be correlated with the bulk strain Amongst these complications probably the most common one is the growth of new minerals as for example in phyllites schists and gneisses In these cases the explanation of schistosity may be bound up with the origin of the metamorphic texture more than with the strain of the rock (Fig 17) (Borradaile et at 1986)

Experimental studies

Although there has been some early interest in the effects of stress on magnetic susceptibility (eg Nagata 1966 1970 Kean et al 1976) this was associated with strains within the elastic limit Of interest here are the susceptibility changes that occur with large strains due to deformation that is macroscopically ductile if not actually plastic at the crystalline level The problem in the laboratory

bullbull bull bullbull bull bull

bullbull

14

environment is that even at the slowest strain rates that are practicable (10- 6 to 10-9 S-I) most rocks and minerals are not sufficiently ductile at room temperature to fail by the natural mechanisms of metamorphic rocks

Owens and Rutter (1978) first tackled this subshyject with a study of marbles and of calcite Alshythough the diamagnetic susceptibility of calcite is low the mineral is relatively easily deformed in a plastic manner at moderate confining pressures It is also stable at modest experimental temperatures so that Owens and Rutter were able to enhance the ductility by using temperatures up to 500 0 C in combination with pressures of 150 to 300 MPa (15 to 3 kbar) at strain-rates of approximately 10 - 4 to 10 - s s - 1 They achieved strains up to 50 axial-symmetrical (coaxial) shortening of the cylindrical specimens

The marbles they used had essentially isotropic magnetic and optical-crystallographic fabrics inishytially The magnetic anisotropy rapidly reached a plateau intensity at about 45 shortening The optical fabrics and the susceptibility fabric rapidly became axisymmetric to the shortening axis of the specimens This study didmiddot much to confirm the value of magnetic fabrics as indicators of strain and kinematics of deformation but most natural studies are based on ferrirnagnetic or parashymagnetic materials

Natural paramagnetic and ferrimagnetic matershyials are difficult to deform in a realistic manner without raising the temperature Heating will not normally be possible without inducing mineralogishycal changes that might mask susceptibility changes due to deformation Borradaile and Alford (1987) approached this problem by using a synthetic aggregate of sand enriched with magnetite that was cemented with commercial Portland cement The latter has a negligible (diamagnetic) susceptshyibility in comparison with the aggregate and pershymitted the aggregate to shorten by 35 in a ductile manner by axial symmetrical shortening The deshyformation did not involve cataclasis of the sand grains Rather the deformation was accommodshyated by the shearing of the cement gel This pershymitted a grain-shape alignment to develop by rollshying and sliding of the grains The magnetite grains were of the same grain-size as the matrix sand so

bulll1pl -04

bull 03

02 bull bull

01 bullbull01 02 03 04 In (XZ)

00 I I bull I I ~

11 12 13 14 15 (XI Z)

Fig 18 A correlation between the change in degree (fl) of susceptibility anisotropy and the strain ratio in some pure shear experiments on synthetic magnetite-bearing sandshy

stones (From Borradaile and Alford 1987)

that these experiments essentially addressed the problem of the rotational behaviour of the clasts (In most natural sandstones the iron oxide grains are much smaller than the sand clasts) The experiments were at carefully controlled strainshyrates of 5 x 10 - 6 S - 1 and confining pressures of 150 MPa (15 kbar) The maximum and intershymediate principal directions of susceptibility of these specimens rotated very rapidly towards the plane of flattening at rates exceeding the rate of rotation of a line undergoing homogeneous strain (cf the lineplane model) It was inferred that the magnetites rotated rigidly possibly with some plastic deformation The rotation was even more rapid when the matrix was composed of calcite instead of silicate mineral grains For initial susshyceptibility fabrics that were suitably oriented it was found that the change in the degree of anishysotropy was related to the strain by a power law (Fig 18) This serves to emphasise the importance of the initial magnetic fabric Relatively little can be deduced of the strain history from the final magnetic fabric alone Just as the initial ellipsoidal shape and orientation is of paramount importance in the strain analysis of ellipsoidal objects so is a knowledge of similar information for the initial magnetic fabric ellipsoid Although a power law relationship between the change in orientation of specially oriented magnetic fabrics exists in cershytain axial-symmetrical ( pure shear) experiments

15

In ( kmox kim J Calcite -cement - magnetite Q9g~gotes

at 150 MPo 05

04

XZHI XZmiddotH403 --

~ U-C3Z ~ AC -10 SHEAR ZOHEt ~ PURE SHEAR

02

t 01 XZ 20 XZ -115

In (kint kmln )

-0 02 03 04 -05 06 -07 os

bull Fig 19 The paths of incremental changes in magnetic anishysotropy are shown for the experimental deformation of syntheshysised calcite-cement-magnetite specimens The pure shear test produces little change in anisotropy even though the XZ strain ratio reaches 135 In contrast the changes produced in a shear zone (transpressive) are much greater despite the fact

that the ultimate XZ strain ratio for the zone is only 114

it is premature to make extrapolations to nature at the present state of knowledge

Recent work on experimental shear zones of synthetic materials at 150 MPa extends these conshyclusions to the case of transpressive deformation -a non-coaxial strain history (Borradaile and Alshyford in press) The susceptibility ellipsoids rotate rapidly toward stable orientations in which the minimum susceptibility is at a high angle to the shear zone boundaries The magnetic anisotropy changes very rapidly in the shear zones they produce a stronger magnetic fabric than axial symmetrical shortening at the same strain This is shown for two typical incremental- tests on the same synthetic calcite-matrix material at 150 Mpa in Fig 19 A further complication recognised in the experiments is that the magnetic fabrics may be planar (F gt L) whereas the mineral fabrics are constricted (a gt b) or plane strain (a = b) It is not known if these observations are transferable to natural shear zones

Conclusions

The interpretation of natural magnetic fabrics may be more complex than was initially recogshynised but progressive changes in magnetic anishysotropy do occur sympathetically with regional strain gradients despite accompanying regional

metamorphism (eg Hrouda and Janak 1976 Hrouda 1976 Coward and Whalley 1979) Indeed Rochette (1987) has shown that the metashymorphic production of pyrrhotite can enhance the susceptibility and produce a magnetically detectashyble isograd Also in certain rocks there are at least weak correlatiCfls between ratios of principal strains and the ratios of principal susceptibilities Numerous examples of the parallelism of principal susceptibility directions and structural directions (or even principal strain directions) support the contention that genetic relationships do exist beshytween strain and susceptibility in some cases Nevshyertheless these correlations are not universal and it is not possible to predict which natural situashytions will yield susceptibility data that _will faithshyfully represent principal strain directions or prinshycipal strain magnitudes or both For exampl~ magnetic fabrics do not always seem to be reliable kinematic indicators for shear zones and in the case of polyphase deformation later magnetic fabrics do not uniformly overprint earlier ones Magnetic fabrics should not be used for routine methods of strain analysis without further study A more profitable avenue is to determine how the susceptibility and strain tensors relate taking account of the actual strain-response model (deshyformation mechanisms) and the actual minerashylogical sources of susceptibility in that rock inshycluding phases produced by metamorphism A fruitful approach would be to consider the tensorial combination of coexisting magnetic subshyfabrics and successive episodes of magnetic fabric development along the lines initiated by Hrouda (1979)

Relationships between susceptibility and strain are in vogue However the earliest uses of magshynetic studies simply to investigate bulk petroshyfabrics are not yet been fully developed or inshytegrated with detailed petrofabric studies by optishycalor X-ray means Furthermore studies of remashynence and of susceptibility at different field strengths can yield information on magnetic subshyfabrics of different grain-sizes or different mineralogy This information is essential in the study of metamorphism of magnetic phases as well as their preferred orientation The anisotropy of remanence is also a profitable area of study

16 _

because only the ferrimagnetic traces contribute to that sub-fabric

Finally the nondestructive nature of magnetic fabric analysis provides a tool for investigating the progressive deformation or progressive metamorshyphism of a single specimen in laboratory experishyments Experiments on synthetii aggregates indishycate that the initial anisotropy of materials is not easily overprinted by small strains at low tempershyature They demonstrate also that the magnetic fabric ellipsoid spins very rapidly where the chief magnetic mineral is magnetite This is more noticeable when the matrix grains undergo crystal-plastic deformation Experimental shear zones produce greater changes in magnetic shape fabrics than axial-symmetrical shortening (pure shear) at the same strain they can also produce magnetic fabrics differing in symmetry from the grain fabric Such results develop an awareness for the greater complexities of natural structures

Acknowledgments

I wish to thank the Natural Sciences and Enshygineering Research Council of Canada for the continuing support of my work Frantisek Hrouda and Brian Bayly are thanked for constructive criticism of this article Karel Zapletal is thanked for some data on biotite Mel Friedman and Jan Tullis provided helpful reviews

Postscript

Since this paper was accepted for publication P Rochette has drawn attention to unusual inshyverse magnetic fabrics probably produced by single-domain magnetite (Thesis University of Grenoble 1988211 pp)

APPENDIX

Presentation of anisotropy of susceptibility

Magnetic susceptibility is a second rank tensor property conveniently envisaged as a magnitude ellipsoid (see Hrouda 1982 p 38) with three principal axes k max bull kim and k min or k ll bull kn k 33 The average or bulk susceptibility is comshy

monly defined as the arithmetic mean of the three principal values (Ellwood et al 1986-Symshyposium recommendations) but it is not clear why the arithmetic mean is a more appropriate represhysentation of bulk susceptibility than the geometric mean Susceptibility anisotropies for rocks are so low (Figs 9 and 10) that there is often little difference between these two expressions For exshyample seventeen specimens of strongly strained fine schist of the English Borrowdale Volcanic Series have principal susceptibilities in the ratio 104 102 0943 ~

Hrouda (1982) lists 25 different parameters that have been used at various times to represent anishysotropy The most useful are sometimes termed the magnetic lineation and the magnetic foliashytion

L = kmaxkint and F= kintkmin

Note that some authors chose alternative definishytions for Land F (eg Coward 1976) The parameters L and F are plotted vertically and horizontally respectively and compare directly with the ratios used to describe the strain ellipsoid on a Flinn-diagram

a=XY and b= YZ where X 2 Y ~ Z are the principal strains In some instances it is clearer if the natural logarithms of L F and of a and b are plotted

If the ratios of principal susceptibilities are listed individually it is helpful to normalise them so that their product is unity The normalised versions of the principal susceptibilities are related to their ratios by the following relations

kmax = L 2 3 bull pl3

kml

= L -13 F I 3

k = L -13 bull F- 23mm

It is advisable also to present a mean (bulk) susceptibility value This enables the reader to assess the significance of the results (Conference recommendations Ellwood et al 1986) Unforshytunately this has often not been done in the past Commonly one finds that anisotropies are poorly reproducible for rocks with susceptibility lt 10-4

SIjvol Providing cones of confidence about principal directions and standard errors for prinshycipal magnitudes is also useful in this regard

bull

30

2-5

20

-5

10 F=~ WI shy - middotmiddotV j Y

0 5 20 25 30 35

F =(klnkmin)

Fig AI The relationship between Jelineks (1981) P and T parameters and the conventional anisotropy parameters L and

F

The ratios L and F like their counterparts in strain (a and b) are very useful in describing the ellipsoids shape or sense of anisotropy However the distance of the point (L F) from the origin is also a measure of the degree of anisotropy that is to say its departure from sphericity Jelineks (1981) parameters pi and T overcome this T represents sense of anisotropy and ranges from -1 (prolate) to + 1 (oblate) pi (gt 1) expresses degree of anisotropy These are defined as

[ 2(In k -In k~]T= -1

In k itM - In k min 1

pi = exp [ 2( af + a ~ + a~ ) ] ~ where a1 = In(kmaxkb) etc and kb = (kmax k inl

kmin )(l3) The relationship of p and T to L and F is shown in Fig AI

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17

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19

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der Korngestait bei afrmer Deformation Z Kristallogrmiddot 81 285-297

Means WD 1977 A deformation experiment in transmitted light Earth Planet Sci Lett 35 169-179

Nagata T 1966 Magnetic susceptibility of compressed rocks J Goomag Geoelectr 18 73-80

Nagata T 1970 Anisotropic magnetic susceptibility of rocks under mechanical stresses Pure App Goophys 78

110-122 Nye JF 1957 The Physical Properties of Crystals Clarendon

Press Oxford 322 pp Oertel G 1983 The relationship of strain and preferred

orientation of phyllosilicale grains in rocks-a review Tectonophysics 100 413-447

Owens WH 1974 Mathematical model studies on factors affecting the magnetic anisotropy of deformed rocks Tectonophysics 24 115-131

Owens WH and Bamford D 1976 Magnetic seismic and other anisotropic properties of rock fabrics Philos Trans R Soc London Ser A 283 55-68

Owens WH and Rutter EH 1978 The development of magnetic susceptibility anisotropy through crystallographic preferred orientation in a calcite rock Phys Earth Planet Inter 16 215-222

Park JKmiddot1983 Paleomagnetism for geologists Geosci Can 4 180-188

Rathore JS 1979 Magnetic susceptibility anisotropy in the Cambrian Slate Belt of North Wales and correlation with strain Tectonophysics 53 83-97

Rathore JS 1985 Some magnetic characteristics of sheared zones J Geodyn 2 291-301

Rathore JS and Henry B 1982 Comparison of strained magnetic fabrics in Dalradian rocks from the southwest Highlands of Scotland J Struc Geol 4 373-384

Rees AI 1965 The use of anisotropy of magnetic susceptshyibility in the estimation of sedimentary fabric Sedimentolshyogy 4 257-271

Rees AI 1968 The production of preferred orientation in a concentrated dispersion of elongated and flattened grains J Geol 76 457-465

Rochetle P 1987 Metamorphic control of the mineralogy of black shales in the Swiss Alps toward the use of magnetic isograds Eanh Planet Sci Lett 84 446-456

Rochette P 1988 Relation entre deformation et metamorshy

f

bull

phisme Alpin dans les schistes noirs Helvetiques Iapport de la fabrique magnetique Geodin Acta 2 (in press)

Rochette P and Vialon P 1984 Development of planar and linear fabrics in Dauphinois shales and slates (French Alps) studied by magnetic anisotropy and its mineralogical conshytrol J Struct Geo 6 33-38

Schwarz E 1974 Magnetic fabrics in massive sulfide deposits Can J Earth Sci 11 1669-1675

Schwartz EJ 1975 Magnetic properties of pyrrhotite and their use in applied geology and geophysics Geo Surv Can Pap 74-59 24 pp

Singh J (now Rathore J) Sanderson DJ and Tariing DH 1975 The magnetic susceptibility anisotropy of deformed rocks from North Cornwall England Tectonophysics 27 141-153

Smith GM and Banetjee SK bull 1987 The dependence of weak field susceptibility on applied magnetic field Phys Earth Planet Inter 46 71-76

Stott GM and Schwerdtner WM 1981 A structural analyshysis of the central part of the Shebandowan metavolcanicshymetasedimentary belt Ontario Dep Mines Toronto Final Repbull Onto Geosci Res Rep No 5349 44 pp

Strangway DW 1970 History of the Earths Magnetic Field McGraw-Hili New York NY 168 pp

Tarling DH 1983 Paleomagnetism Chapman and Hall London 379 pp

Tullis TEbull 1976 Experiments on the origin of slaty cleavage and schistosity Geo Soc Am Bull 87 745-753

Tullis TE and Wood DS 1975 Correlation of finite strain from both reduction bodies and preferred orientation of mica in slate from Wales Geol Soc Am Bull 86 632-638

Urrutia-Fucugauchi J and Odabachian Y 1982 A Bibiograshyphy of Magnetic Susceptibility Anisotropy of Rocks Inshystituto de Geofisica Universidad Nacional Autonoma de Mexico Mexico 42 pp

Uyeda S Fuller MD Belshe JC and Girdler RW 1963 Anisotropy of magnetic susceptibility of rocks and minershyals J Geophys Res 68 279-291

Van den Ende C 1975 On the origin of anisotropy of magshynetic susceptibility in Permian Redbeds from the western part of the Dome de Barrot (S France) In GJ Borradaile et al (Editors) Progress in Geodynamics North-Holland Pub Co Amsterdam pp 176-189

Voight W and Kinoshita S 1907 Bestimmung absoluler Wene von Magnelisierungszahlen insbesondere fUr Krisshytalle Ann Phys 24 492-514

Wagner JJ Hedley FG Steen D Tinkler C and Vaugnat M 1981 Magnetic anisotropy and fabric of some progresshysively deformed ophiolitic gabbros J Geophys Res 86 307-315

Weast RC and Astle MJ (Editors) 1978 CRC handbook of Chemistry and Physics 59th edn CRC Press Palm Beach Fla

20

II

Wing-Fatt L and Stacey FD 1966 Magnetic anisotropy of laboratory materials in which magma flow is simulated Pure AppJ Geophys 6478-80

Wood DS Oertel G Singh J and Bennett HF 1976 Strain and anisotropy in rocks Philos Trans R Soc London Ser A 283 27-42

Zavoyskiy VN 1982 Use of magnetic susceptibility tensor for solving problems in structural geology Izv Akad Nauk SSSR Earth Phys Ser 18 217-223

bull bull bull bull

10

003

Mj maximum (i -I) values

006 I intermediate I

( i bull 2 l values 1 ~~---------~~------

- 003 -lmiddotmiddot - 006

bull bull III(L -middot00

II I

minimum (imiddot 3) values

I NmiddotI 000

Fig 11 Nonnalised measures of principal susceptibility magnishytudes (M) and o( principal strain magnitudes (Ni ) (or specishymens o( a metavolcanic rock with a single tectonic fabric There is no correlation between minimum values of susceptibilshyity and strain nor between intennediate values etc Nevertheshyless it would be possible to infer a correlation incorrectly by considering all the data laquo(or maximum intermediate and minimum susceptibilities) simultaneously (From Borradaile

and Mothersill 1984)

fabric with the petrofabric of a slightly smaller sample detennined by means of X-ray texture goniometry (eg Wood et al 1976 Hrouda et al 1985b) This overcomes the criticism that different scales will be sampled but there is the added complication of interpreting the texture goniomeshyter data in terms of finite strain (Oertel 1983)

One of the earliest attempts to relate the strain and susceptibility tensors was by Kneen (1976) She plotted ratios of principal strains against ratios of principal susceptibilities and inferred correlashytions Similar studies that compared strain ratios with susceptibility anisotropy used special loga-

M 02

rithmic parameters to normalise values (Wood et al 1976 Rathore 1979 1980 Rathore and Henry 1982 Kligfield et al 1982) These are termed IV (for strain) and M (for susceptibility) where i = 1 2 or 3 for the appropriate principal value The actual algebraic definition of N and M varies in the literature and care should be taken in comparshying data from one paper to another) Unforshytunately in most of these cases the authors plotted the data for all three principal directions on the same axes and generally established correlation coefficients for the maximum intermediate and minimum values simultaneously Strictly speaking this is invalid (Fig 11) and in one instance the correlation of anisotropies attempted in this manner has been disproved (Borradaile and Mothersill 1984)

This may give a discouraging view of the correshylations of strain and susceptibility but the data already published do give some indication that correlations may exist although weaker than origishynally claimed For example comparing data for just minimum (normalised) strains and minimum (normalised) susceptibilities it is possible to reshycognise modest correlations between susceptibility and strain in the case of the Welsh slates (eg Wood et al 1976) here in Fig 12 Clendenen et al (1988) have recently recognised that this kind of weaker correlation between the strain of conshycretions and susceptibility can be statistically sigshynificant

Thus although weak correlations of the kind

klk2 =(XY) may exist these must only be of local siginificance

I I I bullbullbullbullbullbullbull bull

I ttl bullbull~

ol------------r ------ shy bull V

~- fmiddot I maximum (i1) and -0middot2 r I intermediate (middot 2 ) values

minimum values (i 3) I

~~~____~____~I~____~ Nj -~ -~ 0 ~

Fig 12 Nonnalised measures of principal susceptibilities (M) and of principal strains (Ni ) for slates with a single tectonic fabric Note that a weak correlation exists between minimum strains and minimum susceptibilities (From Wood et al 1976)

11

Q Z p Marchian rofafion

S ~ b

t1- y p 0- Zr +y~

k X L oL

X SI bull bull S

Fig 13 a Theoretical outline of the March model as applied to the rotation and preferred orientation of phyUosilicate grains For strain axes X ~ Y ~ Z the rotation of a pole p of a platelet is shown schematically as is the rotation of the long axis of a rod-like element Such elements are considered to be dispersed and perfectly rigid b Schematic cross-section of a typical natural preferred orientation of phyllosilicate grains defining a schistosity Sl Grains with less favoured orientations are truncated and their volumetric contribution to the magnetic fabric may be reduced Usually the pattern of

preferred orientation can only be explained by the March model to a limited degree

and it seems unduly optimistic to consider them as universal relationships that may be extrapolated from one region to another Within a single reshygion with a limited range of deformation mechashynisms and lithological uniformity it might be posshysible to extrapolate some correlations of magnetic fabric with strain

The approaches reviewed so far in this section are essentially empirical and in most cases the susceptibility was attributed to disseminated magshynetite The studies of Coward and Whalley (1979) and of Henry and Daly (1983) were exceptions they recognised multiple sources of susceptibility and Kligfield et al (1982) also investigated the sources thoroughly The latter authors demonshystrated susceptibility anisotropy was due to iron oxides whose distributions and orientations were controlled mimetically by their position on the surfaces of the oolites used as strain markers The other studies mentioned adopt the premise or imply that magnetite grains were distributed throughout the rocks and were tectonically aligned to produce a magnetite shape-fabric which in turn dictated the magnetic fabric The underlying mechanistic model that appears to have influenced this train of thought is attributed to March (1932) This model (eg Wood et al 1976) outlines the situation in which platy elements that do not impinge upon oneanother and that are preferably randomly oriented in their initial configuration

become systematically re-oriented by homogeshyneous strain and are not impeded by the matrix (Fig 13a) Consequently the orientation-distribushytion of the poles to these platelets after constantshyvolume strain is directly related to the strain Thus for a given direction i the strain e is related to the normalised density (d) of platelet poles by

emiddot = d(-1j3 - 1 I bull

In the structural geology literature some considershyation has been given to the aspect ratios of the platelets as well as accompanying volume changes of tqe aggregate (Tullis 1976 Tullis and Wood 1975) However these modifications still fall short of reality The March model is difficult to adapt to three-dimensional grains and even more difficult to reconcile with the premises of passive beshyhaviour and non-impingement of the rotating grains on each other A worse shortcoming is the inherent assumption that the grains are spatially separated whereas in a typical metamorphic rock the variation in orientation imposes restrictions on the degree to which differently oriented crystals grow (Fig 13b) Nevertheless it has found applishycations in magnetic studies (eg Cogne and Gapais 1986) and studies of comparable mathematical models (Hrouda 1980) and is frequently cited in petrofabric studies (Oertel 1983)

Hrouda (1987) has extended these arguments to situations in which it is known that paramagnetic

12

sheet silicates such as chlorite and biotite0

dominate the anisotropy of susceptibility An inshyteresting development of this study is that in slates of the Carpathians in which the anisotropy is due to paramagnetic phyllosilicates the degree of anishysotropy is proportional to the bulk or mean susshyceptibility This has also been reported in Archean slates (Borradaile et aI in press)

Strain response models and multiple sources of susshy

ceptibility

Owens (1974) first drew attention to two imshyportant items that must be taken into account in any interpretation of susceptibility anisotropy in terms of strain Firstly the mineralogical source of the susceptibility should be defined If there are multiple sources of susceptibility the direct applishycation of the simple March model or any other model assuming a penetrative homogeneous magshynetic response is invalid Rochette and Vialon (1984) and Henry (1983) enforced this argument in different ways Slight variations in the proporshytions of minerals with different magnetic anishysotropies may under certain circumstances proshyduce changes in the bulk anisotropy that override any changes in anisotropy due to strain (Borshyradaile 1987b)

The second major point raised by Owens was that the actual strain response model has a major influence on the way in which the anisotropy accumulates from the pre-strain situation For simplicity he considered three models The first was a lineplane model that we can compare to the March model already referred to above (Fig 13a) The second was the viscous or Jeffery model in which the magnetic grain is likened to a rigid ellipsoid undergoing strain-induced motion in a viscous medium The third passive model likens the magnetic grains to passive strain markers Structural geologists may compare this to the model proposed by Ramsays school of structshyural geology to approximate the shape and conseshyquent orientation changes of for example a tectonically deforming passive ellipsoidal marker by the Rrcp equations see Fig 14 (Borradaile 1987a) Care should be taken with the term passhysive some geophysicists use the term to refer to

$e85 ~_068 fRo= 15 ~t=135

C)-shystrain ellipse (j) ~5middot Rs= 20 0_01409lt

Ro= 15 iff=15

original possive passive markers markers after strain

Fig 14 The R rlt1gt model Particles with the original orientashy J

tions (8) shown as a result of strain indicated by the strain ellipse take up new orientations (lt1raquo At the same time the ratios of the original shapes (R1f) change to final shapes (Ry2) The shape-ratio of the strain ellipse is 2 1 as indicated

the lineplane or March model and where they do not appear to imply any similarity to the Rrcp model (eg Cogne and Gapais 1986)

The mechanical response is usually neglected in the correlation of strains and susceptibility anishysotropies Indeed it is likely that many rocks and many types of deformation mechanisms are unsuishytable for establishing a correlation using the preshymises of simple mathematical models involving a single mode of deformation For example if there are relict components of sedimentary magnetic fabrics mixed with the tectonic fabrics or magshynetic fabrics of different tectonic ages a model assuming homogeneity will fail Similarly deforshymation structures that produce domainal fabrics that differently influence the magnetic fabric will cause complications if the magnetic fabric is samshypled on a scale that does not take this into account In particulate flow (Fig 15) the movement of grains may be poorly ordered Some grains move more than their neighbours rotate more or even exchange neighbours despite the fact that on a suitably large polygranular scale the strain may be approximately homogeneous Movement in polyshygranular units is also possible (Fig 16) as has been shown by experiments on analog materials (Means 1977) The scale on which magnetic susceptibility is defined will determine whether or not this preshysents a problem

The deformation mechanisms may be still more complicated The deformation may cause the rock

I bull

13

(01 (bl

Fig IS Particulate flow of a simulated (two-dimensional) aggregate Deformation proceeds from (a) through (c) The motions of particles is somewhat disordered whereas on a large scale the strain may appear to be approximately homogeneous as shown by the

strain ellipse defined by the black particles

J mm Fig 16 Experimentally produced particulate flow of groups of alum grains involving intergranular displacement surfaces

(From Means 1977)

et

deformation gt

bull00 bull

Fig 17 Possible deformation processes in metamorphic rocks that could be significant in the evolution of magnetic fabrics c -intergranular displacement surfaces (may be invisible) d-ductile (may be plastic) deformation of grains e-styloshylitie surfaces and grain-truncation f -penetration of grains g -microfaults (cleavage slip) h-rotation of blocks or groups of grains between faults or other discontinuities m-pressureshysolution material transfer (may be out of system) n-new

minerals crystallise

to be a discontinuum on various scales Lozenges of rock may rotate mass removal may occur loshycally or even to outside the system while grains plastically deform by intercrystalline processes and slide and roll past oneanother (Fig 16) At the same time new minerals may form with their crystallographic orientations controlled by the contemporary stress system Any of these factors could complicate the strain-response model of the rock and the development of its magnetic fabric While all of these processes are unlikely to occur at once the roles of several of these (or others not discussed) have to be assessed before the magnetic fabric can be correlated with the bulk strain Amongst these complications probably the most common one is the growth of new minerals as for example in phyllites schists and gneisses In these cases the explanation of schistosity may be bound up with the origin of the metamorphic texture more than with the strain of the rock (Fig 17) (Borradaile et at 1986)

Experimental studies

Although there has been some early interest in the effects of stress on magnetic susceptibility (eg Nagata 1966 1970 Kean et al 1976) this was associated with strains within the elastic limit Of interest here are the susceptibility changes that occur with large strains due to deformation that is macroscopically ductile if not actually plastic at the crystalline level The problem in the laboratory

bullbull bull bullbull bull bull

bullbull

14

environment is that even at the slowest strain rates that are practicable (10- 6 to 10-9 S-I) most rocks and minerals are not sufficiently ductile at room temperature to fail by the natural mechanisms of metamorphic rocks

Owens and Rutter (1978) first tackled this subshyject with a study of marbles and of calcite Alshythough the diamagnetic susceptibility of calcite is low the mineral is relatively easily deformed in a plastic manner at moderate confining pressures It is also stable at modest experimental temperatures so that Owens and Rutter were able to enhance the ductility by using temperatures up to 500 0 C in combination with pressures of 150 to 300 MPa (15 to 3 kbar) at strain-rates of approximately 10 - 4 to 10 - s s - 1 They achieved strains up to 50 axial-symmetrical (coaxial) shortening of the cylindrical specimens

The marbles they used had essentially isotropic magnetic and optical-crystallographic fabrics inishytially The magnetic anisotropy rapidly reached a plateau intensity at about 45 shortening The optical fabrics and the susceptibility fabric rapidly became axisymmetric to the shortening axis of the specimens This study didmiddot much to confirm the value of magnetic fabrics as indicators of strain and kinematics of deformation but most natural studies are based on ferrirnagnetic or parashymagnetic materials

Natural paramagnetic and ferrimagnetic matershyials are difficult to deform in a realistic manner without raising the temperature Heating will not normally be possible without inducing mineralogishycal changes that might mask susceptibility changes due to deformation Borradaile and Alford (1987) approached this problem by using a synthetic aggregate of sand enriched with magnetite that was cemented with commercial Portland cement The latter has a negligible (diamagnetic) susceptshyibility in comparison with the aggregate and pershymitted the aggregate to shorten by 35 in a ductile manner by axial symmetrical shortening The deshyformation did not involve cataclasis of the sand grains Rather the deformation was accommodshyated by the shearing of the cement gel This pershymitted a grain-shape alignment to develop by rollshying and sliding of the grains The magnetite grains were of the same grain-size as the matrix sand so

bulll1pl -04

bull 03

02 bull bull

01 bullbull01 02 03 04 In (XZ)

00 I I bull I I ~

11 12 13 14 15 (XI Z)

Fig 18 A correlation between the change in degree (fl) of susceptibility anisotropy and the strain ratio in some pure shear experiments on synthetic magnetite-bearing sandshy

stones (From Borradaile and Alford 1987)

that these experiments essentially addressed the problem of the rotational behaviour of the clasts (In most natural sandstones the iron oxide grains are much smaller than the sand clasts) The experiments were at carefully controlled strainshyrates of 5 x 10 - 6 S - 1 and confining pressures of 150 MPa (15 kbar) The maximum and intershymediate principal directions of susceptibility of these specimens rotated very rapidly towards the plane of flattening at rates exceeding the rate of rotation of a line undergoing homogeneous strain (cf the lineplane model) It was inferred that the magnetites rotated rigidly possibly with some plastic deformation The rotation was even more rapid when the matrix was composed of calcite instead of silicate mineral grains For initial susshyceptibility fabrics that were suitably oriented it was found that the change in the degree of anishysotropy was related to the strain by a power law (Fig 18) This serves to emphasise the importance of the initial magnetic fabric Relatively little can be deduced of the strain history from the final magnetic fabric alone Just as the initial ellipsoidal shape and orientation is of paramount importance in the strain analysis of ellipsoidal objects so is a knowledge of similar information for the initial magnetic fabric ellipsoid Although a power law relationship between the change in orientation of specially oriented magnetic fabrics exists in cershytain axial-symmetrical ( pure shear) experiments

15

In ( kmox kim J Calcite -cement - magnetite Q9g~gotes

at 150 MPo 05

04

XZHI XZmiddotH403 --

~ U-C3Z ~ AC -10 SHEAR ZOHEt ~ PURE SHEAR

02

t 01 XZ 20 XZ -115

In (kint kmln )

-0 02 03 04 -05 06 -07 os

bull Fig 19 The paths of incremental changes in magnetic anishysotropy are shown for the experimental deformation of syntheshysised calcite-cement-magnetite specimens The pure shear test produces little change in anisotropy even though the XZ strain ratio reaches 135 In contrast the changes produced in a shear zone (transpressive) are much greater despite the fact

that the ultimate XZ strain ratio for the zone is only 114

it is premature to make extrapolations to nature at the present state of knowledge

Recent work on experimental shear zones of synthetic materials at 150 MPa extends these conshyclusions to the case of transpressive deformation -a non-coaxial strain history (Borradaile and Alshyford in press) The susceptibility ellipsoids rotate rapidly toward stable orientations in which the minimum susceptibility is at a high angle to the shear zone boundaries The magnetic anisotropy changes very rapidly in the shear zones they produce a stronger magnetic fabric than axial symmetrical shortening at the same strain This is shown for two typical incremental- tests on the same synthetic calcite-matrix material at 150 Mpa in Fig 19 A further complication recognised in the experiments is that the magnetic fabrics may be planar (F gt L) whereas the mineral fabrics are constricted (a gt b) or plane strain (a = b) It is not known if these observations are transferable to natural shear zones

Conclusions

The interpretation of natural magnetic fabrics may be more complex than was initially recogshynised but progressive changes in magnetic anishysotropy do occur sympathetically with regional strain gradients despite accompanying regional

metamorphism (eg Hrouda and Janak 1976 Hrouda 1976 Coward and Whalley 1979) Indeed Rochette (1987) has shown that the metashymorphic production of pyrrhotite can enhance the susceptibility and produce a magnetically detectashyble isograd Also in certain rocks there are at least weak correlatiCfls between ratios of principal strains and the ratios of principal susceptibilities Numerous examples of the parallelism of principal susceptibility directions and structural directions (or even principal strain directions) support the contention that genetic relationships do exist beshytween strain and susceptibility in some cases Nevshyertheless these correlations are not universal and it is not possible to predict which natural situashytions will yield susceptibility data that _will faithshyfully represent principal strain directions or prinshycipal strain magnitudes or both For exampl~ magnetic fabrics do not always seem to be reliable kinematic indicators for shear zones and in the case of polyphase deformation later magnetic fabrics do not uniformly overprint earlier ones Magnetic fabrics should not be used for routine methods of strain analysis without further study A more profitable avenue is to determine how the susceptibility and strain tensors relate taking account of the actual strain-response model (deshyformation mechanisms) and the actual minerashylogical sources of susceptibility in that rock inshycluding phases produced by metamorphism A fruitful approach would be to consider the tensorial combination of coexisting magnetic subshyfabrics and successive episodes of magnetic fabric development along the lines initiated by Hrouda (1979)

Relationships between susceptibility and strain are in vogue However the earliest uses of magshynetic studies simply to investigate bulk petroshyfabrics are not yet been fully developed or inshytegrated with detailed petrofabric studies by optishycalor X-ray means Furthermore studies of remashynence and of susceptibility at different field strengths can yield information on magnetic subshyfabrics of different grain-sizes or different mineralogy This information is essential in the study of metamorphism of magnetic phases as well as their preferred orientation The anisotropy of remanence is also a profitable area of study

16 _

because only the ferrimagnetic traces contribute to that sub-fabric

Finally the nondestructive nature of magnetic fabric analysis provides a tool for investigating the progressive deformation or progressive metamorshyphism of a single specimen in laboratory experishyments Experiments on synthetii aggregates indishycate that the initial anisotropy of materials is not easily overprinted by small strains at low tempershyature They demonstrate also that the magnetic fabric ellipsoid spins very rapidly where the chief magnetic mineral is magnetite This is more noticeable when the matrix grains undergo crystal-plastic deformation Experimental shear zones produce greater changes in magnetic shape fabrics than axial-symmetrical shortening (pure shear) at the same strain they can also produce magnetic fabrics differing in symmetry from the grain fabric Such results develop an awareness for the greater complexities of natural structures

Acknowledgments

I wish to thank the Natural Sciences and Enshygineering Research Council of Canada for the continuing support of my work Frantisek Hrouda and Brian Bayly are thanked for constructive criticism of this article Karel Zapletal is thanked for some data on biotite Mel Friedman and Jan Tullis provided helpful reviews

Postscript

Since this paper was accepted for publication P Rochette has drawn attention to unusual inshyverse magnetic fabrics probably produced by single-domain magnetite (Thesis University of Grenoble 1988211 pp)

APPENDIX

Presentation of anisotropy of susceptibility

Magnetic susceptibility is a second rank tensor property conveniently envisaged as a magnitude ellipsoid (see Hrouda 1982 p 38) with three principal axes k max bull kim and k min or k ll bull kn k 33 The average or bulk susceptibility is comshy

monly defined as the arithmetic mean of the three principal values (Ellwood et al 1986-Symshyposium recommendations) but it is not clear why the arithmetic mean is a more appropriate represhysentation of bulk susceptibility than the geometric mean Susceptibility anisotropies for rocks are so low (Figs 9 and 10) that there is often little difference between these two expressions For exshyample seventeen specimens of strongly strained fine schist of the English Borrowdale Volcanic Series have principal susceptibilities in the ratio 104 102 0943 ~

Hrouda (1982) lists 25 different parameters that have been used at various times to represent anishysotropy The most useful are sometimes termed the magnetic lineation and the magnetic foliashytion

L = kmaxkint and F= kintkmin

Note that some authors chose alternative definishytions for Land F (eg Coward 1976) The parameters L and F are plotted vertically and horizontally respectively and compare directly with the ratios used to describe the strain ellipsoid on a Flinn-diagram

a=XY and b= YZ where X 2 Y ~ Z are the principal strains In some instances it is clearer if the natural logarithms of L F and of a and b are plotted

If the ratios of principal susceptibilities are listed individually it is helpful to normalise them so that their product is unity The normalised versions of the principal susceptibilities are related to their ratios by the following relations

kmax = L 2 3 bull pl3

kml

= L -13 F I 3

k = L -13 bull F- 23mm

It is advisable also to present a mean (bulk) susceptibility value This enables the reader to assess the significance of the results (Conference recommendations Ellwood et al 1986) Unforshytunately this has often not been done in the past Commonly one finds that anisotropies are poorly reproducible for rocks with susceptibility lt 10-4

SIjvol Providing cones of confidence about principal directions and standard errors for prinshycipal magnitudes is also useful in this regard

bull

30

2-5

20

-5

10 F=~ WI shy - middotmiddotV j Y

0 5 20 25 30 35

F =(klnkmin)

Fig AI The relationship between Jelineks (1981) P and T parameters and the conventional anisotropy parameters L and

F

The ratios L and F like their counterparts in strain (a and b) are very useful in describing the ellipsoids shape or sense of anisotropy However the distance of the point (L F) from the origin is also a measure of the degree of anisotropy that is to say its departure from sphericity Jelineks (1981) parameters pi and T overcome this T represents sense of anisotropy and ranges from -1 (prolate) to + 1 (oblate) pi (gt 1) expresses degree of anisotropy These are defined as

[ 2(In k -In k~]T= -1

In k itM - In k min 1

pi = exp [ 2( af + a ~ + a~ ) ] ~ where a1 = In(kmaxkb) etc and kb = (kmax k inl

kmin )(l3) The relationship of p and T to L and F is shown in Fig AI

References

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Borradaile GJ 1987a Analysis of strained sedimentary fabrics Can J Earth Sci 131 121-125

Borradaile GJ 1987b Anisotropy of magnetic susceptibility rock composition versus strain Tectonophysics 138 327-329

Borradaile GJ and Alford C 1987 Relationship between

17

magnetic susceptibility and strain in laboratory experishyments Tectonophysics 133 121-135

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Borradaile GJ Mothersill JS Tarling D and Alford C 1986 Sources of magnetic susceptibility in a slate Earth Planet Sci Lett 76 336-340

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II

Goldstein AG bull 1980 Magnetic susceptibility anisotropy of mylonites from the Lake Char Mylonite Zone SE New England Tectonophysics 66 197-211

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Hamilton N and Rees AI 1971 The anisotropy of magnetic susceptibility of the Franciscan Rocks of the Diablo Range Central California Geo Rundsch 60 1103-1124

Hamilton N Owens WH and Rees AI 1968 Laboratory experiments on the production of grain orientation in shearing sand l Goo 76 465-472

Hargraves RB 1959 Magnetic anisotropy and remanent magnetism in hemo-ilmenite from ore deposits at Allard Lake Quebec l Goophys Res 68 293-309

Heider Fbull Dunlop DJ and Sugiura N 1987 Magnetic properties oC hydrothermally recrystallized magnetite crystals Science 236 1287-1290

Henry B 1983 Interpretation quantitative de lanisotropie de susceptibilite magnetique Tectonophysics 91 165-177

Henry B and Daly L 1983 From qualitative to quantitative magnetic anisotropy analysis the prospect of finite strain calibration Tectonophysics 98 327-336

Hirt AM Lowrie W bull Clendenen WS and Kligfield R 1988 The correlation of magnetic anisotropy with strain in the Chelmsford Formation of the Sudbury Basin Ontario Tectonophysics 145 177-189

Hrouda F 1976 The origin of cleavage in the light of magnetic anisotropy investigations Pbys Earth Planet Inshyter 13 132-142

Hrouda F 1979 (reponed 1977) The strain interpretation of magnetic anisotropy in rocks of the Nizky lesenik Mounmiddot tains (Czechoslovakia) Sb Gool Ved (Uzit Geofyz) 16 27-62

Hrouda F 1980 Magnetocrystalline anisotropy of rocks and massive ores a mathematical model study and its fabric implications l Struct Geo1bull 2 459-462

Hrouda F 1982 Magnetic anisotropy of rocks and its apmiddot plication in geology and geophysics Geophys Surv 5 37-82

Hrouda F 1986 The effect of quanz on the magnetic ani sotropy of quartzite Studia Geophys Geod 30 39-45

Hrouda F bull 1987 Mathematical model relationships between

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Hrouda F and Chlupacova M bull 1980 The magnetic fabric in the Nasavrky massif Cas Mineral Goo 25 17-27

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Hrouda F and Jelinek V in prep Resolution of ferromagmiddot netic and paramagnetic components of magnetic anishysotropy using combined low-field and high-field anishysotropy measurements I

Hrouda F Chlupacova M and Rejl L 1971 The mimetic fabric of magnetite in some foliated granodiorites as indio cated by magnetic anisotropy Earth Planet Sci Leu 11 381-384

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Kean WF Day R Fuller M and Schmidt VA 1976 The effect of uniaxial compression on the initial susceptibility of rocks as a function of grain-size and composition of their constituent titanomagnetites J Geophys Res 81 861-874

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Kneen SJ 1976 The relationship between the magnetic and

19

strain fabrics of some hematite-bearing Welsh Slates Earth Planet Sci Lett 31 413-416

Lamarche G and Rochette P 1987 Microstructural analysis and origin of lineations in the magnetic fabric of some Alpine slates Tectonophysics 139 285-293

Lapointe P Morris WA and Harding KL 1986 Interpreshytation of magnetic susceptibility a new approach 10 geoshyphysical evaluation of the degree of rock alteration Can J

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Means WD 1977 A deformation experiment in transmitted light Earth Planet Sci Lett 35 169-179

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Nagata T 1970 Anisotropic magnetic susceptibility of rocks under mechanical stresses Pure App Goophys 78

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Owens WH 1974 Mathematical model studies on factors affecting the magnetic anisotropy of deformed rocks Tectonophysics 24 115-131

Owens WH and Bamford D 1976 Magnetic seismic and other anisotropic properties of rock fabrics Philos Trans R Soc London Ser A 283 55-68

Owens WH and Rutter EH 1978 The development of magnetic susceptibility anisotropy through crystallographic preferred orientation in a calcite rock Phys Earth Planet Inter 16 215-222

Park JKmiddot1983 Paleomagnetism for geologists Geosci Can 4 180-188

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Rathore JS 1985 Some magnetic characteristics of sheared zones J Geodyn 2 291-301

Rathore JS and Henry B 1982 Comparison of strained magnetic fabrics in Dalradian rocks from the southwest Highlands of Scotland J Struc Geol 4 373-384

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Rees AI 1968 The production of preferred orientation in a concentrated dispersion of elongated and flattened grains J Geol 76 457-465

Rochetle P 1987 Metamorphic control of the mineralogy of black shales in the Swiss Alps toward the use of magnetic isograds Eanh Planet Sci Lett 84 446-456

Rochette P 1988 Relation entre deformation et metamorshy

f

bull

phisme Alpin dans les schistes noirs Helvetiques Iapport de la fabrique magnetique Geodin Acta 2 (in press)

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Schwartz EJ 1975 Magnetic properties of pyrrhotite and their use in applied geology and geophysics Geo Surv Can Pap 74-59 24 pp

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Uyeda S Fuller MD Belshe JC and Girdler RW 1963 Anisotropy of magnetic susceptibility of rocks and minershyals J Geophys Res 68 279-291

Van den Ende C 1975 On the origin of anisotropy of magshynetic susceptibility in Permian Redbeds from the western part of the Dome de Barrot (S France) In GJ Borradaile et al (Editors) Progress in Geodynamics North-Holland Pub Co Amsterdam pp 176-189

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Weast RC and Astle MJ (Editors) 1978 CRC handbook of Chemistry and Physics 59th edn CRC Press Palm Beach Fla

20

II

Wing-Fatt L and Stacey FD 1966 Magnetic anisotropy of laboratory materials in which magma flow is simulated Pure AppJ Geophys 6478-80

Wood DS Oertel G Singh J and Bennett HF 1976 Strain and anisotropy in rocks Philos Trans R Soc London Ser A 283 27-42

Zavoyskiy VN 1982 Use of magnetic susceptibility tensor for solving problems in structural geology Izv Akad Nauk SSSR Earth Phys Ser 18 217-223

11

Q Z p Marchian rofafion

S ~ b

t1- y p 0- Zr +y~

k X L oL

X SI bull bull S

Fig 13 a Theoretical outline of the March model as applied to the rotation and preferred orientation of phyUosilicate grains For strain axes X ~ Y ~ Z the rotation of a pole p of a platelet is shown schematically as is the rotation of the long axis of a rod-like element Such elements are considered to be dispersed and perfectly rigid b Schematic cross-section of a typical natural preferred orientation of phyllosilicate grains defining a schistosity Sl Grains with less favoured orientations are truncated and their volumetric contribution to the magnetic fabric may be reduced Usually the pattern of

preferred orientation can only be explained by the March model to a limited degree

and it seems unduly optimistic to consider them as universal relationships that may be extrapolated from one region to another Within a single reshygion with a limited range of deformation mechashynisms and lithological uniformity it might be posshysible to extrapolate some correlations of magnetic fabric with strain

The approaches reviewed so far in this section are essentially empirical and in most cases the susceptibility was attributed to disseminated magshynetite The studies of Coward and Whalley (1979) and of Henry and Daly (1983) were exceptions they recognised multiple sources of susceptibility and Kligfield et al (1982) also investigated the sources thoroughly The latter authors demonshystrated susceptibility anisotropy was due to iron oxides whose distributions and orientations were controlled mimetically by their position on the surfaces of the oolites used as strain markers The other studies mentioned adopt the premise or imply that magnetite grains were distributed throughout the rocks and were tectonically aligned to produce a magnetite shape-fabric which in turn dictated the magnetic fabric The underlying mechanistic model that appears to have influenced this train of thought is attributed to March (1932) This model (eg Wood et al 1976) outlines the situation in which platy elements that do not impinge upon oneanother and that are preferably randomly oriented in their initial configuration

become systematically re-oriented by homogeshyneous strain and are not impeded by the matrix (Fig 13a) Consequently the orientation-distribushytion of the poles to these platelets after constantshyvolume strain is directly related to the strain Thus for a given direction i the strain e is related to the normalised density (d) of platelet poles by

emiddot = d(-1j3 - 1 I bull

In the structural geology literature some considershyation has been given to the aspect ratios of the platelets as well as accompanying volume changes of tqe aggregate (Tullis 1976 Tullis and Wood 1975) However these modifications still fall short of reality The March model is difficult to adapt to three-dimensional grains and even more difficult to reconcile with the premises of passive beshyhaviour and non-impingement of the rotating grains on each other A worse shortcoming is the inherent assumption that the grains are spatially separated whereas in a typical metamorphic rock the variation in orientation imposes restrictions on the degree to which differently oriented crystals grow (Fig 13b) Nevertheless it has found applishycations in magnetic studies (eg Cogne and Gapais 1986) and studies of comparable mathematical models (Hrouda 1980) and is frequently cited in petrofabric studies (Oertel 1983)

Hrouda (1987) has extended these arguments to situations in which it is known that paramagnetic

12

sheet silicates such as chlorite and biotite0

dominate the anisotropy of susceptibility An inshyteresting development of this study is that in slates of the Carpathians in which the anisotropy is due to paramagnetic phyllosilicates the degree of anishysotropy is proportional to the bulk or mean susshyceptibility This has also been reported in Archean slates (Borradaile et aI in press)

Strain response models and multiple sources of susshy

ceptibility

Owens (1974) first drew attention to two imshyportant items that must be taken into account in any interpretation of susceptibility anisotropy in terms of strain Firstly the mineralogical source of the susceptibility should be defined If there are multiple sources of susceptibility the direct applishycation of the simple March model or any other model assuming a penetrative homogeneous magshynetic response is invalid Rochette and Vialon (1984) and Henry (1983) enforced this argument in different ways Slight variations in the proporshytions of minerals with different magnetic anishysotropies may under certain circumstances proshyduce changes in the bulk anisotropy that override any changes in anisotropy due to strain (Borshyradaile 1987b)

The second major point raised by Owens was that the actual strain response model has a major influence on the way in which the anisotropy accumulates from the pre-strain situation For simplicity he considered three models The first was a lineplane model that we can compare to the March model already referred to above (Fig 13a) The second was the viscous or Jeffery model in which the magnetic grain is likened to a rigid ellipsoid undergoing strain-induced motion in a viscous medium The third passive model likens the magnetic grains to passive strain markers Structural geologists may compare this to the model proposed by Ramsays school of structshyural geology to approximate the shape and conseshyquent orientation changes of for example a tectonically deforming passive ellipsoidal marker by the Rrcp equations see Fig 14 (Borradaile 1987a) Care should be taken with the term passhysive some geophysicists use the term to refer to

$e85 ~_068 fRo= 15 ~t=135

C)-shystrain ellipse (j) ~5middot Rs= 20 0_01409lt

Ro= 15 iff=15

original possive passive markers markers after strain

Fig 14 The R rlt1gt model Particles with the original orientashy J

tions (8) shown as a result of strain indicated by the strain ellipse take up new orientations (lt1raquo At the same time the ratios of the original shapes (R1f) change to final shapes (Ry2) The shape-ratio of the strain ellipse is 2 1 as indicated

the lineplane or March model and where they do not appear to imply any similarity to the Rrcp model (eg Cogne and Gapais 1986)

The mechanical response is usually neglected in the correlation of strains and susceptibility anishysotropies Indeed it is likely that many rocks and many types of deformation mechanisms are unsuishytable for establishing a correlation using the preshymises of simple mathematical models involving a single mode of deformation For example if there are relict components of sedimentary magnetic fabrics mixed with the tectonic fabrics or magshynetic fabrics of different tectonic ages a model assuming homogeneity will fail Similarly deforshymation structures that produce domainal fabrics that differently influence the magnetic fabric will cause complications if the magnetic fabric is samshypled on a scale that does not take this into account In particulate flow (Fig 15) the movement of grains may be poorly ordered Some grains move more than their neighbours rotate more or even exchange neighbours despite the fact that on a suitably large polygranular scale the strain may be approximately homogeneous Movement in polyshygranular units is also possible (Fig 16) as has been shown by experiments on analog materials (Means 1977) The scale on which magnetic susceptibility is defined will determine whether or not this preshysents a problem

The deformation mechanisms may be still more complicated The deformation may cause the rock

I bull

13

(01 (bl

Fig IS Particulate flow of a simulated (two-dimensional) aggregate Deformation proceeds from (a) through (c) The motions of particles is somewhat disordered whereas on a large scale the strain may appear to be approximately homogeneous as shown by the

strain ellipse defined by the black particles

J mm Fig 16 Experimentally produced particulate flow of groups of alum grains involving intergranular displacement surfaces

(From Means 1977)

et

deformation gt

bull00 bull

Fig 17 Possible deformation processes in metamorphic rocks that could be significant in the evolution of magnetic fabrics c -intergranular displacement surfaces (may be invisible) d-ductile (may be plastic) deformation of grains e-styloshylitie surfaces and grain-truncation f -penetration of grains g -microfaults (cleavage slip) h-rotation of blocks or groups of grains between faults or other discontinuities m-pressureshysolution material transfer (may be out of system) n-new

minerals crystallise

to be a discontinuum on various scales Lozenges of rock may rotate mass removal may occur loshycally or even to outside the system while grains plastically deform by intercrystalline processes and slide and roll past oneanother (Fig 16) At the same time new minerals may form with their crystallographic orientations controlled by the contemporary stress system Any of these factors could complicate the strain-response model of the rock and the development of its magnetic fabric While all of these processes are unlikely to occur at once the roles of several of these (or others not discussed) have to be assessed before the magnetic fabric can be correlated with the bulk strain Amongst these complications probably the most common one is the growth of new minerals as for example in phyllites schists and gneisses In these cases the explanation of schistosity may be bound up with the origin of the metamorphic texture more than with the strain of the rock (Fig 17) (Borradaile et at 1986)

Experimental studies

Although there has been some early interest in the effects of stress on magnetic susceptibility (eg Nagata 1966 1970 Kean et al 1976) this was associated with strains within the elastic limit Of interest here are the susceptibility changes that occur with large strains due to deformation that is macroscopically ductile if not actually plastic at the crystalline level The problem in the laboratory

bullbull bull bullbull bull bull

bullbull

14

environment is that even at the slowest strain rates that are practicable (10- 6 to 10-9 S-I) most rocks and minerals are not sufficiently ductile at room temperature to fail by the natural mechanisms of metamorphic rocks

Owens and Rutter (1978) first tackled this subshyject with a study of marbles and of calcite Alshythough the diamagnetic susceptibility of calcite is low the mineral is relatively easily deformed in a plastic manner at moderate confining pressures It is also stable at modest experimental temperatures so that Owens and Rutter were able to enhance the ductility by using temperatures up to 500 0 C in combination with pressures of 150 to 300 MPa (15 to 3 kbar) at strain-rates of approximately 10 - 4 to 10 - s s - 1 They achieved strains up to 50 axial-symmetrical (coaxial) shortening of the cylindrical specimens

The marbles they used had essentially isotropic magnetic and optical-crystallographic fabrics inishytially The magnetic anisotropy rapidly reached a plateau intensity at about 45 shortening The optical fabrics and the susceptibility fabric rapidly became axisymmetric to the shortening axis of the specimens This study didmiddot much to confirm the value of magnetic fabrics as indicators of strain and kinematics of deformation but most natural studies are based on ferrirnagnetic or parashymagnetic materials

Natural paramagnetic and ferrimagnetic matershyials are difficult to deform in a realistic manner without raising the temperature Heating will not normally be possible without inducing mineralogishycal changes that might mask susceptibility changes due to deformation Borradaile and Alford (1987) approached this problem by using a synthetic aggregate of sand enriched with magnetite that was cemented with commercial Portland cement The latter has a negligible (diamagnetic) susceptshyibility in comparison with the aggregate and pershymitted the aggregate to shorten by 35 in a ductile manner by axial symmetrical shortening The deshyformation did not involve cataclasis of the sand grains Rather the deformation was accommodshyated by the shearing of the cement gel This pershymitted a grain-shape alignment to develop by rollshying and sliding of the grains The magnetite grains were of the same grain-size as the matrix sand so

bulll1pl -04

bull 03

02 bull bull

01 bullbull01 02 03 04 In (XZ)

00 I I bull I I ~

11 12 13 14 15 (XI Z)

Fig 18 A correlation between the change in degree (fl) of susceptibility anisotropy and the strain ratio in some pure shear experiments on synthetic magnetite-bearing sandshy

stones (From Borradaile and Alford 1987)

that these experiments essentially addressed the problem of the rotational behaviour of the clasts (In most natural sandstones the iron oxide grains are much smaller than the sand clasts) The experiments were at carefully controlled strainshyrates of 5 x 10 - 6 S - 1 and confining pressures of 150 MPa (15 kbar) The maximum and intershymediate principal directions of susceptibility of these specimens rotated very rapidly towards the plane of flattening at rates exceeding the rate of rotation of a line undergoing homogeneous strain (cf the lineplane model) It was inferred that the magnetites rotated rigidly possibly with some plastic deformation The rotation was even more rapid when the matrix was composed of calcite instead of silicate mineral grains For initial susshyceptibility fabrics that were suitably oriented it was found that the change in the degree of anishysotropy was related to the strain by a power law (Fig 18) This serves to emphasise the importance of the initial magnetic fabric Relatively little can be deduced of the strain history from the final magnetic fabric alone Just as the initial ellipsoidal shape and orientation is of paramount importance in the strain analysis of ellipsoidal objects so is a knowledge of similar information for the initial magnetic fabric ellipsoid Although a power law relationship between the change in orientation of specially oriented magnetic fabrics exists in cershytain axial-symmetrical ( pure shear) experiments

15

In ( kmox kim J Calcite -cement - magnetite Q9g~gotes

at 150 MPo 05

04

XZHI XZmiddotH403 --

~ U-C3Z ~ AC -10 SHEAR ZOHEt ~ PURE SHEAR

02

t 01 XZ 20 XZ -115

In (kint kmln )

-0 02 03 04 -05 06 -07 os

bull Fig 19 The paths of incremental changes in magnetic anishysotropy are shown for the experimental deformation of syntheshysised calcite-cement-magnetite specimens The pure shear test produces little change in anisotropy even though the XZ strain ratio reaches 135 In contrast the changes produced in a shear zone (transpressive) are much greater despite the fact

that the ultimate XZ strain ratio for the zone is only 114

it is premature to make extrapolations to nature at the present state of knowledge

Recent work on experimental shear zones of synthetic materials at 150 MPa extends these conshyclusions to the case of transpressive deformation -a non-coaxial strain history (Borradaile and Alshyford in press) The susceptibility ellipsoids rotate rapidly toward stable orientations in which the minimum susceptibility is at a high angle to the shear zone boundaries The magnetic anisotropy changes very rapidly in the shear zones they produce a stronger magnetic fabric than axial symmetrical shortening at the same strain This is shown for two typical incremental- tests on the same synthetic calcite-matrix material at 150 Mpa in Fig 19 A further complication recognised in the experiments is that the magnetic fabrics may be planar (F gt L) whereas the mineral fabrics are constricted (a gt b) or plane strain (a = b) It is not known if these observations are transferable to natural shear zones

Conclusions

The interpretation of natural magnetic fabrics may be more complex than was initially recogshynised but progressive changes in magnetic anishysotropy do occur sympathetically with regional strain gradients despite accompanying regional

metamorphism (eg Hrouda and Janak 1976 Hrouda 1976 Coward and Whalley 1979) Indeed Rochette (1987) has shown that the metashymorphic production of pyrrhotite can enhance the susceptibility and produce a magnetically detectashyble isograd Also in certain rocks there are at least weak correlatiCfls between ratios of principal strains and the ratios of principal susceptibilities Numerous examples of the parallelism of principal susceptibility directions and structural directions (or even principal strain directions) support the contention that genetic relationships do exist beshytween strain and susceptibility in some cases Nevshyertheless these correlations are not universal and it is not possible to predict which natural situashytions will yield susceptibility data that _will faithshyfully represent principal strain directions or prinshycipal strain magnitudes or both For exampl~ magnetic fabrics do not always seem to be reliable kinematic indicators for shear zones and in the case of polyphase deformation later magnetic fabrics do not uniformly overprint earlier ones Magnetic fabrics should not be used for routine methods of strain analysis without further study A more profitable avenue is to determine how the susceptibility and strain tensors relate taking account of the actual strain-response model (deshyformation mechanisms) and the actual minerashylogical sources of susceptibility in that rock inshycluding phases produced by metamorphism A fruitful approach would be to consider the tensorial combination of coexisting magnetic subshyfabrics and successive episodes of magnetic fabric development along the lines initiated by Hrouda (1979)

Relationships between susceptibility and strain are in vogue However the earliest uses of magshynetic studies simply to investigate bulk petroshyfabrics are not yet been fully developed or inshytegrated with detailed petrofabric studies by optishycalor X-ray means Furthermore studies of remashynence and of susceptibility at different field strengths can yield information on magnetic subshyfabrics of different grain-sizes or different mineralogy This information is essential in the study of metamorphism of magnetic phases as well as their preferred orientation The anisotropy of remanence is also a profitable area of study

16 _

because only the ferrimagnetic traces contribute to that sub-fabric

Finally the nondestructive nature of magnetic fabric analysis provides a tool for investigating the progressive deformation or progressive metamorshyphism of a single specimen in laboratory experishyments Experiments on synthetii aggregates indishycate that the initial anisotropy of materials is not easily overprinted by small strains at low tempershyature They demonstrate also that the magnetic fabric ellipsoid spins very rapidly where the chief magnetic mineral is magnetite This is more noticeable when the matrix grains undergo crystal-plastic deformation Experimental shear zones produce greater changes in magnetic shape fabrics than axial-symmetrical shortening (pure shear) at the same strain they can also produce magnetic fabrics differing in symmetry from the grain fabric Such results develop an awareness for the greater complexities of natural structures

Acknowledgments

I wish to thank the Natural Sciences and Enshygineering Research Council of Canada for the continuing support of my work Frantisek Hrouda and Brian Bayly are thanked for constructive criticism of this article Karel Zapletal is thanked for some data on biotite Mel Friedman and Jan Tullis provided helpful reviews

Postscript

Since this paper was accepted for publication P Rochette has drawn attention to unusual inshyverse magnetic fabrics probably produced by single-domain magnetite (Thesis University of Grenoble 1988211 pp)

APPENDIX

Presentation of anisotropy of susceptibility

Magnetic susceptibility is a second rank tensor property conveniently envisaged as a magnitude ellipsoid (see Hrouda 1982 p 38) with three principal axes k max bull kim and k min or k ll bull kn k 33 The average or bulk susceptibility is comshy

monly defined as the arithmetic mean of the three principal values (Ellwood et al 1986-Symshyposium recommendations) but it is not clear why the arithmetic mean is a more appropriate represhysentation of bulk susceptibility than the geometric mean Susceptibility anisotropies for rocks are so low (Figs 9 and 10) that there is often little difference between these two expressions For exshyample seventeen specimens of strongly strained fine schist of the English Borrowdale Volcanic Series have principal susceptibilities in the ratio 104 102 0943 ~

Hrouda (1982) lists 25 different parameters that have been used at various times to represent anishysotropy The most useful are sometimes termed the magnetic lineation and the magnetic foliashytion

L = kmaxkint and F= kintkmin

Note that some authors chose alternative definishytions for Land F (eg Coward 1976) The parameters L and F are plotted vertically and horizontally respectively and compare directly with the ratios used to describe the strain ellipsoid on a Flinn-diagram

a=XY and b= YZ where X 2 Y ~ Z are the principal strains In some instances it is clearer if the natural logarithms of L F and of a and b are plotted

If the ratios of principal susceptibilities are listed individually it is helpful to normalise them so that their product is unity The normalised versions of the principal susceptibilities are related to their ratios by the following relations

kmax = L 2 3 bull pl3

kml

= L -13 F I 3

k = L -13 bull F- 23mm

It is advisable also to present a mean (bulk) susceptibility value This enables the reader to assess the significance of the results (Conference recommendations Ellwood et al 1986) Unforshytunately this has often not been done in the past Commonly one finds that anisotropies are poorly reproducible for rocks with susceptibility lt 10-4

SIjvol Providing cones of confidence about principal directions and standard errors for prinshycipal magnitudes is also useful in this regard

bull

30

2-5

20

-5

10 F=~ WI shy - middotmiddotV j Y

0 5 20 25 30 35

F =(klnkmin)

Fig AI The relationship between Jelineks (1981) P and T parameters and the conventional anisotropy parameters L and

F

The ratios L and F like their counterparts in strain (a and b) are very useful in describing the ellipsoids shape or sense of anisotropy However the distance of the point (L F) from the origin is also a measure of the degree of anisotropy that is to say its departure from sphericity Jelineks (1981) parameters pi and T overcome this T represents sense of anisotropy and ranges from -1 (prolate) to + 1 (oblate) pi (gt 1) expresses degree of anisotropy These are defined as

[ 2(In k -In k~]T= -1

In k itM - In k min 1

pi = exp [ 2( af + a ~ + a~ ) ] ~ where a1 = In(kmaxkb) etc and kb = (kmax k inl

kmin )(l3) The relationship of p and T to L and F is shown in Fig AI

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Borradaile GJ 1987a Analysis of strained sedimentary fabrics Can J Earth Sci 131 121-125

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Borradaile GJ and Alford C 1987 Relationship between

17

magnetic susceptibility and strain in laboratory experishyments Tectonophysics 133 121-135

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Borradaile GJ Mothersill JS Tarling D and Alford C 1986 Sources of magnetic susceptibility in a slate Earth Planet Sci Lett 76 336-340

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Coward MP and Whalley 1S 1979 Texture and fabric studies across the Kishorn Nappe near Kyle of Lochalsh Western Scotland J Struct Geol 1 259-273

Crimes TP and Oldershaw MA 1967 Paleocurrent demiddot terminations by magnetic fabri measurement on the Cambrian rocks of St Tudwals peninsula North Wales Geol J 5 217-232

Ellwood BBbull Hrouda F and Wagner J-J 1988 Symposia on magnetic fabrics Introductory comments Phys Earth Planet Inter 51 249-252

Fuller MDbull 1964 On the magnetic fabrics of certain rocks 1 Geol 72 368-376

18

II

Goldstein AG bull 1980 Magnetic susceptibility anisotropy of mylonites from the Lake Char Mylonite Zone SE New England Tectonophysics 66 197-211

Graham lW 1954 Magnetic susceptibility anisotropy an unexploited petrofabric element Bull Gool Soc Am 65 1257-1258

Graham lWbull 1966 Significance of magnetic anisotropy in Appalachian sedimentary rocks In lS Steinhard and Tl Smith (Editors) The Earth beneath the Continents Gooshyphys Monogr Am Geophys Union 10 627-648

Hamano Y and Yom ida K 1982 Magnetic anisotropy and porosity of Antarctic chondrites Mem Natl Inst Polar Res Tokyo 25 281-290

Hamilton N 1963 Susceptibility anisotropy measurements on some Silurian siltstones Nature 197 170-171

Hamilton N and Rees AI 1970 The use of magnetic fabric in paleocurrent estimation In SK Runcorn (Editor) Paleogeophysics Academic Press New York NY pp 445-464

Hamilton N and Rees AI 1971 The anisotropy of magnetic susceptibility of the Franciscan Rocks of the Diablo Range Central California Geo Rundsch 60 1103-1124

Hamilton N Owens WH and Rees AI 1968 Laboratory experiments on the production of grain orientation in shearing sand l Goo 76 465-472

Hargraves RB 1959 Magnetic anisotropy and remanent magnetism in hemo-ilmenite from ore deposits at Allard Lake Quebec l Goophys Res 68 293-309

Heider Fbull Dunlop DJ and Sugiura N 1987 Magnetic properties oC hydrothermally recrystallized magnetite crystals Science 236 1287-1290

Henry B 1983 Interpretation quantitative de lanisotropie de susceptibilite magnetique Tectonophysics 91 165-177

Henry B and Daly L 1983 From qualitative to quantitative magnetic anisotropy analysis the prospect of finite strain calibration Tectonophysics 98 327-336

Hirt AM Lowrie W bull Clendenen WS and Kligfield R 1988 The correlation of magnetic anisotropy with strain in the Chelmsford Formation of the Sudbury Basin Ontario Tectonophysics 145 177-189

Hrouda F 1976 The origin of cleavage in the light of magnetic anisotropy investigations Pbys Earth Planet Inshyter 13 132-142

Hrouda F 1979 (reponed 1977) The strain interpretation of magnetic anisotropy in rocks of the Nizky lesenik Mounmiddot tains (Czechoslovakia) Sb Gool Ved (Uzit Geofyz) 16 27-62

Hrouda F 1980 Magnetocrystalline anisotropy of rocks and massive ores a mathematical model study and its fabric implications l Struct Geo1bull 2 459-462

Hrouda F 1982 Magnetic anisotropy of rocks and its apmiddot plication in geology and geophysics Geophys Surv 5 37-82

Hrouda F 1986 The effect of quanz on the magnetic ani sotropy of quartzite Studia Geophys Geod 30 39-45

Hrouda F bull 1987 Mathematical model relationships between

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Hrouda F and Chlupacova M bull 1980 The magnetic fabric in the Nasavrky massif Cas Mineral Goo 25 17-27

Hrouda F and lanak F 1971 A study of the hematite fabric of some red sediments on the basis of their magnetic susceptibility anisotropy Sediment Geol 6 187-199

Hrouda F and Janak F 1976 The changes in shape of the magnetic susceptibility ellipsoid during progressive metashymorphism and deformation Tectonophysics 34 135-148

Hrouda F and Jelinek V in prep Resolution of ferromagmiddot netic and paramagnetic components of magnetic anishysotropy using combined low-field and high-field anishysotropy measurements I

Hrouda F Chlupacova M and Rejl L 1971 The mimetic fabric of magnetite in some foliated granodiorites as indio cated by magnetic anisotropy Earth Planet Sci Leu 11 381-384

Hrouda F Chlupacova M and Rejl L bull 1972 Changes in magnetite content and magnetite fabric during Cenitization as investigated by petromagnetic methods Neues Jahrb Mineral Abh 117 61-72

Hrouda F Janalc F and Rejl L 1978 Magnetic fabric and ductile deformation of rocks in zones of progressive reshygional metamorphism Ger Beitr Goophys 87 126-134

Hrouda F Jelinek V and Zapletal K 1985a Use of magshynetic propenies of rocks in ore and petroleum geophysics (in Czech) Res rep Goofyz Brno pp 54-75

Hrouda F Siemes H Herres N and Hennig-Micbaeli c 1985b The relationship between the magnetic anisotropy and the cmiddotaxis fabric in a massive hematite ore J Geophys bull 56 174-182

International Critical Tables 1929 McGrawmiddotHiIl New York NY

Ising G 1942 On the magnetic propenies of varved clay Ark Mat Astron Fys 29A 1-37

Jelinek V 1981 Characterization of the magnetic fabrics of rocks Tectonophysics 79 T63-T67

Karlin R Lyle M and Heath GR 1987 Authigenic magmiddot netite formation in suboxic marine sediments Nature 326 490--493

Kean WF Day R Fuller M and Schmidt VA 1976 The effect of uniaxial compression on the initial susceptibility of rocks as a function of grain-size and composition of their constituent titanomagnetites J Geophys Res 81 861-874

Khan MA 1962 Anisotropy of magnetic susceptibility of some igneous and metamorphic rocks J Geophys Res 67 2873-2885

KJigfie1d R Lowrie W and Dalziel I 1977 Magnetic susshyceptibility anisotropy as a strain indicator in the Sudbury Basin Ontario Tectonophysics 40 287-308

KJigfield R Lowrie W and Pfiffner OA 1982 Magnetic propenies of deformed oolitic limestones from the Swiss Alps the correlation of magnetic anisotropy and strain Eclogae Geo He1v 75 127-157

Kneen SJ 1976 The relationship between the magnetic and

19

strain fabrics of some hematite-bearing Welsh Slates Earth Planet Sci Lett 31 413-416

Lamarche G and Rochette P 1987 Microstructural analysis and origin of lineations in the magnetic fabric of some Alpine slates Tectonophysics 139 285-293

Lapointe P Morris WA and Harding KL 1986 Interpreshytation of magnetic susceptibility a new approach 10 geoshyphysical evaluation of the degree of rock alteration Can J

Earth Sci 23 393-401 March A 1932 Mathematische Theorie der Regelung nach

der Korngestait bei afrmer Deformation Z Kristallogrmiddot 81 285-297

Means WD 1977 A deformation experiment in transmitted light Earth Planet Sci Lett 35 169-179

Nagata T 1966 Magnetic susceptibility of compressed rocks J Goomag Geoelectr 18 73-80

Nagata T 1970 Anisotropic magnetic susceptibility of rocks under mechanical stresses Pure App Goophys 78

110-122 Nye JF 1957 The Physical Properties of Crystals Clarendon

Press Oxford 322 pp Oertel G 1983 The relationship of strain and preferred

orientation of phyllosilicale grains in rocks-a review Tectonophysics 100 413-447

Owens WH 1974 Mathematical model studies on factors affecting the magnetic anisotropy of deformed rocks Tectonophysics 24 115-131

Owens WH and Bamford D 1976 Magnetic seismic and other anisotropic properties of rock fabrics Philos Trans R Soc London Ser A 283 55-68

Owens WH and Rutter EH 1978 The development of magnetic susceptibility anisotropy through crystallographic preferred orientation in a calcite rock Phys Earth Planet Inter 16 215-222

Park JKmiddot1983 Paleomagnetism for geologists Geosci Can 4 180-188

Rathore JS 1979 Magnetic susceptibility anisotropy in the Cambrian Slate Belt of North Wales and correlation with strain Tectonophysics 53 83-97

Rathore JS 1985 Some magnetic characteristics of sheared zones J Geodyn 2 291-301

Rathore JS and Henry B 1982 Comparison of strained magnetic fabrics in Dalradian rocks from the southwest Highlands of Scotland J Struc Geol 4 373-384

Rees AI 1965 The use of anisotropy of magnetic susceptshyibility in the estimation of sedimentary fabric Sedimentolshyogy 4 257-271

Rees AI 1968 The production of preferred orientation in a concentrated dispersion of elongated and flattened grains J Geol 76 457-465

Rochetle P 1987 Metamorphic control of the mineralogy of black shales in the Swiss Alps toward the use of magnetic isograds Eanh Planet Sci Lett 84 446-456

Rochette P 1988 Relation entre deformation et metamorshy

f

bull

phisme Alpin dans les schistes noirs Helvetiques Iapport de la fabrique magnetique Geodin Acta 2 (in press)

Rochette P and Vialon P 1984 Development of planar and linear fabrics in Dauphinois shales and slates (French Alps) studied by magnetic anisotropy and its mineralogical conshytrol J Struct Geo 6 33-38

Schwarz E 1974 Magnetic fabrics in massive sulfide deposits Can J Earth Sci 11 1669-1675

Schwartz EJ 1975 Magnetic properties of pyrrhotite and their use in applied geology and geophysics Geo Surv Can Pap 74-59 24 pp

Singh J (now Rathore J) Sanderson DJ and Tariing DH 1975 The magnetic susceptibility anisotropy of deformed rocks from North Cornwall England Tectonophysics 27 141-153

Smith GM and Banetjee SK bull 1987 The dependence of weak field susceptibility on applied magnetic field Phys Earth Planet Inter 46 71-76

Stott GM and Schwerdtner WM 1981 A structural analyshysis of the central part of the Shebandowan metavolcanicshymetasedimentary belt Ontario Dep Mines Toronto Final Repbull Onto Geosci Res Rep No 5349 44 pp

Strangway DW 1970 History of the Earths Magnetic Field McGraw-Hili New York NY 168 pp

Tarling DH 1983 Paleomagnetism Chapman and Hall London 379 pp

Tullis TEbull 1976 Experiments on the origin of slaty cleavage and schistosity Geo Soc Am Bull 87 745-753

Tullis TE and Wood DS 1975 Correlation of finite strain from both reduction bodies and preferred orientation of mica in slate from Wales Geol Soc Am Bull 86 632-638

Urrutia-Fucugauchi J and Odabachian Y 1982 A Bibiograshyphy of Magnetic Susceptibility Anisotropy of Rocks Inshystituto de Geofisica Universidad Nacional Autonoma de Mexico Mexico 42 pp

Uyeda S Fuller MD Belshe JC and Girdler RW 1963 Anisotropy of magnetic susceptibility of rocks and minershyals J Geophys Res 68 279-291

Van den Ende C 1975 On the origin of anisotropy of magshynetic susceptibility in Permian Redbeds from the western part of the Dome de Barrot (S France) In GJ Borradaile et al (Editors) Progress in Geodynamics North-Holland Pub Co Amsterdam pp 176-189

Voight W and Kinoshita S 1907 Bestimmung absoluler Wene von Magnelisierungszahlen insbesondere fUr Krisshytalle Ann Phys 24 492-514

Wagner JJ Hedley FG Steen D Tinkler C and Vaugnat M 1981 Magnetic anisotropy and fabric of some progresshysively deformed ophiolitic gabbros J Geophys Res 86 307-315

Weast RC and Astle MJ (Editors) 1978 CRC handbook of Chemistry and Physics 59th edn CRC Press Palm Beach Fla

20

II

Wing-Fatt L and Stacey FD 1966 Magnetic anisotropy of laboratory materials in which magma flow is simulated Pure AppJ Geophys 6478-80

Wood DS Oertel G Singh J and Bennett HF 1976 Strain and anisotropy in rocks Philos Trans R Soc London Ser A 283 27-42

Zavoyskiy VN 1982 Use of magnetic susceptibility tensor for solving problems in structural geology Izv Akad Nauk SSSR Earth Phys Ser 18 217-223

12

sheet silicates such as chlorite and biotite0

dominate the anisotropy of susceptibility An inshyteresting development of this study is that in slates of the Carpathians in which the anisotropy is due to paramagnetic phyllosilicates the degree of anishysotropy is proportional to the bulk or mean susshyceptibility This has also been reported in Archean slates (Borradaile et aI in press)

Strain response models and multiple sources of susshy

ceptibility

Owens (1974) first drew attention to two imshyportant items that must be taken into account in any interpretation of susceptibility anisotropy in terms of strain Firstly the mineralogical source of the susceptibility should be defined If there are multiple sources of susceptibility the direct applishycation of the simple March model or any other model assuming a penetrative homogeneous magshynetic response is invalid Rochette and Vialon (1984) and Henry (1983) enforced this argument in different ways Slight variations in the proporshytions of minerals with different magnetic anishysotropies may under certain circumstances proshyduce changes in the bulk anisotropy that override any changes in anisotropy due to strain (Borshyradaile 1987b)

The second major point raised by Owens was that the actual strain response model has a major influence on the way in which the anisotropy accumulates from the pre-strain situation For simplicity he considered three models The first was a lineplane model that we can compare to the March model already referred to above (Fig 13a) The second was the viscous or Jeffery model in which the magnetic grain is likened to a rigid ellipsoid undergoing strain-induced motion in a viscous medium The third passive model likens the magnetic grains to passive strain markers Structural geologists may compare this to the model proposed by Ramsays school of structshyural geology to approximate the shape and conseshyquent orientation changes of for example a tectonically deforming passive ellipsoidal marker by the Rrcp equations see Fig 14 (Borradaile 1987a) Care should be taken with the term passhysive some geophysicists use the term to refer to

$e85 ~_068 fRo= 15 ~t=135

C)-shystrain ellipse (j) ~5middot Rs= 20 0_01409lt

Ro= 15 iff=15

original possive passive markers markers after strain

Fig 14 The R rlt1gt model Particles with the original orientashy J

tions (8) shown as a result of strain indicated by the strain ellipse take up new orientations (lt1raquo At the same time the ratios of the original shapes (R1f) change to final shapes (Ry2) The shape-ratio of the strain ellipse is 2 1 as indicated

the lineplane or March model and where they do not appear to imply any similarity to the Rrcp model (eg Cogne and Gapais 1986)

The mechanical response is usually neglected in the correlation of strains and susceptibility anishysotropies Indeed it is likely that many rocks and many types of deformation mechanisms are unsuishytable for establishing a correlation using the preshymises of simple mathematical models involving a single mode of deformation For example if there are relict components of sedimentary magnetic fabrics mixed with the tectonic fabrics or magshynetic fabrics of different tectonic ages a model assuming homogeneity will fail Similarly deforshymation structures that produce domainal fabrics that differently influence the magnetic fabric will cause complications if the magnetic fabric is samshypled on a scale that does not take this into account In particulate flow (Fig 15) the movement of grains may be poorly ordered Some grains move more than their neighbours rotate more or even exchange neighbours despite the fact that on a suitably large polygranular scale the strain may be approximately homogeneous Movement in polyshygranular units is also possible (Fig 16) as has been shown by experiments on analog materials (Means 1977) The scale on which magnetic susceptibility is defined will determine whether or not this preshysents a problem

The deformation mechanisms may be still more complicated The deformation may cause the rock

I bull

13

(01 (bl

Fig IS Particulate flow of a simulated (two-dimensional) aggregate Deformation proceeds from (a) through (c) The motions of particles is somewhat disordered whereas on a large scale the strain may appear to be approximately homogeneous as shown by the

strain ellipse defined by the black particles

J mm Fig 16 Experimentally produced particulate flow of groups of alum grains involving intergranular displacement surfaces

(From Means 1977)

et

deformation gt

bull00 bull

Fig 17 Possible deformation processes in metamorphic rocks that could be significant in the evolution of magnetic fabrics c -intergranular displacement surfaces (may be invisible) d-ductile (may be plastic) deformation of grains e-styloshylitie surfaces and grain-truncation f -penetration of grains g -microfaults (cleavage slip) h-rotation of blocks or groups of grains between faults or other discontinuities m-pressureshysolution material transfer (may be out of system) n-new

minerals crystallise

to be a discontinuum on various scales Lozenges of rock may rotate mass removal may occur loshycally or even to outside the system while grains plastically deform by intercrystalline processes and slide and roll past oneanother (Fig 16) At the same time new minerals may form with their crystallographic orientations controlled by the contemporary stress system Any of these factors could complicate the strain-response model of the rock and the development of its magnetic fabric While all of these processes are unlikely to occur at once the roles of several of these (or others not discussed) have to be assessed before the magnetic fabric can be correlated with the bulk strain Amongst these complications probably the most common one is the growth of new minerals as for example in phyllites schists and gneisses In these cases the explanation of schistosity may be bound up with the origin of the metamorphic texture more than with the strain of the rock (Fig 17) (Borradaile et at 1986)

Experimental studies

Although there has been some early interest in the effects of stress on magnetic susceptibility (eg Nagata 1966 1970 Kean et al 1976) this was associated with strains within the elastic limit Of interest here are the susceptibility changes that occur with large strains due to deformation that is macroscopically ductile if not actually plastic at the crystalline level The problem in the laboratory

bullbull bull bullbull bull bull

bullbull

14

environment is that even at the slowest strain rates that are practicable (10- 6 to 10-9 S-I) most rocks and minerals are not sufficiently ductile at room temperature to fail by the natural mechanisms of metamorphic rocks

Owens and Rutter (1978) first tackled this subshyject with a study of marbles and of calcite Alshythough the diamagnetic susceptibility of calcite is low the mineral is relatively easily deformed in a plastic manner at moderate confining pressures It is also stable at modest experimental temperatures so that Owens and Rutter were able to enhance the ductility by using temperatures up to 500 0 C in combination with pressures of 150 to 300 MPa (15 to 3 kbar) at strain-rates of approximately 10 - 4 to 10 - s s - 1 They achieved strains up to 50 axial-symmetrical (coaxial) shortening of the cylindrical specimens

The marbles they used had essentially isotropic magnetic and optical-crystallographic fabrics inishytially The magnetic anisotropy rapidly reached a plateau intensity at about 45 shortening The optical fabrics and the susceptibility fabric rapidly became axisymmetric to the shortening axis of the specimens This study didmiddot much to confirm the value of magnetic fabrics as indicators of strain and kinematics of deformation but most natural studies are based on ferrirnagnetic or parashymagnetic materials

Natural paramagnetic and ferrimagnetic matershyials are difficult to deform in a realistic manner without raising the temperature Heating will not normally be possible without inducing mineralogishycal changes that might mask susceptibility changes due to deformation Borradaile and Alford (1987) approached this problem by using a synthetic aggregate of sand enriched with magnetite that was cemented with commercial Portland cement The latter has a negligible (diamagnetic) susceptshyibility in comparison with the aggregate and pershymitted the aggregate to shorten by 35 in a ductile manner by axial symmetrical shortening The deshyformation did not involve cataclasis of the sand grains Rather the deformation was accommodshyated by the shearing of the cement gel This pershymitted a grain-shape alignment to develop by rollshying and sliding of the grains The magnetite grains were of the same grain-size as the matrix sand so

bulll1pl -04

bull 03

02 bull bull

01 bullbull01 02 03 04 In (XZ)

00 I I bull I I ~

11 12 13 14 15 (XI Z)

Fig 18 A correlation between the change in degree (fl) of susceptibility anisotropy and the strain ratio in some pure shear experiments on synthetic magnetite-bearing sandshy

stones (From Borradaile and Alford 1987)

that these experiments essentially addressed the problem of the rotational behaviour of the clasts (In most natural sandstones the iron oxide grains are much smaller than the sand clasts) The experiments were at carefully controlled strainshyrates of 5 x 10 - 6 S - 1 and confining pressures of 150 MPa (15 kbar) The maximum and intershymediate principal directions of susceptibility of these specimens rotated very rapidly towards the plane of flattening at rates exceeding the rate of rotation of a line undergoing homogeneous strain (cf the lineplane model) It was inferred that the magnetites rotated rigidly possibly with some plastic deformation The rotation was even more rapid when the matrix was composed of calcite instead of silicate mineral grains For initial susshyceptibility fabrics that were suitably oriented it was found that the change in the degree of anishysotropy was related to the strain by a power law (Fig 18) This serves to emphasise the importance of the initial magnetic fabric Relatively little can be deduced of the strain history from the final magnetic fabric alone Just as the initial ellipsoidal shape and orientation is of paramount importance in the strain analysis of ellipsoidal objects so is a knowledge of similar information for the initial magnetic fabric ellipsoid Although a power law relationship between the change in orientation of specially oriented magnetic fabrics exists in cershytain axial-symmetrical ( pure shear) experiments

15

In ( kmox kim J Calcite -cement - magnetite Q9g~gotes

at 150 MPo 05

04

XZHI XZmiddotH403 --

~ U-C3Z ~ AC -10 SHEAR ZOHEt ~ PURE SHEAR

02

t 01 XZ 20 XZ -115

In (kint kmln )

-0 02 03 04 -05 06 -07 os

bull Fig 19 The paths of incremental changes in magnetic anishysotropy are shown for the experimental deformation of syntheshysised calcite-cement-magnetite specimens The pure shear test produces little change in anisotropy even though the XZ strain ratio reaches 135 In contrast the changes produced in a shear zone (transpressive) are much greater despite the fact

that the ultimate XZ strain ratio for the zone is only 114

it is premature to make extrapolations to nature at the present state of knowledge

Recent work on experimental shear zones of synthetic materials at 150 MPa extends these conshyclusions to the case of transpressive deformation -a non-coaxial strain history (Borradaile and Alshyford in press) The susceptibility ellipsoids rotate rapidly toward stable orientations in which the minimum susceptibility is at a high angle to the shear zone boundaries The magnetic anisotropy changes very rapidly in the shear zones they produce a stronger magnetic fabric than axial symmetrical shortening at the same strain This is shown for two typical incremental- tests on the same synthetic calcite-matrix material at 150 Mpa in Fig 19 A further complication recognised in the experiments is that the magnetic fabrics may be planar (F gt L) whereas the mineral fabrics are constricted (a gt b) or plane strain (a = b) It is not known if these observations are transferable to natural shear zones

Conclusions

The interpretation of natural magnetic fabrics may be more complex than was initially recogshynised but progressive changes in magnetic anishysotropy do occur sympathetically with regional strain gradients despite accompanying regional

metamorphism (eg Hrouda and Janak 1976 Hrouda 1976 Coward and Whalley 1979) Indeed Rochette (1987) has shown that the metashymorphic production of pyrrhotite can enhance the susceptibility and produce a magnetically detectashyble isograd Also in certain rocks there are at least weak correlatiCfls between ratios of principal strains and the ratios of principal susceptibilities Numerous examples of the parallelism of principal susceptibility directions and structural directions (or even principal strain directions) support the contention that genetic relationships do exist beshytween strain and susceptibility in some cases Nevshyertheless these correlations are not universal and it is not possible to predict which natural situashytions will yield susceptibility data that _will faithshyfully represent principal strain directions or prinshycipal strain magnitudes or both For exampl~ magnetic fabrics do not always seem to be reliable kinematic indicators for shear zones and in the case of polyphase deformation later magnetic fabrics do not uniformly overprint earlier ones Magnetic fabrics should not be used for routine methods of strain analysis without further study A more profitable avenue is to determine how the susceptibility and strain tensors relate taking account of the actual strain-response model (deshyformation mechanisms) and the actual minerashylogical sources of susceptibility in that rock inshycluding phases produced by metamorphism A fruitful approach would be to consider the tensorial combination of coexisting magnetic subshyfabrics and successive episodes of magnetic fabric development along the lines initiated by Hrouda (1979)

Relationships between susceptibility and strain are in vogue However the earliest uses of magshynetic studies simply to investigate bulk petroshyfabrics are not yet been fully developed or inshytegrated with detailed petrofabric studies by optishycalor X-ray means Furthermore studies of remashynence and of susceptibility at different field strengths can yield information on magnetic subshyfabrics of different grain-sizes or different mineralogy This information is essential in the study of metamorphism of magnetic phases as well as their preferred orientation The anisotropy of remanence is also a profitable area of study

16 _

because only the ferrimagnetic traces contribute to that sub-fabric

Finally the nondestructive nature of magnetic fabric analysis provides a tool for investigating the progressive deformation or progressive metamorshyphism of a single specimen in laboratory experishyments Experiments on synthetii aggregates indishycate that the initial anisotropy of materials is not easily overprinted by small strains at low tempershyature They demonstrate also that the magnetic fabric ellipsoid spins very rapidly where the chief magnetic mineral is magnetite This is more noticeable when the matrix grains undergo crystal-plastic deformation Experimental shear zones produce greater changes in magnetic shape fabrics than axial-symmetrical shortening (pure shear) at the same strain they can also produce magnetic fabrics differing in symmetry from the grain fabric Such results develop an awareness for the greater complexities of natural structures

Acknowledgments

I wish to thank the Natural Sciences and Enshygineering Research Council of Canada for the continuing support of my work Frantisek Hrouda and Brian Bayly are thanked for constructive criticism of this article Karel Zapletal is thanked for some data on biotite Mel Friedman and Jan Tullis provided helpful reviews

Postscript

Since this paper was accepted for publication P Rochette has drawn attention to unusual inshyverse magnetic fabrics probably produced by single-domain magnetite (Thesis University of Grenoble 1988211 pp)

APPENDIX

Presentation of anisotropy of susceptibility

Magnetic susceptibility is a second rank tensor property conveniently envisaged as a magnitude ellipsoid (see Hrouda 1982 p 38) with three principal axes k max bull kim and k min or k ll bull kn k 33 The average or bulk susceptibility is comshy

monly defined as the arithmetic mean of the three principal values (Ellwood et al 1986-Symshyposium recommendations) but it is not clear why the arithmetic mean is a more appropriate represhysentation of bulk susceptibility than the geometric mean Susceptibility anisotropies for rocks are so low (Figs 9 and 10) that there is often little difference between these two expressions For exshyample seventeen specimens of strongly strained fine schist of the English Borrowdale Volcanic Series have principal susceptibilities in the ratio 104 102 0943 ~

Hrouda (1982) lists 25 different parameters that have been used at various times to represent anishysotropy The most useful are sometimes termed the magnetic lineation and the magnetic foliashytion

L = kmaxkint and F= kintkmin

Note that some authors chose alternative definishytions for Land F (eg Coward 1976) The parameters L and F are plotted vertically and horizontally respectively and compare directly with the ratios used to describe the strain ellipsoid on a Flinn-diagram

a=XY and b= YZ where X 2 Y ~ Z are the principal strains In some instances it is clearer if the natural logarithms of L F and of a and b are plotted

If the ratios of principal susceptibilities are listed individually it is helpful to normalise them so that their product is unity The normalised versions of the principal susceptibilities are related to their ratios by the following relations

kmax = L 2 3 bull pl3

kml

= L -13 F I 3

k = L -13 bull F- 23mm

It is advisable also to present a mean (bulk) susceptibility value This enables the reader to assess the significance of the results (Conference recommendations Ellwood et al 1986) Unforshytunately this has often not been done in the past Commonly one finds that anisotropies are poorly reproducible for rocks with susceptibility lt 10-4

SIjvol Providing cones of confidence about principal directions and standard errors for prinshycipal magnitudes is also useful in this regard

bull

30

2-5

20

-5

10 F=~ WI shy - middotmiddotV j Y

0 5 20 25 30 35

F =(klnkmin)

Fig AI The relationship between Jelineks (1981) P and T parameters and the conventional anisotropy parameters L and

F

The ratios L and F like their counterparts in strain (a and b) are very useful in describing the ellipsoids shape or sense of anisotropy However the distance of the point (L F) from the origin is also a measure of the degree of anisotropy that is to say its departure from sphericity Jelineks (1981) parameters pi and T overcome this T represents sense of anisotropy and ranges from -1 (prolate) to + 1 (oblate) pi (gt 1) expresses degree of anisotropy These are defined as

[ 2(In k -In k~]T= -1

In k itM - In k min 1

pi = exp [ 2( af + a ~ + a~ ) ] ~ where a1 = In(kmaxkb) etc and kb = (kmax k inl

kmin )(l3) The relationship of p and T to L and F is shown in Fig AI

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Borradaile GJ 1981 Particulate flow of rock and the formashytion of rock cleavage Tectonophysics 24 442-455

Borradaile GJ 1987a Analysis of strained sedimentary fabrics Can J Earth Sci 131 121-125

Borradaile GJ 1987b Anisotropy of magnetic susceptibility rock composition versus strain Tectonophysics 138 327-329

Borradaile GJ and Alford C 1987 Relationship between

17

magnetic susceptibility and strain in laboratory experishyments Tectonophysics 133 121-135

Borradaile GJ and Alford C in press Experimental shear zones and magnetic fabrics J Struct Geol

Borradaile GJ and Brown HG 1987 The Shebandowan Group Timiskaming-like Archean rocks in northwestern Ontario Can J Earth Sci 24 185-188

Borradaile GJ and Mothersill JS bull 1984 Coaxial deformed and magnetic fabrics without simply correlated magnitudes of principal values Phys Earth Planet Inter 35 294-300

Borradaile GJ and Tarling D bull 1981 The influence of deforshymation mechanisms on magnetic fabrics in weakly deshyformed rocks Tectonophysics 77 151-168

Borradaile GJ and Tarling D bull 1984 Strain partitioning and magnetic fabrics in particulate flow Can J Earth Sci 21 694-697

Borradaile GJ Mothersill JS Tarling D and Alford C 1986 Sources of magnetic susceptibility in a slate Earth Planet Sci Lett 76 336-340

Borradaile GJ Keeler W Alford C and Sarvas P 1987 Anisotropy of magnetic susceptibility of some metamorphic minerals Phys Earth Planet Inter 48 161-166

Borradaile G Sarvas P Dutka R Stewart R and Stubley M in press Dextral transpression of the northern margin of the Quetico subprovince-magnetic fabrics and microshyfabrics Can J Earth Sci

Carmichael RS 1982 Magnetic properties of minerals and rocks In RC Weast and MJ Ashe (Editors) CRC Handbook of Physical Constants for Rocks CRC Press Roca Baton Fla pp 229-287

Chang SoBR Kirschvink JL and Stolz JF 1987 Biogenic magnetite as a primary remanence carrier in limestone deposits Phys Earth Planet Inter 46 289-303

Clendenen WS Kligfield R Hirt AM and Lowrie W 1988 Strain studies of cleavage development in the Chelmsford Formation Sudbury Basin Ontario Tectonophysics 145 191-211

Cognc JP and Gapais D bull 1986 Passive rotation of hematite during deformation a comparison of simulated and natural redbeds fabrics Tectonophysics 121 365-372

Collinson DW 1983 Methods in Paleomagnetism and Rock Magnetism Chapman and Hall London 500 pp

Coward MP 1976 Strain within ductile shear wnes Tectonophysics 34 181-197

Coward MP and Whalley 1S 1979 Texture and fabric studies across the Kishorn Nappe near Kyle of Lochalsh Western Scotland J Struct Geol 1 259-273

Crimes TP and Oldershaw MA 1967 Paleocurrent demiddot terminations by magnetic fabri measurement on the Cambrian rocks of St Tudwals peninsula North Wales Geol J 5 217-232

Ellwood BBbull Hrouda F and Wagner J-J 1988 Symposia on magnetic fabrics Introductory comments Phys Earth Planet Inter 51 249-252

Fuller MDbull 1964 On the magnetic fabrics of certain rocks 1 Geol 72 368-376

18

II

Goldstein AG bull 1980 Magnetic susceptibility anisotropy of mylonites from the Lake Char Mylonite Zone SE New England Tectonophysics 66 197-211

Graham lW 1954 Magnetic susceptibility anisotropy an unexploited petrofabric element Bull Gool Soc Am 65 1257-1258

Graham lWbull 1966 Significance of magnetic anisotropy in Appalachian sedimentary rocks In lS Steinhard and Tl Smith (Editors) The Earth beneath the Continents Gooshyphys Monogr Am Geophys Union 10 627-648

Hamano Y and Yom ida K 1982 Magnetic anisotropy and porosity of Antarctic chondrites Mem Natl Inst Polar Res Tokyo 25 281-290

Hamilton N 1963 Susceptibility anisotropy measurements on some Silurian siltstones Nature 197 170-171

Hamilton N and Rees AI 1970 The use of magnetic fabric in paleocurrent estimation In SK Runcorn (Editor) Paleogeophysics Academic Press New York NY pp 445-464

Hamilton N and Rees AI 1971 The anisotropy of magnetic susceptibility of the Franciscan Rocks of the Diablo Range Central California Geo Rundsch 60 1103-1124

Hamilton N Owens WH and Rees AI 1968 Laboratory experiments on the production of grain orientation in shearing sand l Goo 76 465-472

Hargraves RB 1959 Magnetic anisotropy and remanent magnetism in hemo-ilmenite from ore deposits at Allard Lake Quebec l Goophys Res 68 293-309

Heider Fbull Dunlop DJ and Sugiura N 1987 Magnetic properties oC hydrothermally recrystallized magnetite crystals Science 236 1287-1290

Henry B 1983 Interpretation quantitative de lanisotropie de susceptibilite magnetique Tectonophysics 91 165-177

Henry B and Daly L 1983 From qualitative to quantitative magnetic anisotropy analysis the prospect of finite strain calibration Tectonophysics 98 327-336

Hirt AM Lowrie W bull Clendenen WS and Kligfield R 1988 The correlation of magnetic anisotropy with strain in the Chelmsford Formation of the Sudbury Basin Ontario Tectonophysics 145 177-189

Hrouda F 1976 The origin of cleavage in the light of magnetic anisotropy investigations Pbys Earth Planet Inshyter 13 132-142

Hrouda F 1979 (reponed 1977) The strain interpretation of magnetic anisotropy in rocks of the Nizky lesenik Mounmiddot tains (Czechoslovakia) Sb Gool Ved (Uzit Geofyz) 16 27-62

Hrouda F 1980 Magnetocrystalline anisotropy of rocks and massive ores a mathematical model study and its fabric implications l Struct Geo1bull 2 459-462

Hrouda F 1982 Magnetic anisotropy of rocks and its apmiddot plication in geology and geophysics Geophys Surv 5 37-82

Hrouda F 1986 The effect of quanz on the magnetic ani sotropy of quartzite Studia Geophys Geod 30 39-45

Hrouda F bull 1987 Mathematical model relationships between

the paramagnetic anisotropy and strain in slates Tectonophysics 142 323-327

Hrouda F and Chlupacova M bull 1980 The magnetic fabric in the Nasavrky massif Cas Mineral Goo 25 17-27

Hrouda F and lanak F 1971 A study of the hematite fabric of some red sediments on the basis of their magnetic susceptibility anisotropy Sediment Geol 6 187-199

Hrouda F and Janak F 1976 The changes in shape of the magnetic susceptibility ellipsoid during progressive metashymorphism and deformation Tectonophysics 34 135-148

Hrouda F and Jelinek V in prep Resolution of ferromagmiddot netic and paramagnetic components of magnetic anishysotropy using combined low-field and high-field anishysotropy measurements I

Hrouda F Chlupacova M and Rejl L 1971 The mimetic fabric of magnetite in some foliated granodiorites as indio cated by magnetic anisotropy Earth Planet Sci Leu 11 381-384

Hrouda F Chlupacova M and Rejl L bull 1972 Changes in magnetite content and magnetite fabric during Cenitization as investigated by petromagnetic methods Neues Jahrb Mineral Abh 117 61-72

Hrouda F Janalc F and Rejl L 1978 Magnetic fabric and ductile deformation of rocks in zones of progressive reshygional metamorphism Ger Beitr Goophys 87 126-134

Hrouda F Jelinek V and Zapletal K 1985a Use of magshynetic propenies of rocks in ore and petroleum geophysics (in Czech) Res rep Goofyz Brno pp 54-75

Hrouda F Siemes H Herres N and Hennig-Micbaeli c 1985b The relationship between the magnetic anisotropy and the cmiddotaxis fabric in a massive hematite ore J Geophys bull 56 174-182

International Critical Tables 1929 McGrawmiddotHiIl New York NY

Ising G 1942 On the magnetic propenies of varved clay Ark Mat Astron Fys 29A 1-37

Jelinek V 1981 Characterization of the magnetic fabrics of rocks Tectonophysics 79 T63-T67

Karlin R Lyle M and Heath GR 1987 Authigenic magmiddot netite formation in suboxic marine sediments Nature 326 490--493

Kean WF Day R Fuller M and Schmidt VA 1976 The effect of uniaxial compression on the initial susceptibility of rocks as a function of grain-size and composition of their constituent titanomagnetites J Geophys Res 81 861-874

Khan MA 1962 Anisotropy of magnetic susceptibility of some igneous and metamorphic rocks J Geophys Res 67 2873-2885

KJigfie1d R Lowrie W and Dalziel I 1977 Magnetic susshyceptibility anisotropy as a strain indicator in the Sudbury Basin Ontario Tectonophysics 40 287-308

KJigfield R Lowrie W and Pfiffner OA 1982 Magnetic propenies of deformed oolitic limestones from the Swiss Alps the correlation of magnetic anisotropy and strain Eclogae Geo He1v 75 127-157

Kneen SJ 1976 The relationship between the magnetic and

19

strain fabrics of some hematite-bearing Welsh Slates Earth Planet Sci Lett 31 413-416

Lamarche G and Rochette P 1987 Microstructural analysis and origin of lineations in the magnetic fabric of some Alpine slates Tectonophysics 139 285-293

Lapointe P Morris WA and Harding KL 1986 Interpreshytation of magnetic susceptibility a new approach 10 geoshyphysical evaluation of the degree of rock alteration Can J

Earth Sci 23 393-401 March A 1932 Mathematische Theorie der Regelung nach

der Korngestait bei afrmer Deformation Z Kristallogrmiddot 81 285-297

Means WD 1977 A deformation experiment in transmitted light Earth Planet Sci Lett 35 169-179

Nagata T 1966 Magnetic susceptibility of compressed rocks J Goomag Geoelectr 18 73-80

Nagata T 1970 Anisotropic magnetic susceptibility of rocks under mechanical stresses Pure App Goophys 78

110-122 Nye JF 1957 The Physical Properties of Crystals Clarendon

Press Oxford 322 pp Oertel G 1983 The relationship of strain and preferred

orientation of phyllosilicale grains in rocks-a review Tectonophysics 100 413-447

Owens WH 1974 Mathematical model studies on factors affecting the magnetic anisotropy of deformed rocks Tectonophysics 24 115-131

Owens WH and Bamford D 1976 Magnetic seismic and other anisotropic properties of rock fabrics Philos Trans R Soc London Ser A 283 55-68

Owens WH and Rutter EH 1978 The development of magnetic susceptibility anisotropy through crystallographic preferred orientation in a calcite rock Phys Earth Planet Inter 16 215-222

Park JKmiddot1983 Paleomagnetism for geologists Geosci Can 4 180-188

Rathore JS 1979 Magnetic susceptibility anisotropy in the Cambrian Slate Belt of North Wales and correlation with strain Tectonophysics 53 83-97

Rathore JS 1985 Some magnetic characteristics of sheared zones J Geodyn 2 291-301

Rathore JS and Henry B 1982 Comparison of strained magnetic fabrics in Dalradian rocks from the southwest Highlands of Scotland J Struc Geol 4 373-384

Rees AI 1965 The use of anisotropy of magnetic susceptshyibility in the estimation of sedimentary fabric Sedimentolshyogy 4 257-271

Rees AI 1968 The production of preferred orientation in a concentrated dispersion of elongated and flattened grains J Geol 76 457-465

Rochetle P 1987 Metamorphic control of the mineralogy of black shales in the Swiss Alps toward the use of magnetic isograds Eanh Planet Sci Lett 84 446-456

Rochette P 1988 Relation entre deformation et metamorshy

f

bull

phisme Alpin dans les schistes noirs Helvetiques Iapport de la fabrique magnetique Geodin Acta 2 (in press)

Rochette P and Vialon P 1984 Development of planar and linear fabrics in Dauphinois shales and slates (French Alps) studied by magnetic anisotropy and its mineralogical conshytrol J Struct Geo 6 33-38

Schwarz E 1974 Magnetic fabrics in massive sulfide deposits Can J Earth Sci 11 1669-1675

Schwartz EJ 1975 Magnetic properties of pyrrhotite and their use in applied geology and geophysics Geo Surv Can Pap 74-59 24 pp

Singh J (now Rathore J) Sanderson DJ and Tariing DH 1975 The magnetic susceptibility anisotropy of deformed rocks from North Cornwall England Tectonophysics 27 141-153

Smith GM and Banetjee SK bull 1987 The dependence of weak field susceptibility on applied magnetic field Phys Earth Planet Inter 46 71-76

Stott GM and Schwerdtner WM 1981 A structural analyshysis of the central part of the Shebandowan metavolcanicshymetasedimentary belt Ontario Dep Mines Toronto Final Repbull Onto Geosci Res Rep No 5349 44 pp

Strangway DW 1970 History of the Earths Magnetic Field McGraw-Hili New York NY 168 pp

Tarling DH 1983 Paleomagnetism Chapman and Hall London 379 pp

Tullis TEbull 1976 Experiments on the origin of slaty cleavage and schistosity Geo Soc Am Bull 87 745-753

Tullis TE and Wood DS 1975 Correlation of finite strain from both reduction bodies and preferred orientation of mica in slate from Wales Geol Soc Am Bull 86 632-638

Urrutia-Fucugauchi J and Odabachian Y 1982 A Bibiograshyphy of Magnetic Susceptibility Anisotropy of Rocks Inshystituto de Geofisica Universidad Nacional Autonoma de Mexico Mexico 42 pp

Uyeda S Fuller MD Belshe JC and Girdler RW 1963 Anisotropy of magnetic susceptibility of rocks and minershyals J Geophys Res 68 279-291

Van den Ende C 1975 On the origin of anisotropy of magshynetic susceptibility in Permian Redbeds from the western part of the Dome de Barrot (S France) In GJ Borradaile et al (Editors) Progress in Geodynamics North-Holland Pub Co Amsterdam pp 176-189

Voight W and Kinoshita S 1907 Bestimmung absoluler Wene von Magnelisierungszahlen insbesondere fUr Krisshytalle Ann Phys 24 492-514

Wagner JJ Hedley FG Steen D Tinkler C and Vaugnat M 1981 Magnetic anisotropy and fabric of some progresshysively deformed ophiolitic gabbros J Geophys Res 86 307-315

Weast RC and Astle MJ (Editors) 1978 CRC handbook of Chemistry and Physics 59th edn CRC Press Palm Beach Fla

20

II

Wing-Fatt L and Stacey FD 1966 Magnetic anisotropy of laboratory materials in which magma flow is simulated Pure AppJ Geophys 6478-80

Wood DS Oertel G Singh J and Bennett HF 1976 Strain and anisotropy in rocks Philos Trans R Soc London Ser A 283 27-42

Zavoyskiy VN 1982 Use of magnetic susceptibility tensor for solving problems in structural geology Izv Akad Nauk SSSR Earth Phys Ser 18 217-223

I bull

13

(01 (bl

Fig IS Particulate flow of a simulated (two-dimensional) aggregate Deformation proceeds from (a) through (c) The motions of particles is somewhat disordered whereas on a large scale the strain may appear to be approximately homogeneous as shown by the

strain ellipse defined by the black particles

J mm Fig 16 Experimentally produced particulate flow of groups of alum grains involving intergranular displacement surfaces

(From Means 1977)

et

deformation gt

bull00 bull

Fig 17 Possible deformation processes in metamorphic rocks that could be significant in the evolution of magnetic fabrics c -intergranular displacement surfaces (may be invisible) d-ductile (may be plastic) deformation of grains e-styloshylitie surfaces and grain-truncation f -penetration of grains g -microfaults (cleavage slip) h-rotation of blocks or groups of grains between faults or other discontinuities m-pressureshysolution material transfer (may be out of system) n-new

minerals crystallise

to be a discontinuum on various scales Lozenges of rock may rotate mass removal may occur loshycally or even to outside the system while grains plastically deform by intercrystalline processes and slide and roll past oneanother (Fig 16) At the same time new minerals may form with their crystallographic orientations controlled by the contemporary stress system Any of these factors could complicate the strain-response model of the rock and the development of its magnetic fabric While all of these processes are unlikely to occur at once the roles of several of these (or others not discussed) have to be assessed before the magnetic fabric can be correlated with the bulk strain Amongst these complications probably the most common one is the growth of new minerals as for example in phyllites schists and gneisses In these cases the explanation of schistosity may be bound up with the origin of the metamorphic texture more than with the strain of the rock (Fig 17) (Borradaile et at 1986)

Experimental studies

Although there has been some early interest in the effects of stress on magnetic susceptibility (eg Nagata 1966 1970 Kean et al 1976) this was associated with strains within the elastic limit Of interest here are the susceptibility changes that occur with large strains due to deformation that is macroscopically ductile if not actually plastic at the crystalline level The problem in the laboratory

bullbull bull bullbull bull bull

bullbull

14

environment is that even at the slowest strain rates that are practicable (10- 6 to 10-9 S-I) most rocks and minerals are not sufficiently ductile at room temperature to fail by the natural mechanisms of metamorphic rocks

Owens and Rutter (1978) first tackled this subshyject with a study of marbles and of calcite Alshythough the diamagnetic susceptibility of calcite is low the mineral is relatively easily deformed in a plastic manner at moderate confining pressures It is also stable at modest experimental temperatures so that Owens and Rutter were able to enhance the ductility by using temperatures up to 500 0 C in combination with pressures of 150 to 300 MPa (15 to 3 kbar) at strain-rates of approximately 10 - 4 to 10 - s s - 1 They achieved strains up to 50 axial-symmetrical (coaxial) shortening of the cylindrical specimens

The marbles they used had essentially isotropic magnetic and optical-crystallographic fabrics inishytially The magnetic anisotropy rapidly reached a plateau intensity at about 45 shortening The optical fabrics and the susceptibility fabric rapidly became axisymmetric to the shortening axis of the specimens This study didmiddot much to confirm the value of magnetic fabrics as indicators of strain and kinematics of deformation but most natural studies are based on ferrirnagnetic or parashymagnetic materials

Natural paramagnetic and ferrimagnetic matershyials are difficult to deform in a realistic manner without raising the temperature Heating will not normally be possible without inducing mineralogishycal changes that might mask susceptibility changes due to deformation Borradaile and Alford (1987) approached this problem by using a synthetic aggregate of sand enriched with magnetite that was cemented with commercial Portland cement The latter has a negligible (diamagnetic) susceptshyibility in comparison with the aggregate and pershymitted the aggregate to shorten by 35 in a ductile manner by axial symmetrical shortening The deshyformation did not involve cataclasis of the sand grains Rather the deformation was accommodshyated by the shearing of the cement gel This pershymitted a grain-shape alignment to develop by rollshying and sliding of the grains The magnetite grains were of the same grain-size as the matrix sand so

bulll1pl -04

bull 03

02 bull bull

01 bullbull01 02 03 04 In (XZ)

00 I I bull I I ~

11 12 13 14 15 (XI Z)

Fig 18 A correlation between the change in degree (fl) of susceptibility anisotropy and the strain ratio in some pure shear experiments on synthetic magnetite-bearing sandshy

stones (From Borradaile and Alford 1987)

that these experiments essentially addressed the problem of the rotational behaviour of the clasts (In most natural sandstones the iron oxide grains are much smaller than the sand clasts) The experiments were at carefully controlled strainshyrates of 5 x 10 - 6 S - 1 and confining pressures of 150 MPa (15 kbar) The maximum and intershymediate principal directions of susceptibility of these specimens rotated very rapidly towards the plane of flattening at rates exceeding the rate of rotation of a line undergoing homogeneous strain (cf the lineplane model) It was inferred that the magnetites rotated rigidly possibly with some plastic deformation The rotation was even more rapid when the matrix was composed of calcite instead of silicate mineral grains For initial susshyceptibility fabrics that were suitably oriented it was found that the change in the degree of anishysotropy was related to the strain by a power law (Fig 18) This serves to emphasise the importance of the initial magnetic fabric Relatively little can be deduced of the strain history from the final magnetic fabric alone Just as the initial ellipsoidal shape and orientation is of paramount importance in the strain analysis of ellipsoidal objects so is a knowledge of similar information for the initial magnetic fabric ellipsoid Although a power law relationship between the change in orientation of specially oriented magnetic fabrics exists in cershytain axial-symmetrical ( pure shear) experiments

15

In ( kmox kim J Calcite -cement - magnetite Q9g~gotes

at 150 MPo 05

04

XZHI XZmiddotH403 --

~ U-C3Z ~ AC -10 SHEAR ZOHEt ~ PURE SHEAR

02

t 01 XZ 20 XZ -115

In (kint kmln )

-0 02 03 04 -05 06 -07 os

bull Fig 19 The paths of incremental changes in magnetic anishysotropy are shown for the experimental deformation of syntheshysised calcite-cement-magnetite specimens The pure shear test produces little change in anisotropy even though the XZ strain ratio reaches 135 In contrast the changes produced in a shear zone (transpressive) are much greater despite the fact

that the ultimate XZ strain ratio for the zone is only 114

it is premature to make extrapolations to nature at the present state of knowledge

Recent work on experimental shear zones of synthetic materials at 150 MPa extends these conshyclusions to the case of transpressive deformation -a non-coaxial strain history (Borradaile and Alshyford in press) The susceptibility ellipsoids rotate rapidly toward stable orientations in which the minimum susceptibility is at a high angle to the shear zone boundaries The magnetic anisotropy changes very rapidly in the shear zones they produce a stronger magnetic fabric than axial symmetrical shortening at the same strain This is shown for two typical incremental- tests on the same synthetic calcite-matrix material at 150 Mpa in Fig 19 A further complication recognised in the experiments is that the magnetic fabrics may be planar (F gt L) whereas the mineral fabrics are constricted (a gt b) or plane strain (a = b) It is not known if these observations are transferable to natural shear zones

Conclusions

The interpretation of natural magnetic fabrics may be more complex than was initially recogshynised but progressive changes in magnetic anishysotropy do occur sympathetically with regional strain gradients despite accompanying regional

metamorphism (eg Hrouda and Janak 1976 Hrouda 1976 Coward and Whalley 1979) Indeed Rochette (1987) has shown that the metashymorphic production of pyrrhotite can enhance the susceptibility and produce a magnetically detectashyble isograd Also in certain rocks there are at least weak correlatiCfls between ratios of principal strains and the ratios of principal susceptibilities Numerous examples of the parallelism of principal susceptibility directions and structural directions (or even principal strain directions) support the contention that genetic relationships do exist beshytween strain and susceptibility in some cases Nevshyertheless these correlations are not universal and it is not possible to predict which natural situashytions will yield susceptibility data that _will faithshyfully represent principal strain directions or prinshycipal strain magnitudes or both For exampl~ magnetic fabrics do not always seem to be reliable kinematic indicators for shear zones and in the case of polyphase deformation later magnetic fabrics do not uniformly overprint earlier ones Magnetic fabrics should not be used for routine methods of strain analysis without further study A more profitable avenue is to determine how the susceptibility and strain tensors relate taking account of the actual strain-response model (deshyformation mechanisms) and the actual minerashylogical sources of susceptibility in that rock inshycluding phases produced by metamorphism A fruitful approach would be to consider the tensorial combination of coexisting magnetic subshyfabrics and successive episodes of magnetic fabric development along the lines initiated by Hrouda (1979)

Relationships between susceptibility and strain are in vogue However the earliest uses of magshynetic studies simply to investigate bulk petroshyfabrics are not yet been fully developed or inshytegrated with detailed petrofabric studies by optishycalor X-ray means Furthermore studies of remashynence and of susceptibility at different field strengths can yield information on magnetic subshyfabrics of different grain-sizes or different mineralogy This information is essential in the study of metamorphism of magnetic phases as well as their preferred orientation The anisotropy of remanence is also a profitable area of study

16 _

because only the ferrimagnetic traces contribute to that sub-fabric

Finally the nondestructive nature of magnetic fabric analysis provides a tool for investigating the progressive deformation or progressive metamorshyphism of a single specimen in laboratory experishyments Experiments on synthetii aggregates indishycate that the initial anisotropy of materials is not easily overprinted by small strains at low tempershyature They demonstrate also that the magnetic fabric ellipsoid spins very rapidly where the chief magnetic mineral is magnetite This is more noticeable when the matrix grains undergo crystal-plastic deformation Experimental shear zones produce greater changes in magnetic shape fabrics than axial-symmetrical shortening (pure shear) at the same strain they can also produce magnetic fabrics differing in symmetry from the grain fabric Such results develop an awareness for the greater complexities of natural structures

Acknowledgments

I wish to thank the Natural Sciences and Enshygineering Research Council of Canada for the continuing support of my work Frantisek Hrouda and Brian Bayly are thanked for constructive criticism of this article Karel Zapletal is thanked for some data on biotite Mel Friedman and Jan Tullis provided helpful reviews

Postscript

Since this paper was accepted for publication P Rochette has drawn attention to unusual inshyverse magnetic fabrics probably produced by single-domain magnetite (Thesis University of Grenoble 1988211 pp)

APPENDIX

Presentation of anisotropy of susceptibility

Magnetic susceptibility is a second rank tensor property conveniently envisaged as a magnitude ellipsoid (see Hrouda 1982 p 38) with three principal axes k max bull kim and k min or k ll bull kn k 33 The average or bulk susceptibility is comshy

monly defined as the arithmetic mean of the three principal values (Ellwood et al 1986-Symshyposium recommendations) but it is not clear why the arithmetic mean is a more appropriate represhysentation of bulk susceptibility than the geometric mean Susceptibility anisotropies for rocks are so low (Figs 9 and 10) that there is often little difference between these two expressions For exshyample seventeen specimens of strongly strained fine schist of the English Borrowdale Volcanic Series have principal susceptibilities in the ratio 104 102 0943 ~

Hrouda (1982) lists 25 different parameters that have been used at various times to represent anishysotropy The most useful are sometimes termed the magnetic lineation and the magnetic foliashytion

L = kmaxkint and F= kintkmin

Note that some authors chose alternative definishytions for Land F (eg Coward 1976) The parameters L and F are plotted vertically and horizontally respectively and compare directly with the ratios used to describe the strain ellipsoid on a Flinn-diagram

a=XY and b= YZ where X 2 Y ~ Z are the principal strains In some instances it is clearer if the natural logarithms of L F and of a and b are plotted

If the ratios of principal susceptibilities are listed individually it is helpful to normalise them so that their product is unity The normalised versions of the principal susceptibilities are related to their ratios by the following relations

kmax = L 2 3 bull pl3

kml

= L -13 F I 3

k = L -13 bull F- 23mm

It is advisable also to present a mean (bulk) susceptibility value This enables the reader to assess the significance of the results (Conference recommendations Ellwood et al 1986) Unforshytunately this has often not been done in the past Commonly one finds that anisotropies are poorly reproducible for rocks with susceptibility lt 10-4

SIjvol Providing cones of confidence about principal directions and standard errors for prinshycipal magnitudes is also useful in this regard

bull

30

2-5

20

-5

10 F=~ WI shy - middotmiddotV j Y

0 5 20 25 30 35

F =(klnkmin)

Fig AI The relationship between Jelineks (1981) P and T parameters and the conventional anisotropy parameters L and

F

The ratios L and F like their counterparts in strain (a and b) are very useful in describing the ellipsoids shape or sense of anisotropy However the distance of the point (L F) from the origin is also a measure of the degree of anisotropy that is to say its departure from sphericity Jelineks (1981) parameters pi and T overcome this T represents sense of anisotropy and ranges from -1 (prolate) to + 1 (oblate) pi (gt 1) expresses degree of anisotropy These are defined as

[ 2(In k -In k~]T= -1

In k itM - In k min 1

pi = exp [ 2( af + a ~ + a~ ) ] ~ where a1 = In(kmaxkb) etc and kb = (kmax k inl

kmin )(l3) The relationship of p and T to L and F is shown in Fig AI

References

Borradaile GJ 1981 Particulate flow of rock and the formashytion of rock cleavage Tectonophysics 24 442-455

Borradaile GJ 1987a Analysis of strained sedimentary fabrics Can J Earth Sci 131 121-125

Borradaile GJ 1987b Anisotropy of magnetic susceptibility rock composition versus strain Tectonophysics 138 327-329

Borradaile GJ and Alford C 1987 Relationship between

17

magnetic susceptibility and strain in laboratory experishyments Tectonophysics 133 121-135

Borradaile GJ and Alford C in press Experimental shear zones and magnetic fabrics J Struct Geol

Borradaile GJ and Brown HG 1987 The Shebandowan Group Timiskaming-like Archean rocks in northwestern Ontario Can J Earth Sci 24 185-188

Borradaile GJ and Mothersill JS bull 1984 Coaxial deformed and magnetic fabrics without simply correlated magnitudes of principal values Phys Earth Planet Inter 35 294-300

Borradaile GJ and Tarling D bull 1981 The influence of deforshymation mechanisms on magnetic fabrics in weakly deshyformed rocks Tectonophysics 77 151-168

Borradaile GJ and Tarling D bull 1984 Strain partitioning and magnetic fabrics in particulate flow Can J Earth Sci 21 694-697

Borradaile GJ Mothersill JS Tarling D and Alford C 1986 Sources of magnetic susceptibility in a slate Earth Planet Sci Lett 76 336-340

Borradaile GJ Keeler W Alford C and Sarvas P 1987 Anisotropy of magnetic susceptibility of some metamorphic minerals Phys Earth Planet Inter 48 161-166

Borradaile G Sarvas P Dutka R Stewart R and Stubley M in press Dextral transpression of the northern margin of the Quetico subprovince-magnetic fabrics and microshyfabrics Can J Earth Sci

Carmichael RS 1982 Magnetic properties of minerals and rocks In RC Weast and MJ Ashe (Editors) CRC Handbook of Physical Constants for Rocks CRC Press Roca Baton Fla pp 229-287

Chang SoBR Kirschvink JL and Stolz JF 1987 Biogenic magnetite as a primary remanence carrier in limestone deposits Phys Earth Planet Inter 46 289-303

Clendenen WS Kligfield R Hirt AM and Lowrie W 1988 Strain studies of cleavage development in the Chelmsford Formation Sudbury Basin Ontario Tectonophysics 145 191-211

Cognc JP and Gapais D bull 1986 Passive rotation of hematite during deformation a comparison of simulated and natural redbeds fabrics Tectonophysics 121 365-372

Collinson DW 1983 Methods in Paleomagnetism and Rock Magnetism Chapman and Hall London 500 pp

Coward MP 1976 Strain within ductile shear wnes Tectonophysics 34 181-197

Coward MP and Whalley 1S 1979 Texture and fabric studies across the Kishorn Nappe near Kyle of Lochalsh Western Scotland J Struct Geol 1 259-273

Crimes TP and Oldershaw MA 1967 Paleocurrent demiddot terminations by magnetic fabri measurement on the Cambrian rocks of St Tudwals peninsula North Wales Geol J 5 217-232

Ellwood BBbull Hrouda F and Wagner J-J 1988 Symposia on magnetic fabrics Introductory comments Phys Earth Planet Inter 51 249-252

Fuller MDbull 1964 On the magnetic fabrics of certain rocks 1 Geol 72 368-376

18

II

Goldstein AG bull 1980 Magnetic susceptibility anisotropy of mylonites from the Lake Char Mylonite Zone SE New England Tectonophysics 66 197-211

Graham lW 1954 Magnetic susceptibility anisotropy an unexploited petrofabric element Bull Gool Soc Am 65 1257-1258

Graham lWbull 1966 Significance of magnetic anisotropy in Appalachian sedimentary rocks In lS Steinhard and Tl Smith (Editors) The Earth beneath the Continents Gooshyphys Monogr Am Geophys Union 10 627-648

Hamano Y and Yom ida K 1982 Magnetic anisotropy and porosity of Antarctic chondrites Mem Natl Inst Polar Res Tokyo 25 281-290

Hamilton N 1963 Susceptibility anisotropy measurements on some Silurian siltstones Nature 197 170-171

Hamilton N and Rees AI 1970 The use of magnetic fabric in paleocurrent estimation In SK Runcorn (Editor) Paleogeophysics Academic Press New York NY pp 445-464

Hamilton N and Rees AI 1971 The anisotropy of magnetic susceptibility of the Franciscan Rocks of the Diablo Range Central California Geo Rundsch 60 1103-1124

Hamilton N Owens WH and Rees AI 1968 Laboratory experiments on the production of grain orientation in shearing sand l Goo 76 465-472

Hargraves RB 1959 Magnetic anisotropy and remanent magnetism in hemo-ilmenite from ore deposits at Allard Lake Quebec l Goophys Res 68 293-309

Heider Fbull Dunlop DJ and Sugiura N 1987 Magnetic properties oC hydrothermally recrystallized magnetite crystals Science 236 1287-1290

Henry B 1983 Interpretation quantitative de lanisotropie de susceptibilite magnetique Tectonophysics 91 165-177

Henry B and Daly L 1983 From qualitative to quantitative magnetic anisotropy analysis the prospect of finite strain calibration Tectonophysics 98 327-336

Hirt AM Lowrie W bull Clendenen WS and Kligfield R 1988 The correlation of magnetic anisotropy with strain in the Chelmsford Formation of the Sudbury Basin Ontario Tectonophysics 145 177-189

Hrouda F 1976 The origin of cleavage in the light of magnetic anisotropy investigations Pbys Earth Planet Inshyter 13 132-142

Hrouda F 1979 (reponed 1977) The strain interpretation of magnetic anisotropy in rocks of the Nizky lesenik Mounmiddot tains (Czechoslovakia) Sb Gool Ved (Uzit Geofyz) 16 27-62

Hrouda F 1980 Magnetocrystalline anisotropy of rocks and massive ores a mathematical model study and its fabric implications l Struct Geo1bull 2 459-462

Hrouda F 1982 Magnetic anisotropy of rocks and its apmiddot plication in geology and geophysics Geophys Surv 5 37-82

Hrouda F 1986 The effect of quanz on the magnetic ani sotropy of quartzite Studia Geophys Geod 30 39-45

Hrouda F bull 1987 Mathematical model relationships between

the paramagnetic anisotropy and strain in slates Tectonophysics 142 323-327

Hrouda F and Chlupacova M bull 1980 The magnetic fabric in the Nasavrky massif Cas Mineral Goo 25 17-27

Hrouda F and lanak F 1971 A study of the hematite fabric of some red sediments on the basis of their magnetic susceptibility anisotropy Sediment Geol 6 187-199

Hrouda F and Janak F 1976 The changes in shape of the magnetic susceptibility ellipsoid during progressive metashymorphism and deformation Tectonophysics 34 135-148

Hrouda F and Jelinek V in prep Resolution of ferromagmiddot netic and paramagnetic components of magnetic anishysotropy using combined low-field and high-field anishysotropy measurements I

Hrouda F Chlupacova M and Rejl L 1971 The mimetic fabric of magnetite in some foliated granodiorites as indio cated by magnetic anisotropy Earth Planet Sci Leu 11 381-384

Hrouda F Chlupacova M and Rejl L bull 1972 Changes in magnetite content and magnetite fabric during Cenitization as investigated by petromagnetic methods Neues Jahrb Mineral Abh 117 61-72

Hrouda F Janalc F and Rejl L 1978 Magnetic fabric and ductile deformation of rocks in zones of progressive reshygional metamorphism Ger Beitr Goophys 87 126-134

Hrouda F Jelinek V and Zapletal K 1985a Use of magshynetic propenies of rocks in ore and petroleum geophysics (in Czech) Res rep Goofyz Brno pp 54-75

Hrouda F Siemes H Herres N and Hennig-Micbaeli c 1985b The relationship between the magnetic anisotropy and the cmiddotaxis fabric in a massive hematite ore J Geophys bull 56 174-182

International Critical Tables 1929 McGrawmiddotHiIl New York NY

Ising G 1942 On the magnetic propenies of varved clay Ark Mat Astron Fys 29A 1-37

Jelinek V 1981 Characterization of the magnetic fabrics of rocks Tectonophysics 79 T63-T67

Karlin R Lyle M and Heath GR 1987 Authigenic magmiddot netite formation in suboxic marine sediments Nature 326 490--493

Kean WF Day R Fuller M and Schmidt VA 1976 The effect of uniaxial compression on the initial susceptibility of rocks as a function of grain-size and composition of their constituent titanomagnetites J Geophys Res 81 861-874

Khan MA 1962 Anisotropy of magnetic susceptibility of some igneous and metamorphic rocks J Geophys Res 67 2873-2885

KJigfie1d R Lowrie W and Dalziel I 1977 Magnetic susshyceptibility anisotropy as a strain indicator in the Sudbury Basin Ontario Tectonophysics 40 287-308

KJigfield R Lowrie W and Pfiffner OA 1982 Magnetic propenies of deformed oolitic limestones from the Swiss Alps the correlation of magnetic anisotropy and strain Eclogae Geo He1v 75 127-157

Kneen SJ 1976 The relationship between the magnetic and

19

strain fabrics of some hematite-bearing Welsh Slates Earth Planet Sci Lett 31 413-416

Lamarche G and Rochette P 1987 Microstructural analysis and origin of lineations in the magnetic fabric of some Alpine slates Tectonophysics 139 285-293

Lapointe P Morris WA and Harding KL 1986 Interpreshytation of magnetic susceptibility a new approach 10 geoshyphysical evaluation of the degree of rock alteration Can J

Earth Sci 23 393-401 March A 1932 Mathematische Theorie der Regelung nach

der Korngestait bei afrmer Deformation Z Kristallogrmiddot 81 285-297

Means WD 1977 A deformation experiment in transmitted light Earth Planet Sci Lett 35 169-179

Nagata T 1966 Magnetic susceptibility of compressed rocks J Goomag Geoelectr 18 73-80

Nagata T 1970 Anisotropic magnetic susceptibility of rocks under mechanical stresses Pure App Goophys 78

110-122 Nye JF 1957 The Physical Properties of Crystals Clarendon

Press Oxford 322 pp Oertel G 1983 The relationship of strain and preferred

orientation of phyllosilicale grains in rocks-a review Tectonophysics 100 413-447

Owens WH 1974 Mathematical model studies on factors affecting the magnetic anisotropy of deformed rocks Tectonophysics 24 115-131

Owens WH and Bamford D 1976 Magnetic seismic and other anisotropic properties of rock fabrics Philos Trans R Soc London Ser A 283 55-68

Owens WH and Rutter EH 1978 The development of magnetic susceptibility anisotropy through crystallographic preferred orientation in a calcite rock Phys Earth Planet Inter 16 215-222

Park JKmiddot1983 Paleomagnetism for geologists Geosci Can 4 180-188

Rathore JS 1979 Magnetic susceptibility anisotropy in the Cambrian Slate Belt of North Wales and correlation with strain Tectonophysics 53 83-97

Rathore JS 1985 Some magnetic characteristics of sheared zones J Geodyn 2 291-301

Rathore JS and Henry B 1982 Comparison of strained magnetic fabrics in Dalradian rocks from the southwest Highlands of Scotland J Struc Geol 4 373-384

Rees AI 1965 The use of anisotropy of magnetic susceptshyibility in the estimation of sedimentary fabric Sedimentolshyogy 4 257-271

Rees AI 1968 The production of preferred orientation in a concentrated dispersion of elongated and flattened grains J Geol 76 457-465

Rochetle P 1987 Metamorphic control of the mineralogy of black shales in the Swiss Alps toward the use of magnetic isograds Eanh Planet Sci Lett 84 446-456

Rochette P 1988 Relation entre deformation et metamorshy

f

bull

phisme Alpin dans les schistes noirs Helvetiques Iapport de la fabrique magnetique Geodin Acta 2 (in press)

Rochette P and Vialon P 1984 Development of planar and linear fabrics in Dauphinois shales and slates (French Alps) studied by magnetic anisotropy and its mineralogical conshytrol J Struct Geo 6 33-38

Schwarz E 1974 Magnetic fabrics in massive sulfide deposits Can J Earth Sci 11 1669-1675

Schwartz EJ 1975 Magnetic properties of pyrrhotite and their use in applied geology and geophysics Geo Surv Can Pap 74-59 24 pp

Singh J (now Rathore J) Sanderson DJ and Tariing DH 1975 The magnetic susceptibility anisotropy of deformed rocks from North Cornwall England Tectonophysics 27 141-153

Smith GM and Banetjee SK bull 1987 The dependence of weak field susceptibility on applied magnetic field Phys Earth Planet Inter 46 71-76

Stott GM and Schwerdtner WM 1981 A structural analyshysis of the central part of the Shebandowan metavolcanicshymetasedimentary belt Ontario Dep Mines Toronto Final Repbull Onto Geosci Res Rep No 5349 44 pp

Strangway DW 1970 History of the Earths Magnetic Field McGraw-Hili New York NY 168 pp

Tarling DH 1983 Paleomagnetism Chapman and Hall London 379 pp

Tullis TEbull 1976 Experiments on the origin of slaty cleavage and schistosity Geo Soc Am Bull 87 745-753

Tullis TE and Wood DS 1975 Correlation of finite strain from both reduction bodies and preferred orientation of mica in slate from Wales Geol Soc Am Bull 86 632-638

Urrutia-Fucugauchi J and Odabachian Y 1982 A Bibiograshyphy of Magnetic Susceptibility Anisotropy of Rocks Inshystituto de Geofisica Universidad Nacional Autonoma de Mexico Mexico 42 pp

Uyeda S Fuller MD Belshe JC and Girdler RW 1963 Anisotropy of magnetic susceptibility of rocks and minershyals J Geophys Res 68 279-291

Van den Ende C 1975 On the origin of anisotropy of magshynetic susceptibility in Permian Redbeds from the western part of the Dome de Barrot (S France) In GJ Borradaile et al (Editors) Progress in Geodynamics North-Holland Pub Co Amsterdam pp 176-189

Voight W and Kinoshita S 1907 Bestimmung absoluler Wene von Magnelisierungszahlen insbesondere fUr Krisshytalle Ann Phys 24 492-514

Wagner JJ Hedley FG Steen D Tinkler C and Vaugnat M 1981 Magnetic anisotropy and fabric of some progresshysively deformed ophiolitic gabbros J Geophys Res 86 307-315

Weast RC and Astle MJ (Editors) 1978 CRC handbook of Chemistry and Physics 59th edn CRC Press Palm Beach Fla

20

II

Wing-Fatt L and Stacey FD 1966 Magnetic anisotropy of laboratory materials in which magma flow is simulated Pure AppJ Geophys 6478-80

Wood DS Oertel G Singh J and Bennett HF 1976 Strain and anisotropy in rocks Philos Trans R Soc London Ser A 283 27-42

Zavoyskiy VN 1982 Use of magnetic susceptibility tensor for solving problems in structural geology Izv Akad Nauk SSSR Earth Phys Ser 18 217-223

bullbull bull bullbull bull bull

bullbull

14

environment is that even at the slowest strain rates that are practicable (10- 6 to 10-9 S-I) most rocks and minerals are not sufficiently ductile at room temperature to fail by the natural mechanisms of metamorphic rocks

Owens and Rutter (1978) first tackled this subshyject with a study of marbles and of calcite Alshythough the diamagnetic susceptibility of calcite is low the mineral is relatively easily deformed in a plastic manner at moderate confining pressures It is also stable at modest experimental temperatures so that Owens and Rutter were able to enhance the ductility by using temperatures up to 500 0 C in combination with pressures of 150 to 300 MPa (15 to 3 kbar) at strain-rates of approximately 10 - 4 to 10 - s s - 1 They achieved strains up to 50 axial-symmetrical (coaxial) shortening of the cylindrical specimens

The marbles they used had essentially isotropic magnetic and optical-crystallographic fabrics inishytially The magnetic anisotropy rapidly reached a plateau intensity at about 45 shortening The optical fabrics and the susceptibility fabric rapidly became axisymmetric to the shortening axis of the specimens This study didmiddot much to confirm the value of magnetic fabrics as indicators of strain and kinematics of deformation but most natural studies are based on ferrirnagnetic or parashymagnetic materials

Natural paramagnetic and ferrimagnetic matershyials are difficult to deform in a realistic manner without raising the temperature Heating will not normally be possible without inducing mineralogishycal changes that might mask susceptibility changes due to deformation Borradaile and Alford (1987) approached this problem by using a synthetic aggregate of sand enriched with magnetite that was cemented with commercial Portland cement The latter has a negligible (diamagnetic) susceptshyibility in comparison with the aggregate and pershymitted the aggregate to shorten by 35 in a ductile manner by axial symmetrical shortening The deshyformation did not involve cataclasis of the sand grains Rather the deformation was accommodshyated by the shearing of the cement gel This pershymitted a grain-shape alignment to develop by rollshying and sliding of the grains The magnetite grains were of the same grain-size as the matrix sand so

bulll1pl -04

bull 03

02 bull bull

01 bullbull01 02 03 04 In (XZ)

00 I I bull I I ~

11 12 13 14 15 (XI Z)

Fig 18 A correlation between the change in degree (fl) of susceptibility anisotropy and the strain ratio in some pure shear experiments on synthetic magnetite-bearing sandshy

stones (From Borradaile and Alford 1987)

that these experiments essentially addressed the problem of the rotational behaviour of the clasts (In most natural sandstones the iron oxide grains are much smaller than the sand clasts) The experiments were at carefully controlled strainshyrates of 5 x 10 - 6 S - 1 and confining pressures of 150 MPa (15 kbar) The maximum and intershymediate principal directions of susceptibility of these specimens rotated very rapidly towards the plane of flattening at rates exceeding the rate of rotation of a line undergoing homogeneous strain (cf the lineplane model) It was inferred that the magnetites rotated rigidly possibly with some plastic deformation The rotation was even more rapid when the matrix was composed of calcite instead of silicate mineral grains For initial susshyceptibility fabrics that were suitably oriented it was found that the change in the degree of anishysotropy was related to the strain by a power law (Fig 18) This serves to emphasise the importance of the initial magnetic fabric Relatively little can be deduced of the strain history from the final magnetic fabric alone Just as the initial ellipsoidal shape and orientation is of paramount importance in the strain analysis of ellipsoidal objects so is a knowledge of similar information for the initial magnetic fabric ellipsoid Although a power law relationship between the change in orientation of specially oriented magnetic fabrics exists in cershytain axial-symmetrical ( pure shear) experiments

15

In ( kmox kim J Calcite -cement - magnetite Q9g~gotes

at 150 MPo 05

04

XZHI XZmiddotH403 --

~ U-C3Z ~ AC -10 SHEAR ZOHEt ~ PURE SHEAR

02

t 01 XZ 20 XZ -115

In (kint kmln )

-0 02 03 04 -05 06 -07 os

bull Fig 19 The paths of incremental changes in magnetic anishysotropy are shown for the experimental deformation of syntheshysised calcite-cement-magnetite specimens The pure shear test produces little change in anisotropy even though the XZ strain ratio reaches 135 In contrast the changes produced in a shear zone (transpressive) are much greater despite the fact

that the ultimate XZ strain ratio for the zone is only 114

it is premature to make extrapolations to nature at the present state of knowledge

Recent work on experimental shear zones of synthetic materials at 150 MPa extends these conshyclusions to the case of transpressive deformation -a non-coaxial strain history (Borradaile and Alshyford in press) The susceptibility ellipsoids rotate rapidly toward stable orientations in which the minimum susceptibility is at a high angle to the shear zone boundaries The magnetic anisotropy changes very rapidly in the shear zones they produce a stronger magnetic fabric than axial symmetrical shortening at the same strain This is shown for two typical incremental- tests on the same synthetic calcite-matrix material at 150 Mpa in Fig 19 A further complication recognised in the experiments is that the magnetic fabrics may be planar (F gt L) whereas the mineral fabrics are constricted (a gt b) or plane strain (a = b) It is not known if these observations are transferable to natural shear zones

Conclusions

The interpretation of natural magnetic fabrics may be more complex than was initially recogshynised but progressive changes in magnetic anishysotropy do occur sympathetically with regional strain gradients despite accompanying regional

metamorphism (eg Hrouda and Janak 1976 Hrouda 1976 Coward and Whalley 1979) Indeed Rochette (1987) has shown that the metashymorphic production of pyrrhotite can enhance the susceptibility and produce a magnetically detectashyble isograd Also in certain rocks there are at least weak correlatiCfls between ratios of principal strains and the ratios of principal susceptibilities Numerous examples of the parallelism of principal susceptibility directions and structural directions (or even principal strain directions) support the contention that genetic relationships do exist beshytween strain and susceptibility in some cases Nevshyertheless these correlations are not universal and it is not possible to predict which natural situashytions will yield susceptibility data that _will faithshyfully represent principal strain directions or prinshycipal strain magnitudes or both For exampl~ magnetic fabrics do not always seem to be reliable kinematic indicators for shear zones and in the case of polyphase deformation later magnetic fabrics do not uniformly overprint earlier ones Magnetic fabrics should not be used for routine methods of strain analysis without further study A more profitable avenue is to determine how the susceptibility and strain tensors relate taking account of the actual strain-response model (deshyformation mechanisms) and the actual minerashylogical sources of susceptibility in that rock inshycluding phases produced by metamorphism A fruitful approach would be to consider the tensorial combination of coexisting magnetic subshyfabrics and successive episodes of magnetic fabric development along the lines initiated by Hrouda (1979)

Relationships between susceptibility and strain are in vogue However the earliest uses of magshynetic studies simply to investigate bulk petroshyfabrics are not yet been fully developed or inshytegrated with detailed petrofabric studies by optishycalor X-ray means Furthermore studies of remashynence and of susceptibility at different field strengths can yield information on magnetic subshyfabrics of different grain-sizes or different mineralogy This information is essential in the study of metamorphism of magnetic phases as well as their preferred orientation The anisotropy of remanence is also a profitable area of study

16 _

because only the ferrimagnetic traces contribute to that sub-fabric

Finally the nondestructive nature of magnetic fabric analysis provides a tool for investigating the progressive deformation or progressive metamorshyphism of a single specimen in laboratory experishyments Experiments on synthetii aggregates indishycate that the initial anisotropy of materials is not easily overprinted by small strains at low tempershyature They demonstrate also that the magnetic fabric ellipsoid spins very rapidly where the chief magnetic mineral is magnetite This is more noticeable when the matrix grains undergo crystal-plastic deformation Experimental shear zones produce greater changes in magnetic shape fabrics than axial-symmetrical shortening (pure shear) at the same strain they can also produce magnetic fabrics differing in symmetry from the grain fabric Such results develop an awareness for the greater complexities of natural structures

Acknowledgments

I wish to thank the Natural Sciences and Enshygineering Research Council of Canada for the continuing support of my work Frantisek Hrouda and Brian Bayly are thanked for constructive criticism of this article Karel Zapletal is thanked for some data on biotite Mel Friedman and Jan Tullis provided helpful reviews

Postscript

Since this paper was accepted for publication P Rochette has drawn attention to unusual inshyverse magnetic fabrics probably produced by single-domain magnetite (Thesis University of Grenoble 1988211 pp)

APPENDIX

Presentation of anisotropy of susceptibility

Magnetic susceptibility is a second rank tensor property conveniently envisaged as a magnitude ellipsoid (see Hrouda 1982 p 38) with three principal axes k max bull kim and k min or k ll bull kn k 33 The average or bulk susceptibility is comshy

monly defined as the arithmetic mean of the three principal values (Ellwood et al 1986-Symshyposium recommendations) but it is not clear why the arithmetic mean is a more appropriate represhysentation of bulk susceptibility than the geometric mean Susceptibility anisotropies for rocks are so low (Figs 9 and 10) that there is often little difference between these two expressions For exshyample seventeen specimens of strongly strained fine schist of the English Borrowdale Volcanic Series have principal susceptibilities in the ratio 104 102 0943 ~

Hrouda (1982) lists 25 different parameters that have been used at various times to represent anishysotropy The most useful are sometimes termed the magnetic lineation and the magnetic foliashytion

L = kmaxkint and F= kintkmin

Note that some authors chose alternative definishytions for Land F (eg Coward 1976) The parameters L and F are plotted vertically and horizontally respectively and compare directly with the ratios used to describe the strain ellipsoid on a Flinn-diagram

a=XY and b= YZ where X 2 Y ~ Z are the principal strains In some instances it is clearer if the natural logarithms of L F and of a and b are plotted

If the ratios of principal susceptibilities are listed individually it is helpful to normalise them so that their product is unity The normalised versions of the principal susceptibilities are related to their ratios by the following relations

kmax = L 2 3 bull pl3

kml

= L -13 F I 3

k = L -13 bull F- 23mm

It is advisable also to present a mean (bulk) susceptibility value This enables the reader to assess the significance of the results (Conference recommendations Ellwood et al 1986) Unforshytunately this has often not been done in the past Commonly one finds that anisotropies are poorly reproducible for rocks with susceptibility lt 10-4

SIjvol Providing cones of confidence about principal directions and standard errors for prinshycipal magnitudes is also useful in this regard

bull

30

2-5

20

-5

10 F=~ WI shy - middotmiddotV j Y

0 5 20 25 30 35

F =(klnkmin)

Fig AI The relationship between Jelineks (1981) P and T parameters and the conventional anisotropy parameters L and

F

The ratios L and F like their counterparts in strain (a and b) are very useful in describing the ellipsoids shape or sense of anisotropy However the distance of the point (L F) from the origin is also a measure of the degree of anisotropy that is to say its departure from sphericity Jelineks (1981) parameters pi and T overcome this T represents sense of anisotropy and ranges from -1 (prolate) to + 1 (oblate) pi (gt 1) expresses degree of anisotropy These are defined as

[ 2(In k -In k~]T= -1

In k itM - In k min 1

pi = exp [ 2( af + a ~ + a~ ) ] ~ where a1 = In(kmaxkb) etc and kb = (kmax k inl

kmin )(l3) The relationship of p and T to L and F is shown in Fig AI

References

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Borradaile GJ 1987a Analysis of strained sedimentary fabrics Can J Earth Sci 131 121-125

Borradaile GJ 1987b Anisotropy of magnetic susceptibility rock composition versus strain Tectonophysics 138 327-329

Borradaile GJ and Alford C 1987 Relationship between

17

magnetic susceptibility and strain in laboratory experishyments Tectonophysics 133 121-135

Borradaile GJ and Alford C in press Experimental shear zones and magnetic fabrics J Struct Geol

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Borradaile GJ and Tarling D bull 1981 The influence of deforshymation mechanisms on magnetic fabrics in weakly deshyformed rocks Tectonophysics 77 151-168

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Borradaile GJ Mothersill JS Tarling D and Alford C 1986 Sources of magnetic susceptibility in a slate Earth Planet Sci Lett 76 336-340

Borradaile GJ Keeler W Alford C and Sarvas P 1987 Anisotropy of magnetic susceptibility of some metamorphic minerals Phys Earth Planet Inter 48 161-166

Borradaile G Sarvas P Dutka R Stewart R and Stubley M in press Dextral transpression of the northern margin of the Quetico subprovince-magnetic fabrics and microshyfabrics Can J Earth Sci

Carmichael RS 1982 Magnetic properties of minerals and rocks In RC Weast and MJ Ashe (Editors) CRC Handbook of Physical Constants for Rocks CRC Press Roca Baton Fla pp 229-287

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Cognc JP and Gapais D bull 1986 Passive rotation of hematite during deformation a comparison of simulated and natural redbeds fabrics Tectonophysics 121 365-372

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Goldstein AG bull 1980 Magnetic susceptibility anisotropy of mylonites from the Lake Char Mylonite Zone SE New England Tectonophysics 66 197-211

Graham lW 1954 Magnetic susceptibility anisotropy an unexploited petrofabric element Bull Gool Soc Am 65 1257-1258

Graham lWbull 1966 Significance of magnetic anisotropy in Appalachian sedimentary rocks In lS Steinhard and Tl Smith (Editors) The Earth beneath the Continents Gooshyphys Monogr Am Geophys Union 10 627-648

Hamano Y and Yom ida K 1982 Magnetic anisotropy and porosity of Antarctic chondrites Mem Natl Inst Polar Res Tokyo 25 281-290

Hamilton N 1963 Susceptibility anisotropy measurements on some Silurian siltstones Nature 197 170-171

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Hamilton N and Rees AI 1971 The anisotropy of magnetic susceptibility of the Franciscan Rocks of the Diablo Range Central California Geo Rundsch 60 1103-1124

Hamilton N Owens WH and Rees AI 1968 Laboratory experiments on the production of grain orientation in shearing sand l Goo 76 465-472

Hargraves RB 1959 Magnetic anisotropy and remanent magnetism in hemo-ilmenite from ore deposits at Allard Lake Quebec l Goophys Res 68 293-309

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Henry B 1983 Interpretation quantitative de lanisotropie de susceptibilite magnetique Tectonophysics 91 165-177

Henry B and Daly L 1983 From qualitative to quantitative magnetic anisotropy analysis the prospect of finite strain calibration Tectonophysics 98 327-336

Hirt AM Lowrie W bull Clendenen WS and Kligfield R 1988 The correlation of magnetic anisotropy with strain in the Chelmsford Formation of the Sudbury Basin Ontario Tectonophysics 145 177-189

Hrouda F 1976 The origin of cleavage in the light of magnetic anisotropy investigations Pbys Earth Planet Inshyter 13 132-142

Hrouda F 1979 (reponed 1977) The strain interpretation of magnetic anisotropy in rocks of the Nizky lesenik Mounmiddot tains (Czechoslovakia) Sb Gool Ved (Uzit Geofyz) 16 27-62

Hrouda F 1980 Magnetocrystalline anisotropy of rocks and massive ores a mathematical model study and its fabric implications l Struct Geo1bull 2 459-462

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Hrouda F 1986 The effect of quanz on the magnetic ani sotropy of quartzite Studia Geophys Geod 30 39-45

Hrouda F bull 1987 Mathematical model relationships between

the paramagnetic anisotropy and strain in slates Tectonophysics 142 323-327

Hrouda F and Chlupacova M bull 1980 The magnetic fabric in the Nasavrky massif Cas Mineral Goo 25 17-27

Hrouda F and lanak F 1971 A study of the hematite fabric of some red sediments on the basis of their magnetic susceptibility anisotropy Sediment Geol 6 187-199

Hrouda F and Janak F 1976 The changes in shape of the magnetic susceptibility ellipsoid during progressive metashymorphism and deformation Tectonophysics 34 135-148

Hrouda F and Jelinek V in prep Resolution of ferromagmiddot netic and paramagnetic components of magnetic anishysotropy using combined low-field and high-field anishysotropy measurements I

Hrouda F Chlupacova M and Rejl L 1971 The mimetic fabric of magnetite in some foliated granodiorites as indio cated by magnetic anisotropy Earth Planet Sci Leu 11 381-384

Hrouda F Chlupacova M and Rejl L bull 1972 Changes in magnetite content and magnetite fabric during Cenitization as investigated by petromagnetic methods Neues Jahrb Mineral Abh 117 61-72

Hrouda F Janalc F and Rejl L 1978 Magnetic fabric and ductile deformation of rocks in zones of progressive reshygional metamorphism Ger Beitr Goophys 87 126-134

Hrouda F Jelinek V and Zapletal K 1985a Use of magshynetic propenies of rocks in ore and petroleum geophysics (in Czech) Res rep Goofyz Brno pp 54-75

Hrouda F Siemes H Herres N and Hennig-Micbaeli c 1985b The relationship between the magnetic anisotropy and the cmiddotaxis fabric in a massive hematite ore J Geophys bull 56 174-182

International Critical Tables 1929 McGrawmiddotHiIl New York NY

Ising G 1942 On the magnetic propenies of varved clay Ark Mat Astron Fys 29A 1-37

Jelinek V 1981 Characterization of the magnetic fabrics of rocks Tectonophysics 79 T63-T67

Karlin R Lyle M and Heath GR 1987 Authigenic magmiddot netite formation in suboxic marine sediments Nature 326 490--493

Kean WF Day R Fuller M and Schmidt VA 1976 The effect of uniaxial compression on the initial susceptibility of rocks as a function of grain-size and composition of their constituent titanomagnetites J Geophys Res 81 861-874

Khan MA 1962 Anisotropy of magnetic susceptibility of some igneous and metamorphic rocks J Geophys Res 67 2873-2885

KJigfie1d R Lowrie W and Dalziel I 1977 Magnetic susshyceptibility anisotropy as a strain indicator in the Sudbury Basin Ontario Tectonophysics 40 287-308

KJigfield R Lowrie W and Pfiffner OA 1982 Magnetic propenies of deformed oolitic limestones from the Swiss Alps the correlation of magnetic anisotropy and strain Eclogae Geo He1v 75 127-157

Kneen SJ 1976 The relationship between the magnetic and

19

strain fabrics of some hematite-bearing Welsh Slates Earth Planet Sci Lett 31 413-416

Lamarche G and Rochette P 1987 Microstructural analysis and origin of lineations in the magnetic fabric of some Alpine slates Tectonophysics 139 285-293

Lapointe P Morris WA and Harding KL 1986 Interpreshytation of magnetic susceptibility a new approach 10 geoshyphysical evaluation of the degree of rock alteration Can J

Earth Sci 23 393-401 March A 1932 Mathematische Theorie der Regelung nach

der Korngestait bei afrmer Deformation Z Kristallogrmiddot 81 285-297

Means WD 1977 A deformation experiment in transmitted light Earth Planet Sci Lett 35 169-179

Nagata T 1966 Magnetic susceptibility of compressed rocks J Goomag Geoelectr 18 73-80

Nagata T 1970 Anisotropic magnetic susceptibility of rocks under mechanical stresses Pure App Goophys 78

110-122 Nye JF 1957 The Physical Properties of Crystals Clarendon

Press Oxford 322 pp Oertel G 1983 The relationship of strain and preferred

orientation of phyllosilicale grains in rocks-a review Tectonophysics 100 413-447

Owens WH 1974 Mathematical model studies on factors affecting the magnetic anisotropy of deformed rocks Tectonophysics 24 115-131

Owens WH and Bamford D 1976 Magnetic seismic and other anisotropic properties of rock fabrics Philos Trans R Soc London Ser A 283 55-68

Owens WH and Rutter EH 1978 The development of magnetic susceptibility anisotropy through crystallographic preferred orientation in a calcite rock Phys Earth Planet Inter 16 215-222

Park JKmiddot1983 Paleomagnetism for geologists Geosci Can 4 180-188

Rathore JS 1979 Magnetic susceptibility anisotropy in the Cambrian Slate Belt of North Wales and correlation with strain Tectonophysics 53 83-97

Rathore JS 1985 Some magnetic characteristics of sheared zones J Geodyn 2 291-301

Rathore JS and Henry B 1982 Comparison of strained magnetic fabrics in Dalradian rocks from the southwest Highlands of Scotland J Struc Geol 4 373-384

Rees AI 1965 The use of anisotropy of magnetic susceptshyibility in the estimation of sedimentary fabric Sedimentolshyogy 4 257-271

Rees AI 1968 The production of preferred orientation in a concentrated dispersion of elongated and flattened grains J Geol 76 457-465

Rochetle P 1987 Metamorphic control of the mineralogy of black shales in the Swiss Alps toward the use of magnetic isograds Eanh Planet Sci Lett 84 446-456

Rochette P 1988 Relation entre deformation et metamorshy

f

bull

phisme Alpin dans les schistes noirs Helvetiques Iapport de la fabrique magnetique Geodin Acta 2 (in press)

Rochette P and Vialon P 1984 Development of planar and linear fabrics in Dauphinois shales and slates (French Alps) studied by magnetic anisotropy and its mineralogical conshytrol J Struct Geo 6 33-38

Schwarz E 1974 Magnetic fabrics in massive sulfide deposits Can J Earth Sci 11 1669-1675

Schwartz EJ 1975 Magnetic properties of pyrrhotite and their use in applied geology and geophysics Geo Surv Can Pap 74-59 24 pp

Singh J (now Rathore J) Sanderson DJ and Tariing DH 1975 The magnetic susceptibility anisotropy of deformed rocks from North Cornwall England Tectonophysics 27 141-153

Smith GM and Banetjee SK bull 1987 The dependence of weak field susceptibility on applied magnetic field Phys Earth Planet Inter 46 71-76

Stott GM and Schwerdtner WM 1981 A structural analyshysis of the central part of the Shebandowan metavolcanicshymetasedimentary belt Ontario Dep Mines Toronto Final Repbull Onto Geosci Res Rep No 5349 44 pp

Strangway DW 1970 History of the Earths Magnetic Field McGraw-Hili New York NY 168 pp

Tarling DH 1983 Paleomagnetism Chapman and Hall London 379 pp

Tullis TEbull 1976 Experiments on the origin of slaty cleavage and schistosity Geo Soc Am Bull 87 745-753

Tullis TE and Wood DS 1975 Correlation of finite strain from both reduction bodies and preferred orientation of mica in slate from Wales Geol Soc Am Bull 86 632-638

Urrutia-Fucugauchi J and Odabachian Y 1982 A Bibiograshyphy of Magnetic Susceptibility Anisotropy of Rocks Inshystituto de Geofisica Universidad Nacional Autonoma de Mexico Mexico 42 pp

Uyeda S Fuller MD Belshe JC and Girdler RW 1963 Anisotropy of magnetic susceptibility of rocks and minershyals J Geophys Res 68 279-291

Van den Ende C 1975 On the origin of anisotropy of magshynetic susceptibility in Permian Redbeds from the western part of the Dome de Barrot (S France) In GJ Borradaile et al (Editors) Progress in Geodynamics North-Holland Pub Co Amsterdam pp 176-189

Voight W and Kinoshita S 1907 Bestimmung absoluler Wene von Magnelisierungszahlen insbesondere fUr Krisshytalle Ann Phys 24 492-514

Wagner JJ Hedley FG Steen D Tinkler C and Vaugnat M 1981 Magnetic anisotropy and fabric of some progresshysively deformed ophiolitic gabbros J Geophys Res 86 307-315

Weast RC and Astle MJ (Editors) 1978 CRC handbook of Chemistry and Physics 59th edn CRC Press Palm Beach Fla

20

II

Wing-Fatt L and Stacey FD 1966 Magnetic anisotropy of laboratory materials in which magma flow is simulated Pure AppJ Geophys 6478-80

Wood DS Oertel G Singh J and Bennett HF 1976 Strain and anisotropy in rocks Philos Trans R Soc London Ser A 283 27-42

Zavoyskiy VN 1982 Use of magnetic susceptibility tensor for solving problems in structural geology Izv Akad Nauk SSSR Earth Phys Ser 18 217-223

15

In ( kmox kim J Calcite -cement - magnetite Q9g~gotes

at 150 MPo 05

04

XZHI XZmiddotH403 --

~ U-C3Z ~ AC -10 SHEAR ZOHEt ~ PURE SHEAR

02

t 01 XZ 20 XZ -115

In (kint kmln )

-0 02 03 04 -05 06 -07 os

bull Fig 19 The paths of incremental changes in magnetic anishysotropy are shown for the experimental deformation of syntheshysised calcite-cement-magnetite specimens The pure shear test produces little change in anisotropy even though the XZ strain ratio reaches 135 In contrast the changes produced in a shear zone (transpressive) are much greater despite the fact

that the ultimate XZ strain ratio for the zone is only 114

it is premature to make extrapolations to nature at the present state of knowledge

Recent work on experimental shear zones of synthetic materials at 150 MPa extends these conshyclusions to the case of transpressive deformation -a non-coaxial strain history (Borradaile and Alshyford in press) The susceptibility ellipsoids rotate rapidly toward stable orientations in which the minimum susceptibility is at a high angle to the shear zone boundaries The magnetic anisotropy changes very rapidly in the shear zones they produce a stronger magnetic fabric than axial symmetrical shortening at the same strain This is shown for two typical incremental- tests on the same synthetic calcite-matrix material at 150 Mpa in Fig 19 A further complication recognised in the experiments is that the magnetic fabrics may be planar (F gt L) whereas the mineral fabrics are constricted (a gt b) or plane strain (a = b) It is not known if these observations are transferable to natural shear zones

Conclusions

The interpretation of natural magnetic fabrics may be more complex than was initially recogshynised but progressive changes in magnetic anishysotropy do occur sympathetically with regional strain gradients despite accompanying regional

metamorphism (eg Hrouda and Janak 1976 Hrouda 1976 Coward and Whalley 1979) Indeed Rochette (1987) has shown that the metashymorphic production of pyrrhotite can enhance the susceptibility and produce a magnetically detectashyble isograd Also in certain rocks there are at least weak correlatiCfls between ratios of principal strains and the ratios of principal susceptibilities Numerous examples of the parallelism of principal susceptibility directions and structural directions (or even principal strain directions) support the contention that genetic relationships do exist beshytween strain and susceptibility in some cases Nevshyertheless these correlations are not universal and it is not possible to predict which natural situashytions will yield susceptibility data that _will faithshyfully represent principal strain directions or prinshycipal strain magnitudes or both For exampl~ magnetic fabrics do not always seem to be reliable kinematic indicators for shear zones and in the case of polyphase deformation later magnetic fabrics do not uniformly overprint earlier ones Magnetic fabrics should not be used for routine methods of strain analysis without further study A more profitable avenue is to determine how the susceptibility and strain tensors relate taking account of the actual strain-response model (deshyformation mechanisms) and the actual minerashylogical sources of susceptibility in that rock inshycluding phases produced by metamorphism A fruitful approach would be to consider the tensorial combination of coexisting magnetic subshyfabrics and successive episodes of magnetic fabric development along the lines initiated by Hrouda (1979)

Relationships between susceptibility and strain are in vogue However the earliest uses of magshynetic studies simply to investigate bulk petroshyfabrics are not yet been fully developed or inshytegrated with detailed petrofabric studies by optishycalor X-ray means Furthermore studies of remashynence and of susceptibility at different field strengths can yield information on magnetic subshyfabrics of different grain-sizes or different mineralogy This information is essential in the study of metamorphism of magnetic phases as well as their preferred orientation The anisotropy of remanence is also a profitable area of study

16 _

because only the ferrimagnetic traces contribute to that sub-fabric

Finally the nondestructive nature of magnetic fabric analysis provides a tool for investigating the progressive deformation or progressive metamorshyphism of a single specimen in laboratory experishyments Experiments on synthetii aggregates indishycate that the initial anisotropy of materials is not easily overprinted by small strains at low tempershyature They demonstrate also that the magnetic fabric ellipsoid spins very rapidly where the chief magnetic mineral is magnetite This is more noticeable when the matrix grains undergo crystal-plastic deformation Experimental shear zones produce greater changes in magnetic shape fabrics than axial-symmetrical shortening (pure shear) at the same strain they can also produce magnetic fabrics differing in symmetry from the grain fabric Such results develop an awareness for the greater complexities of natural structures

Acknowledgments

I wish to thank the Natural Sciences and Enshygineering Research Council of Canada for the continuing support of my work Frantisek Hrouda and Brian Bayly are thanked for constructive criticism of this article Karel Zapletal is thanked for some data on biotite Mel Friedman and Jan Tullis provided helpful reviews

Postscript

Since this paper was accepted for publication P Rochette has drawn attention to unusual inshyverse magnetic fabrics probably produced by single-domain magnetite (Thesis University of Grenoble 1988211 pp)

APPENDIX

Presentation of anisotropy of susceptibility

Magnetic susceptibility is a second rank tensor property conveniently envisaged as a magnitude ellipsoid (see Hrouda 1982 p 38) with three principal axes k max bull kim and k min or k ll bull kn k 33 The average or bulk susceptibility is comshy

monly defined as the arithmetic mean of the three principal values (Ellwood et al 1986-Symshyposium recommendations) but it is not clear why the arithmetic mean is a more appropriate represhysentation of bulk susceptibility than the geometric mean Susceptibility anisotropies for rocks are so low (Figs 9 and 10) that there is often little difference between these two expressions For exshyample seventeen specimens of strongly strained fine schist of the English Borrowdale Volcanic Series have principal susceptibilities in the ratio 104 102 0943 ~

Hrouda (1982) lists 25 different parameters that have been used at various times to represent anishysotropy The most useful are sometimes termed the magnetic lineation and the magnetic foliashytion

L = kmaxkint and F= kintkmin

Note that some authors chose alternative definishytions for Land F (eg Coward 1976) The parameters L and F are plotted vertically and horizontally respectively and compare directly with the ratios used to describe the strain ellipsoid on a Flinn-diagram

a=XY and b= YZ where X 2 Y ~ Z are the principal strains In some instances it is clearer if the natural logarithms of L F and of a and b are plotted

If the ratios of principal susceptibilities are listed individually it is helpful to normalise them so that their product is unity The normalised versions of the principal susceptibilities are related to their ratios by the following relations

kmax = L 2 3 bull pl3

kml

= L -13 F I 3

k = L -13 bull F- 23mm

It is advisable also to present a mean (bulk) susceptibility value This enables the reader to assess the significance of the results (Conference recommendations Ellwood et al 1986) Unforshytunately this has often not been done in the past Commonly one finds that anisotropies are poorly reproducible for rocks with susceptibility lt 10-4

SIjvol Providing cones of confidence about principal directions and standard errors for prinshycipal magnitudes is also useful in this regard

bull

30

2-5

20

-5

10 F=~ WI shy - middotmiddotV j Y

0 5 20 25 30 35

F =(klnkmin)

Fig AI The relationship between Jelineks (1981) P and T parameters and the conventional anisotropy parameters L and

F

The ratios L and F like their counterparts in strain (a and b) are very useful in describing the ellipsoids shape or sense of anisotropy However the distance of the point (L F) from the origin is also a measure of the degree of anisotropy that is to say its departure from sphericity Jelineks (1981) parameters pi and T overcome this T represents sense of anisotropy and ranges from -1 (prolate) to + 1 (oblate) pi (gt 1) expresses degree of anisotropy These are defined as

[ 2(In k -In k~]T= -1

In k itM - In k min 1

pi = exp [ 2( af + a ~ + a~ ) ] ~ where a1 = In(kmaxkb) etc and kb = (kmax k inl

kmin )(l3) The relationship of p and T to L and F is shown in Fig AI

References

Borradaile GJ 1981 Particulate flow of rock and the formashytion of rock cleavage Tectonophysics 24 442-455

Borradaile GJ 1987a Analysis of strained sedimentary fabrics Can J Earth Sci 131 121-125

Borradaile GJ 1987b Anisotropy of magnetic susceptibility rock composition versus strain Tectonophysics 138 327-329

Borradaile GJ and Alford C 1987 Relationship between

17

magnetic susceptibility and strain in laboratory experishyments Tectonophysics 133 121-135

Borradaile GJ and Alford C in press Experimental shear zones and magnetic fabrics J Struct Geol

Borradaile GJ and Brown HG 1987 The Shebandowan Group Timiskaming-like Archean rocks in northwestern Ontario Can J Earth Sci 24 185-188

Borradaile GJ and Mothersill JS bull 1984 Coaxial deformed and magnetic fabrics without simply correlated magnitudes of principal values Phys Earth Planet Inter 35 294-300

Borradaile GJ and Tarling D bull 1981 The influence of deforshymation mechanisms on magnetic fabrics in weakly deshyformed rocks Tectonophysics 77 151-168

Borradaile GJ and Tarling D bull 1984 Strain partitioning and magnetic fabrics in particulate flow Can J Earth Sci 21 694-697

Borradaile GJ Mothersill JS Tarling D and Alford C 1986 Sources of magnetic susceptibility in a slate Earth Planet Sci Lett 76 336-340

Borradaile GJ Keeler W Alford C and Sarvas P 1987 Anisotropy of magnetic susceptibility of some metamorphic minerals Phys Earth Planet Inter 48 161-166

Borradaile G Sarvas P Dutka R Stewart R and Stubley M in press Dextral transpression of the northern margin of the Quetico subprovince-magnetic fabrics and microshyfabrics Can J Earth Sci

Carmichael RS 1982 Magnetic properties of minerals and rocks In RC Weast and MJ Ashe (Editors) CRC Handbook of Physical Constants for Rocks CRC Press Roca Baton Fla pp 229-287

Chang SoBR Kirschvink JL and Stolz JF 1987 Biogenic magnetite as a primary remanence carrier in limestone deposits Phys Earth Planet Inter 46 289-303

Clendenen WS Kligfield R Hirt AM and Lowrie W 1988 Strain studies of cleavage development in the Chelmsford Formation Sudbury Basin Ontario Tectonophysics 145 191-211

Cognc JP and Gapais D bull 1986 Passive rotation of hematite during deformation a comparison of simulated and natural redbeds fabrics Tectonophysics 121 365-372

Collinson DW 1983 Methods in Paleomagnetism and Rock Magnetism Chapman and Hall London 500 pp

Coward MP 1976 Strain within ductile shear wnes Tectonophysics 34 181-197

Coward MP and Whalley 1S 1979 Texture and fabric studies across the Kishorn Nappe near Kyle of Lochalsh Western Scotland J Struct Geol 1 259-273

Crimes TP and Oldershaw MA 1967 Paleocurrent demiddot terminations by magnetic fabri measurement on the Cambrian rocks of St Tudwals peninsula North Wales Geol J 5 217-232

Ellwood BBbull Hrouda F and Wagner J-J 1988 Symposia on magnetic fabrics Introductory comments Phys Earth Planet Inter 51 249-252

Fuller MDbull 1964 On the magnetic fabrics of certain rocks 1 Geol 72 368-376

18

II

Goldstein AG bull 1980 Magnetic susceptibility anisotropy of mylonites from the Lake Char Mylonite Zone SE New England Tectonophysics 66 197-211

Graham lW 1954 Magnetic susceptibility anisotropy an unexploited petrofabric element Bull Gool Soc Am 65 1257-1258

Graham lWbull 1966 Significance of magnetic anisotropy in Appalachian sedimentary rocks In lS Steinhard and Tl Smith (Editors) The Earth beneath the Continents Gooshyphys Monogr Am Geophys Union 10 627-648

Hamano Y and Yom ida K 1982 Magnetic anisotropy and porosity of Antarctic chondrites Mem Natl Inst Polar Res Tokyo 25 281-290

Hamilton N 1963 Susceptibility anisotropy measurements on some Silurian siltstones Nature 197 170-171

Hamilton N and Rees AI 1970 The use of magnetic fabric in paleocurrent estimation In SK Runcorn (Editor) Paleogeophysics Academic Press New York NY pp 445-464

Hamilton N and Rees AI 1971 The anisotropy of magnetic susceptibility of the Franciscan Rocks of the Diablo Range Central California Geo Rundsch 60 1103-1124

Hamilton N Owens WH and Rees AI 1968 Laboratory experiments on the production of grain orientation in shearing sand l Goo 76 465-472

Hargraves RB 1959 Magnetic anisotropy and remanent magnetism in hemo-ilmenite from ore deposits at Allard Lake Quebec l Goophys Res 68 293-309

Heider Fbull Dunlop DJ and Sugiura N 1987 Magnetic properties oC hydrothermally recrystallized magnetite crystals Science 236 1287-1290

Henry B 1983 Interpretation quantitative de lanisotropie de susceptibilite magnetique Tectonophysics 91 165-177

Henry B and Daly L 1983 From qualitative to quantitative magnetic anisotropy analysis the prospect of finite strain calibration Tectonophysics 98 327-336

Hirt AM Lowrie W bull Clendenen WS and Kligfield R 1988 The correlation of magnetic anisotropy with strain in the Chelmsford Formation of the Sudbury Basin Ontario Tectonophysics 145 177-189

Hrouda F 1976 The origin of cleavage in the light of magnetic anisotropy investigations Pbys Earth Planet Inshyter 13 132-142

Hrouda F 1979 (reponed 1977) The strain interpretation of magnetic anisotropy in rocks of the Nizky lesenik Mounmiddot tains (Czechoslovakia) Sb Gool Ved (Uzit Geofyz) 16 27-62

Hrouda F 1980 Magnetocrystalline anisotropy of rocks and massive ores a mathematical model study and its fabric implications l Struct Geo1bull 2 459-462

Hrouda F 1982 Magnetic anisotropy of rocks and its apmiddot plication in geology and geophysics Geophys Surv 5 37-82

Hrouda F 1986 The effect of quanz on the magnetic ani sotropy of quartzite Studia Geophys Geod 30 39-45

Hrouda F bull 1987 Mathematical model relationships between

the paramagnetic anisotropy and strain in slates Tectonophysics 142 323-327

Hrouda F and Chlupacova M bull 1980 The magnetic fabric in the Nasavrky massif Cas Mineral Goo 25 17-27

Hrouda F and lanak F 1971 A study of the hematite fabric of some red sediments on the basis of their magnetic susceptibility anisotropy Sediment Geol 6 187-199

Hrouda F and Janak F 1976 The changes in shape of the magnetic susceptibility ellipsoid during progressive metashymorphism and deformation Tectonophysics 34 135-148

Hrouda F and Jelinek V in prep Resolution of ferromagmiddot netic and paramagnetic components of magnetic anishysotropy using combined low-field and high-field anishysotropy measurements I

Hrouda F Chlupacova M and Rejl L 1971 The mimetic fabric of magnetite in some foliated granodiorites as indio cated by magnetic anisotropy Earth Planet Sci Leu 11 381-384

Hrouda F Chlupacova M and Rejl L bull 1972 Changes in magnetite content and magnetite fabric during Cenitization as investigated by petromagnetic methods Neues Jahrb Mineral Abh 117 61-72

Hrouda F Janalc F and Rejl L 1978 Magnetic fabric and ductile deformation of rocks in zones of progressive reshygional metamorphism Ger Beitr Goophys 87 126-134

Hrouda F Jelinek V and Zapletal K 1985a Use of magshynetic propenies of rocks in ore and petroleum geophysics (in Czech) Res rep Goofyz Brno pp 54-75

Hrouda F Siemes H Herres N and Hennig-Micbaeli c 1985b The relationship between the magnetic anisotropy and the cmiddotaxis fabric in a massive hematite ore J Geophys bull 56 174-182

International Critical Tables 1929 McGrawmiddotHiIl New York NY

Ising G 1942 On the magnetic propenies of varved clay Ark Mat Astron Fys 29A 1-37

Jelinek V 1981 Characterization of the magnetic fabrics of rocks Tectonophysics 79 T63-T67

Karlin R Lyle M and Heath GR 1987 Authigenic magmiddot netite formation in suboxic marine sediments Nature 326 490--493

Kean WF Day R Fuller M and Schmidt VA 1976 The effect of uniaxial compression on the initial susceptibility of rocks as a function of grain-size and composition of their constituent titanomagnetites J Geophys Res 81 861-874

Khan MA 1962 Anisotropy of magnetic susceptibility of some igneous and metamorphic rocks J Geophys Res 67 2873-2885

KJigfie1d R Lowrie W and Dalziel I 1977 Magnetic susshyceptibility anisotropy as a strain indicator in the Sudbury Basin Ontario Tectonophysics 40 287-308

KJigfield R Lowrie W and Pfiffner OA 1982 Magnetic propenies of deformed oolitic limestones from the Swiss Alps the correlation of magnetic anisotropy and strain Eclogae Geo He1v 75 127-157

Kneen SJ 1976 The relationship between the magnetic and

19

strain fabrics of some hematite-bearing Welsh Slates Earth Planet Sci Lett 31 413-416

Lamarche G and Rochette P 1987 Microstructural analysis and origin of lineations in the magnetic fabric of some Alpine slates Tectonophysics 139 285-293

Lapointe P Morris WA and Harding KL 1986 Interpreshytation of magnetic susceptibility a new approach 10 geoshyphysical evaluation of the degree of rock alteration Can J

Earth Sci 23 393-401 March A 1932 Mathematische Theorie der Regelung nach

der Korngestait bei afrmer Deformation Z Kristallogrmiddot 81 285-297

Means WD 1977 A deformation experiment in transmitted light Earth Planet Sci Lett 35 169-179

Nagata T 1966 Magnetic susceptibility of compressed rocks J Goomag Geoelectr 18 73-80

Nagata T 1970 Anisotropic magnetic susceptibility of rocks under mechanical stresses Pure App Goophys 78

110-122 Nye JF 1957 The Physical Properties of Crystals Clarendon

Press Oxford 322 pp Oertel G 1983 The relationship of strain and preferred

orientation of phyllosilicale grains in rocks-a review Tectonophysics 100 413-447

Owens WH 1974 Mathematical model studies on factors affecting the magnetic anisotropy of deformed rocks Tectonophysics 24 115-131

Owens WH and Bamford D 1976 Magnetic seismic and other anisotropic properties of rock fabrics Philos Trans R Soc London Ser A 283 55-68

Owens WH and Rutter EH 1978 The development of magnetic susceptibility anisotropy through crystallographic preferred orientation in a calcite rock Phys Earth Planet Inter 16 215-222

Park JKmiddot1983 Paleomagnetism for geologists Geosci Can 4 180-188

Rathore JS 1979 Magnetic susceptibility anisotropy in the Cambrian Slate Belt of North Wales and correlation with strain Tectonophysics 53 83-97

Rathore JS 1985 Some magnetic characteristics of sheared zones J Geodyn 2 291-301

Rathore JS and Henry B 1982 Comparison of strained magnetic fabrics in Dalradian rocks from the southwest Highlands of Scotland J Struc Geol 4 373-384

Rees AI 1965 The use of anisotropy of magnetic susceptshyibility in the estimation of sedimentary fabric Sedimentolshyogy 4 257-271

Rees AI 1968 The production of preferred orientation in a concentrated dispersion of elongated and flattened grains J Geol 76 457-465

Rochetle P 1987 Metamorphic control of the mineralogy of black shales in the Swiss Alps toward the use of magnetic isograds Eanh Planet Sci Lett 84 446-456

Rochette P 1988 Relation entre deformation et metamorshy

f

bull

phisme Alpin dans les schistes noirs Helvetiques Iapport de la fabrique magnetique Geodin Acta 2 (in press)

Rochette P and Vialon P 1984 Development of planar and linear fabrics in Dauphinois shales and slates (French Alps) studied by magnetic anisotropy and its mineralogical conshytrol J Struct Geo 6 33-38

Schwarz E 1974 Magnetic fabrics in massive sulfide deposits Can J Earth Sci 11 1669-1675

Schwartz EJ 1975 Magnetic properties of pyrrhotite and their use in applied geology and geophysics Geo Surv Can Pap 74-59 24 pp

Singh J (now Rathore J) Sanderson DJ and Tariing DH 1975 The magnetic susceptibility anisotropy of deformed rocks from North Cornwall England Tectonophysics 27 141-153

Smith GM and Banetjee SK bull 1987 The dependence of weak field susceptibility on applied magnetic field Phys Earth Planet Inter 46 71-76

Stott GM and Schwerdtner WM 1981 A structural analyshysis of the central part of the Shebandowan metavolcanicshymetasedimentary belt Ontario Dep Mines Toronto Final Repbull Onto Geosci Res Rep No 5349 44 pp

Strangway DW 1970 History of the Earths Magnetic Field McGraw-Hili New York NY 168 pp

Tarling DH 1983 Paleomagnetism Chapman and Hall London 379 pp

Tullis TEbull 1976 Experiments on the origin of slaty cleavage and schistosity Geo Soc Am Bull 87 745-753

Tullis TE and Wood DS 1975 Correlation of finite strain from both reduction bodies and preferred orientation of mica in slate from Wales Geol Soc Am Bull 86 632-638

Urrutia-Fucugauchi J and Odabachian Y 1982 A Bibiograshyphy of Magnetic Susceptibility Anisotropy of Rocks Inshystituto de Geofisica Universidad Nacional Autonoma de Mexico Mexico 42 pp

Uyeda S Fuller MD Belshe JC and Girdler RW 1963 Anisotropy of magnetic susceptibility of rocks and minershyals J Geophys Res 68 279-291

Van den Ende C 1975 On the origin of anisotropy of magshynetic susceptibility in Permian Redbeds from the western part of the Dome de Barrot (S France) In GJ Borradaile et al (Editors) Progress in Geodynamics North-Holland Pub Co Amsterdam pp 176-189

Voight W and Kinoshita S 1907 Bestimmung absoluler Wene von Magnelisierungszahlen insbesondere fUr Krisshytalle Ann Phys 24 492-514

Wagner JJ Hedley FG Steen D Tinkler C and Vaugnat M 1981 Magnetic anisotropy and fabric of some progresshysively deformed ophiolitic gabbros J Geophys Res 86 307-315

Weast RC and Astle MJ (Editors) 1978 CRC handbook of Chemistry and Physics 59th edn CRC Press Palm Beach Fla

20

II

Wing-Fatt L and Stacey FD 1966 Magnetic anisotropy of laboratory materials in which magma flow is simulated Pure AppJ Geophys 6478-80

Wood DS Oertel G Singh J and Bennett HF 1976 Strain and anisotropy in rocks Philos Trans R Soc London Ser A 283 27-42

Zavoyskiy VN 1982 Use of magnetic susceptibility tensor for solving problems in structural geology Izv Akad Nauk SSSR Earth Phys Ser 18 217-223

16 _

because only the ferrimagnetic traces contribute to that sub-fabric

Finally the nondestructive nature of magnetic fabric analysis provides a tool for investigating the progressive deformation or progressive metamorshyphism of a single specimen in laboratory experishyments Experiments on synthetii aggregates indishycate that the initial anisotropy of materials is not easily overprinted by small strains at low tempershyature They demonstrate also that the magnetic fabric ellipsoid spins very rapidly where the chief magnetic mineral is magnetite This is more noticeable when the matrix grains undergo crystal-plastic deformation Experimental shear zones produce greater changes in magnetic shape fabrics than axial-symmetrical shortening (pure shear) at the same strain they can also produce magnetic fabrics differing in symmetry from the grain fabric Such results develop an awareness for the greater complexities of natural structures

Acknowledgments

I wish to thank the Natural Sciences and Enshygineering Research Council of Canada for the continuing support of my work Frantisek Hrouda and Brian Bayly are thanked for constructive criticism of this article Karel Zapletal is thanked for some data on biotite Mel Friedman and Jan Tullis provided helpful reviews

Postscript

Since this paper was accepted for publication P Rochette has drawn attention to unusual inshyverse magnetic fabrics probably produced by single-domain magnetite (Thesis University of Grenoble 1988211 pp)

APPENDIX

Presentation of anisotropy of susceptibility

Magnetic susceptibility is a second rank tensor property conveniently envisaged as a magnitude ellipsoid (see Hrouda 1982 p 38) with three principal axes k max bull kim and k min or k ll bull kn k 33 The average or bulk susceptibility is comshy

monly defined as the arithmetic mean of the three principal values (Ellwood et al 1986-Symshyposium recommendations) but it is not clear why the arithmetic mean is a more appropriate represhysentation of bulk susceptibility than the geometric mean Susceptibility anisotropies for rocks are so low (Figs 9 and 10) that there is often little difference between these two expressions For exshyample seventeen specimens of strongly strained fine schist of the English Borrowdale Volcanic Series have principal susceptibilities in the ratio 104 102 0943 ~

Hrouda (1982) lists 25 different parameters that have been used at various times to represent anishysotropy The most useful are sometimes termed the magnetic lineation and the magnetic foliashytion

L = kmaxkint and F= kintkmin

Note that some authors chose alternative definishytions for Land F (eg Coward 1976) The parameters L and F are plotted vertically and horizontally respectively and compare directly with the ratios used to describe the strain ellipsoid on a Flinn-diagram

a=XY and b= YZ where X 2 Y ~ Z are the principal strains In some instances it is clearer if the natural logarithms of L F and of a and b are plotted

If the ratios of principal susceptibilities are listed individually it is helpful to normalise them so that their product is unity The normalised versions of the principal susceptibilities are related to their ratios by the following relations

kmax = L 2 3 bull pl3

kml

= L -13 F I 3

k = L -13 bull F- 23mm

It is advisable also to present a mean (bulk) susceptibility value This enables the reader to assess the significance of the results (Conference recommendations Ellwood et al 1986) Unforshytunately this has often not been done in the past Commonly one finds that anisotropies are poorly reproducible for rocks with susceptibility lt 10-4

SIjvol Providing cones of confidence about principal directions and standard errors for prinshycipal magnitudes is also useful in this regard

bull

30

2-5

20

-5

10 F=~ WI shy - middotmiddotV j Y

0 5 20 25 30 35

F =(klnkmin)

Fig AI The relationship between Jelineks (1981) P and T parameters and the conventional anisotropy parameters L and

F

The ratios L and F like their counterparts in strain (a and b) are very useful in describing the ellipsoids shape or sense of anisotropy However the distance of the point (L F) from the origin is also a measure of the degree of anisotropy that is to say its departure from sphericity Jelineks (1981) parameters pi and T overcome this T represents sense of anisotropy and ranges from -1 (prolate) to + 1 (oblate) pi (gt 1) expresses degree of anisotropy These are defined as

[ 2(In k -In k~]T= -1

In k itM - In k min 1

pi = exp [ 2( af + a ~ + a~ ) ] ~ where a1 = In(kmaxkb) etc and kb = (kmax k inl

kmin )(l3) The relationship of p and T to L and F is shown in Fig AI

References

Borradaile GJ 1981 Particulate flow of rock and the formashytion of rock cleavage Tectonophysics 24 442-455

Borradaile GJ 1987a Analysis of strained sedimentary fabrics Can J Earth Sci 131 121-125

Borradaile GJ 1987b Anisotropy of magnetic susceptibility rock composition versus strain Tectonophysics 138 327-329

Borradaile GJ and Alford C 1987 Relationship between

17

magnetic susceptibility and strain in laboratory experishyments Tectonophysics 133 121-135

Borradaile GJ and Alford C in press Experimental shear zones and magnetic fabrics J Struct Geol

Borradaile GJ and Brown HG 1987 The Shebandowan Group Timiskaming-like Archean rocks in northwestern Ontario Can J Earth Sci 24 185-188

Borradaile GJ and Mothersill JS bull 1984 Coaxial deformed and magnetic fabrics without simply correlated magnitudes of principal values Phys Earth Planet Inter 35 294-300

Borradaile GJ and Tarling D bull 1981 The influence of deforshymation mechanisms on magnetic fabrics in weakly deshyformed rocks Tectonophysics 77 151-168

Borradaile GJ and Tarling D bull 1984 Strain partitioning and magnetic fabrics in particulate flow Can J Earth Sci 21 694-697

Borradaile GJ Mothersill JS Tarling D and Alford C 1986 Sources of magnetic susceptibility in a slate Earth Planet Sci Lett 76 336-340

Borradaile GJ Keeler W Alford C and Sarvas P 1987 Anisotropy of magnetic susceptibility of some metamorphic minerals Phys Earth Planet Inter 48 161-166

Borradaile G Sarvas P Dutka R Stewart R and Stubley M in press Dextral transpression of the northern margin of the Quetico subprovince-magnetic fabrics and microshyfabrics Can J Earth Sci

Carmichael RS 1982 Magnetic properties of minerals and rocks In RC Weast and MJ Ashe (Editors) CRC Handbook of Physical Constants for Rocks CRC Press Roca Baton Fla pp 229-287

Chang SoBR Kirschvink JL and Stolz JF 1987 Biogenic magnetite as a primary remanence carrier in limestone deposits Phys Earth Planet Inter 46 289-303

Clendenen WS Kligfield R Hirt AM and Lowrie W 1988 Strain studies of cleavage development in the Chelmsford Formation Sudbury Basin Ontario Tectonophysics 145 191-211

Cognc JP and Gapais D bull 1986 Passive rotation of hematite during deformation a comparison of simulated and natural redbeds fabrics Tectonophysics 121 365-372

Collinson DW 1983 Methods in Paleomagnetism and Rock Magnetism Chapman and Hall London 500 pp

Coward MP 1976 Strain within ductile shear wnes Tectonophysics 34 181-197

Coward MP and Whalley 1S 1979 Texture and fabric studies across the Kishorn Nappe near Kyle of Lochalsh Western Scotland J Struct Geol 1 259-273

Crimes TP and Oldershaw MA 1967 Paleocurrent demiddot terminations by magnetic fabri measurement on the Cambrian rocks of St Tudwals peninsula North Wales Geol J 5 217-232

Ellwood BBbull Hrouda F and Wagner J-J 1988 Symposia on magnetic fabrics Introductory comments Phys Earth Planet Inter 51 249-252

Fuller MDbull 1964 On the magnetic fabrics of certain rocks 1 Geol 72 368-376

18

II

Goldstein AG bull 1980 Magnetic susceptibility anisotropy of mylonites from the Lake Char Mylonite Zone SE New England Tectonophysics 66 197-211

Graham lW 1954 Magnetic susceptibility anisotropy an unexploited petrofabric element Bull Gool Soc Am 65 1257-1258

Graham lWbull 1966 Significance of magnetic anisotropy in Appalachian sedimentary rocks In lS Steinhard and Tl Smith (Editors) The Earth beneath the Continents Gooshyphys Monogr Am Geophys Union 10 627-648

Hamano Y and Yom ida K 1982 Magnetic anisotropy and porosity of Antarctic chondrites Mem Natl Inst Polar Res Tokyo 25 281-290

Hamilton N 1963 Susceptibility anisotropy measurements on some Silurian siltstones Nature 197 170-171

Hamilton N and Rees AI 1970 The use of magnetic fabric in paleocurrent estimation In SK Runcorn (Editor) Paleogeophysics Academic Press New York NY pp 445-464

Hamilton N and Rees AI 1971 The anisotropy of magnetic susceptibility of the Franciscan Rocks of the Diablo Range Central California Geo Rundsch 60 1103-1124

Hamilton N Owens WH and Rees AI 1968 Laboratory experiments on the production of grain orientation in shearing sand l Goo 76 465-472

Hargraves RB 1959 Magnetic anisotropy and remanent magnetism in hemo-ilmenite from ore deposits at Allard Lake Quebec l Goophys Res 68 293-309

Heider Fbull Dunlop DJ and Sugiura N 1987 Magnetic properties oC hydrothermally recrystallized magnetite crystals Science 236 1287-1290

Henry B 1983 Interpretation quantitative de lanisotropie de susceptibilite magnetique Tectonophysics 91 165-177

Henry B and Daly L 1983 From qualitative to quantitative magnetic anisotropy analysis the prospect of finite strain calibration Tectonophysics 98 327-336

Hirt AM Lowrie W bull Clendenen WS and Kligfield R 1988 The correlation of magnetic anisotropy with strain in the Chelmsford Formation of the Sudbury Basin Ontario Tectonophysics 145 177-189

Hrouda F 1976 The origin of cleavage in the light of magnetic anisotropy investigations Pbys Earth Planet Inshyter 13 132-142

Hrouda F 1979 (reponed 1977) The strain interpretation of magnetic anisotropy in rocks of the Nizky lesenik Mounmiddot tains (Czechoslovakia) Sb Gool Ved (Uzit Geofyz) 16 27-62

Hrouda F 1980 Magnetocrystalline anisotropy of rocks and massive ores a mathematical model study and its fabric implications l Struct Geo1bull 2 459-462

Hrouda F 1982 Magnetic anisotropy of rocks and its apmiddot plication in geology and geophysics Geophys Surv 5 37-82

Hrouda F 1986 The effect of quanz on the magnetic ani sotropy of quartzite Studia Geophys Geod 30 39-45

Hrouda F bull 1987 Mathematical model relationships between

the paramagnetic anisotropy and strain in slates Tectonophysics 142 323-327

Hrouda F and Chlupacova M bull 1980 The magnetic fabric in the Nasavrky massif Cas Mineral Goo 25 17-27

Hrouda F and lanak F 1971 A study of the hematite fabric of some red sediments on the basis of their magnetic susceptibility anisotropy Sediment Geol 6 187-199

Hrouda F and Janak F 1976 The changes in shape of the magnetic susceptibility ellipsoid during progressive metashymorphism and deformation Tectonophysics 34 135-148

Hrouda F and Jelinek V in prep Resolution of ferromagmiddot netic and paramagnetic components of magnetic anishysotropy using combined low-field and high-field anishysotropy measurements I

Hrouda F Chlupacova M and Rejl L 1971 The mimetic fabric of magnetite in some foliated granodiorites as indio cated by magnetic anisotropy Earth Planet Sci Leu 11 381-384

Hrouda F Chlupacova M and Rejl L bull 1972 Changes in magnetite content and magnetite fabric during Cenitization as investigated by petromagnetic methods Neues Jahrb Mineral Abh 117 61-72

Hrouda F Janalc F and Rejl L 1978 Magnetic fabric and ductile deformation of rocks in zones of progressive reshygional metamorphism Ger Beitr Goophys 87 126-134

Hrouda F Jelinek V and Zapletal K 1985a Use of magshynetic propenies of rocks in ore and petroleum geophysics (in Czech) Res rep Goofyz Brno pp 54-75

Hrouda F Siemes H Herres N and Hennig-Micbaeli c 1985b The relationship between the magnetic anisotropy and the cmiddotaxis fabric in a massive hematite ore J Geophys bull 56 174-182

International Critical Tables 1929 McGrawmiddotHiIl New York NY

Ising G 1942 On the magnetic propenies of varved clay Ark Mat Astron Fys 29A 1-37

Jelinek V 1981 Characterization of the magnetic fabrics of rocks Tectonophysics 79 T63-T67

Karlin R Lyle M and Heath GR 1987 Authigenic magmiddot netite formation in suboxic marine sediments Nature 326 490--493

Kean WF Day R Fuller M and Schmidt VA 1976 The effect of uniaxial compression on the initial susceptibility of rocks as a function of grain-size and composition of their constituent titanomagnetites J Geophys Res 81 861-874

Khan MA 1962 Anisotropy of magnetic susceptibility of some igneous and metamorphic rocks J Geophys Res 67 2873-2885

KJigfie1d R Lowrie W and Dalziel I 1977 Magnetic susshyceptibility anisotropy as a strain indicator in the Sudbury Basin Ontario Tectonophysics 40 287-308

KJigfield R Lowrie W and Pfiffner OA 1982 Magnetic propenies of deformed oolitic limestones from the Swiss Alps the correlation of magnetic anisotropy and strain Eclogae Geo He1v 75 127-157

Kneen SJ 1976 The relationship between the magnetic and

19

strain fabrics of some hematite-bearing Welsh Slates Earth Planet Sci Lett 31 413-416

Lamarche G and Rochette P 1987 Microstructural analysis and origin of lineations in the magnetic fabric of some Alpine slates Tectonophysics 139 285-293

Lapointe P Morris WA and Harding KL 1986 Interpreshytation of magnetic susceptibility a new approach 10 geoshyphysical evaluation of the degree of rock alteration Can J

Earth Sci 23 393-401 March A 1932 Mathematische Theorie der Regelung nach

der Korngestait bei afrmer Deformation Z Kristallogrmiddot 81 285-297

Means WD 1977 A deformation experiment in transmitted light Earth Planet Sci Lett 35 169-179

Nagata T 1966 Magnetic susceptibility of compressed rocks J Goomag Geoelectr 18 73-80

Nagata T 1970 Anisotropic magnetic susceptibility of rocks under mechanical stresses Pure App Goophys 78

110-122 Nye JF 1957 The Physical Properties of Crystals Clarendon

Press Oxford 322 pp Oertel G 1983 The relationship of strain and preferred

orientation of phyllosilicale grains in rocks-a review Tectonophysics 100 413-447

Owens WH 1974 Mathematical model studies on factors affecting the magnetic anisotropy of deformed rocks Tectonophysics 24 115-131

Owens WH and Bamford D 1976 Magnetic seismic and other anisotropic properties of rock fabrics Philos Trans R Soc London Ser A 283 55-68

Owens WH and Rutter EH 1978 The development of magnetic susceptibility anisotropy through crystallographic preferred orientation in a calcite rock Phys Earth Planet Inter 16 215-222

Park JKmiddot1983 Paleomagnetism for geologists Geosci Can 4 180-188

Rathore JS 1979 Magnetic susceptibility anisotropy in the Cambrian Slate Belt of North Wales and correlation with strain Tectonophysics 53 83-97

Rathore JS 1985 Some magnetic characteristics of sheared zones J Geodyn 2 291-301

Rathore JS and Henry B 1982 Comparison of strained magnetic fabrics in Dalradian rocks from the southwest Highlands of Scotland J Struc Geol 4 373-384

Rees AI 1965 The use of anisotropy of magnetic susceptshyibility in the estimation of sedimentary fabric Sedimentolshyogy 4 257-271

Rees AI 1968 The production of preferred orientation in a concentrated dispersion of elongated and flattened grains J Geol 76 457-465

Rochetle P 1987 Metamorphic control of the mineralogy of black shales in the Swiss Alps toward the use of magnetic isograds Eanh Planet Sci Lett 84 446-456

Rochette P 1988 Relation entre deformation et metamorshy

f

bull

phisme Alpin dans les schistes noirs Helvetiques Iapport de la fabrique magnetique Geodin Acta 2 (in press)

Rochette P and Vialon P 1984 Development of planar and linear fabrics in Dauphinois shales and slates (French Alps) studied by magnetic anisotropy and its mineralogical conshytrol J Struct Geo 6 33-38

Schwarz E 1974 Magnetic fabrics in massive sulfide deposits Can J Earth Sci 11 1669-1675

Schwartz EJ 1975 Magnetic properties of pyrrhotite and their use in applied geology and geophysics Geo Surv Can Pap 74-59 24 pp

Singh J (now Rathore J) Sanderson DJ and Tariing DH 1975 The magnetic susceptibility anisotropy of deformed rocks from North Cornwall England Tectonophysics 27 141-153

Smith GM and Banetjee SK bull 1987 The dependence of weak field susceptibility on applied magnetic field Phys Earth Planet Inter 46 71-76

Stott GM and Schwerdtner WM 1981 A structural analyshysis of the central part of the Shebandowan metavolcanicshymetasedimentary belt Ontario Dep Mines Toronto Final Repbull Onto Geosci Res Rep No 5349 44 pp

Strangway DW 1970 History of the Earths Magnetic Field McGraw-Hili New York NY 168 pp

Tarling DH 1983 Paleomagnetism Chapman and Hall London 379 pp

Tullis TEbull 1976 Experiments on the origin of slaty cleavage and schistosity Geo Soc Am Bull 87 745-753

Tullis TE and Wood DS 1975 Correlation of finite strain from both reduction bodies and preferred orientation of mica in slate from Wales Geol Soc Am Bull 86 632-638

Urrutia-Fucugauchi J and Odabachian Y 1982 A Bibiograshyphy of Magnetic Susceptibility Anisotropy of Rocks Inshystituto de Geofisica Universidad Nacional Autonoma de Mexico Mexico 42 pp

Uyeda S Fuller MD Belshe JC and Girdler RW 1963 Anisotropy of magnetic susceptibility of rocks and minershyals J Geophys Res 68 279-291

Van den Ende C 1975 On the origin of anisotropy of magshynetic susceptibility in Permian Redbeds from the western part of the Dome de Barrot (S France) In GJ Borradaile et al (Editors) Progress in Geodynamics North-Holland Pub Co Amsterdam pp 176-189

Voight W and Kinoshita S 1907 Bestimmung absoluler Wene von Magnelisierungszahlen insbesondere fUr Krisshytalle Ann Phys 24 492-514

Wagner JJ Hedley FG Steen D Tinkler C and Vaugnat M 1981 Magnetic anisotropy and fabric of some progresshysively deformed ophiolitic gabbros J Geophys Res 86 307-315

Weast RC and Astle MJ (Editors) 1978 CRC handbook of Chemistry and Physics 59th edn CRC Press Palm Beach Fla

20

II

Wing-Fatt L and Stacey FD 1966 Magnetic anisotropy of laboratory materials in which magma flow is simulated Pure AppJ Geophys 6478-80

Wood DS Oertel G Singh J and Bennett HF 1976 Strain and anisotropy in rocks Philos Trans R Soc London Ser A 283 27-42

Zavoyskiy VN 1982 Use of magnetic susceptibility tensor for solving problems in structural geology Izv Akad Nauk SSSR Earth Phys Ser 18 217-223

bull

30

2-5

20

-5

10 F=~ WI shy - middotmiddotV j Y

0 5 20 25 30 35

F =(klnkmin)

Fig AI The relationship between Jelineks (1981) P and T parameters and the conventional anisotropy parameters L and

F

The ratios L and F like their counterparts in strain (a and b) are very useful in describing the ellipsoids shape or sense of anisotropy However the distance of the point (L F) from the origin is also a measure of the degree of anisotropy that is to say its departure from sphericity Jelineks (1981) parameters pi and T overcome this T represents sense of anisotropy and ranges from -1 (prolate) to + 1 (oblate) pi (gt 1) expresses degree of anisotropy These are defined as

[ 2(In k -In k~]T= -1

In k itM - In k min 1

pi = exp [ 2( af + a ~ + a~ ) ] ~ where a1 = In(kmaxkb) etc and kb = (kmax k inl

kmin )(l3) The relationship of p and T to L and F is shown in Fig AI

References

Borradaile GJ 1981 Particulate flow of rock and the formashytion of rock cleavage Tectonophysics 24 442-455

Borradaile GJ 1987a Analysis of strained sedimentary fabrics Can J Earth Sci 131 121-125

Borradaile GJ 1987b Anisotropy of magnetic susceptibility rock composition versus strain Tectonophysics 138 327-329

Borradaile GJ and Alford C 1987 Relationship between

17

magnetic susceptibility and strain in laboratory experishyments Tectonophysics 133 121-135

Borradaile GJ and Alford C in press Experimental shear zones and magnetic fabrics J Struct Geol

Borradaile GJ and Brown HG 1987 The Shebandowan Group Timiskaming-like Archean rocks in northwestern Ontario Can J Earth Sci 24 185-188

Borradaile GJ and Mothersill JS bull 1984 Coaxial deformed and magnetic fabrics without simply correlated magnitudes of principal values Phys Earth Planet Inter 35 294-300

Borradaile GJ and Tarling D bull 1981 The influence of deforshymation mechanisms on magnetic fabrics in weakly deshyformed rocks Tectonophysics 77 151-168

Borradaile GJ and Tarling D bull 1984 Strain partitioning and magnetic fabrics in particulate flow Can J Earth Sci 21 694-697

Borradaile GJ Mothersill JS Tarling D and Alford C 1986 Sources of magnetic susceptibility in a slate Earth Planet Sci Lett 76 336-340

Borradaile GJ Keeler W Alford C and Sarvas P 1987 Anisotropy of magnetic susceptibility of some metamorphic minerals Phys Earth Planet Inter 48 161-166

Borradaile G Sarvas P Dutka R Stewart R and Stubley M in press Dextral transpression of the northern margin of the Quetico subprovince-magnetic fabrics and microshyfabrics Can J Earth Sci

Carmichael RS 1982 Magnetic properties of minerals and rocks In RC Weast and MJ Ashe (Editors) CRC Handbook of Physical Constants for Rocks CRC Press Roca Baton Fla pp 229-287

Chang SoBR Kirschvink JL and Stolz JF 1987 Biogenic magnetite as a primary remanence carrier in limestone deposits Phys Earth Planet Inter 46 289-303

Clendenen WS Kligfield R Hirt AM and Lowrie W 1988 Strain studies of cleavage development in the Chelmsford Formation Sudbury Basin Ontario Tectonophysics 145 191-211

Cognc JP and Gapais D bull 1986 Passive rotation of hematite during deformation a comparison of simulated and natural redbeds fabrics Tectonophysics 121 365-372

Collinson DW 1983 Methods in Paleomagnetism and Rock Magnetism Chapman and Hall London 500 pp

Coward MP 1976 Strain within ductile shear wnes Tectonophysics 34 181-197

Coward MP and Whalley 1S 1979 Texture and fabric studies across the Kishorn Nappe near Kyle of Lochalsh Western Scotland J Struct Geol 1 259-273

Crimes TP and Oldershaw MA 1967 Paleocurrent demiddot terminations by magnetic fabri measurement on the Cambrian rocks of St Tudwals peninsula North Wales Geol J 5 217-232

Ellwood BBbull Hrouda F and Wagner J-J 1988 Symposia on magnetic fabrics Introductory comments Phys Earth Planet Inter 51 249-252

Fuller MDbull 1964 On the magnetic fabrics of certain rocks 1 Geol 72 368-376

18

II

Goldstein AG bull 1980 Magnetic susceptibility anisotropy of mylonites from the Lake Char Mylonite Zone SE New England Tectonophysics 66 197-211

Graham lW 1954 Magnetic susceptibility anisotropy an unexploited petrofabric element Bull Gool Soc Am 65 1257-1258

Graham lWbull 1966 Significance of magnetic anisotropy in Appalachian sedimentary rocks In lS Steinhard and Tl Smith (Editors) The Earth beneath the Continents Gooshyphys Monogr Am Geophys Union 10 627-648

Hamano Y and Yom ida K 1982 Magnetic anisotropy and porosity of Antarctic chondrites Mem Natl Inst Polar Res Tokyo 25 281-290

Hamilton N 1963 Susceptibility anisotropy measurements on some Silurian siltstones Nature 197 170-171

Hamilton N and Rees AI 1970 The use of magnetic fabric in paleocurrent estimation In SK Runcorn (Editor) Paleogeophysics Academic Press New York NY pp 445-464

Hamilton N and Rees AI 1971 The anisotropy of magnetic susceptibility of the Franciscan Rocks of the Diablo Range Central California Geo Rundsch 60 1103-1124

Hamilton N Owens WH and Rees AI 1968 Laboratory experiments on the production of grain orientation in shearing sand l Goo 76 465-472

Hargraves RB 1959 Magnetic anisotropy and remanent magnetism in hemo-ilmenite from ore deposits at Allard Lake Quebec l Goophys Res 68 293-309

Heider Fbull Dunlop DJ and Sugiura N 1987 Magnetic properties oC hydrothermally recrystallized magnetite crystals Science 236 1287-1290

Henry B 1983 Interpretation quantitative de lanisotropie de susceptibilite magnetique Tectonophysics 91 165-177

Henry B and Daly L 1983 From qualitative to quantitative magnetic anisotropy analysis the prospect of finite strain calibration Tectonophysics 98 327-336

Hirt AM Lowrie W bull Clendenen WS and Kligfield R 1988 The correlation of magnetic anisotropy with strain in the Chelmsford Formation of the Sudbury Basin Ontario Tectonophysics 145 177-189

Hrouda F 1976 The origin of cleavage in the light of magnetic anisotropy investigations Pbys Earth Planet Inshyter 13 132-142

Hrouda F 1979 (reponed 1977) The strain interpretation of magnetic anisotropy in rocks of the Nizky lesenik Mounmiddot tains (Czechoslovakia) Sb Gool Ved (Uzit Geofyz) 16 27-62

Hrouda F 1980 Magnetocrystalline anisotropy of rocks and massive ores a mathematical model study and its fabric implications l Struct Geo1bull 2 459-462

Hrouda F 1982 Magnetic anisotropy of rocks and its apmiddot plication in geology and geophysics Geophys Surv 5 37-82

Hrouda F 1986 The effect of quanz on the magnetic ani sotropy of quartzite Studia Geophys Geod 30 39-45

Hrouda F bull 1987 Mathematical model relationships between

the paramagnetic anisotropy and strain in slates Tectonophysics 142 323-327

Hrouda F and Chlupacova M bull 1980 The magnetic fabric in the Nasavrky massif Cas Mineral Goo 25 17-27

Hrouda F and lanak F 1971 A study of the hematite fabric of some red sediments on the basis of their magnetic susceptibility anisotropy Sediment Geol 6 187-199

Hrouda F and Janak F 1976 The changes in shape of the magnetic susceptibility ellipsoid during progressive metashymorphism and deformation Tectonophysics 34 135-148

Hrouda F and Jelinek V in prep Resolution of ferromagmiddot netic and paramagnetic components of magnetic anishysotropy using combined low-field and high-field anishysotropy measurements I

Hrouda F Chlupacova M and Rejl L 1971 The mimetic fabric of magnetite in some foliated granodiorites as indio cated by magnetic anisotropy Earth Planet Sci Leu 11 381-384

Hrouda F Chlupacova M and Rejl L bull 1972 Changes in magnetite content and magnetite fabric during Cenitization as investigated by petromagnetic methods Neues Jahrb Mineral Abh 117 61-72

Hrouda F Janalc F and Rejl L 1978 Magnetic fabric and ductile deformation of rocks in zones of progressive reshygional metamorphism Ger Beitr Goophys 87 126-134

Hrouda F Jelinek V and Zapletal K 1985a Use of magshynetic propenies of rocks in ore and petroleum geophysics (in Czech) Res rep Goofyz Brno pp 54-75

Hrouda F Siemes H Herres N and Hennig-Micbaeli c 1985b The relationship between the magnetic anisotropy and the cmiddotaxis fabric in a massive hematite ore J Geophys bull 56 174-182

International Critical Tables 1929 McGrawmiddotHiIl New York NY

Ising G 1942 On the magnetic propenies of varved clay Ark Mat Astron Fys 29A 1-37

Jelinek V 1981 Characterization of the magnetic fabrics of rocks Tectonophysics 79 T63-T67

Karlin R Lyle M and Heath GR 1987 Authigenic magmiddot netite formation in suboxic marine sediments Nature 326 490--493

Kean WF Day R Fuller M and Schmidt VA 1976 The effect of uniaxial compression on the initial susceptibility of rocks as a function of grain-size and composition of their constituent titanomagnetites J Geophys Res 81 861-874

Khan MA 1962 Anisotropy of magnetic susceptibility of some igneous and metamorphic rocks J Geophys Res 67 2873-2885

KJigfie1d R Lowrie W and Dalziel I 1977 Magnetic susshyceptibility anisotropy as a strain indicator in the Sudbury Basin Ontario Tectonophysics 40 287-308

KJigfield R Lowrie W and Pfiffner OA 1982 Magnetic propenies of deformed oolitic limestones from the Swiss Alps the correlation of magnetic anisotropy and strain Eclogae Geo He1v 75 127-157

Kneen SJ 1976 The relationship between the magnetic and

19

strain fabrics of some hematite-bearing Welsh Slates Earth Planet Sci Lett 31 413-416

Lamarche G and Rochette P 1987 Microstructural analysis and origin of lineations in the magnetic fabric of some Alpine slates Tectonophysics 139 285-293

Lapointe P Morris WA and Harding KL 1986 Interpreshytation of magnetic susceptibility a new approach 10 geoshyphysical evaluation of the degree of rock alteration Can J

Earth Sci 23 393-401 March A 1932 Mathematische Theorie der Regelung nach

der Korngestait bei afrmer Deformation Z Kristallogrmiddot 81 285-297

Means WD 1977 A deformation experiment in transmitted light Earth Planet Sci Lett 35 169-179

Nagata T 1966 Magnetic susceptibility of compressed rocks J Goomag Geoelectr 18 73-80

Nagata T 1970 Anisotropic magnetic susceptibility of rocks under mechanical stresses Pure App Goophys 78

110-122 Nye JF 1957 The Physical Properties of Crystals Clarendon

Press Oxford 322 pp Oertel G 1983 The relationship of strain and preferred

orientation of phyllosilicale grains in rocks-a review Tectonophysics 100 413-447

Owens WH 1974 Mathematical model studies on factors affecting the magnetic anisotropy of deformed rocks Tectonophysics 24 115-131

Owens WH and Bamford D 1976 Magnetic seismic and other anisotropic properties of rock fabrics Philos Trans R Soc London Ser A 283 55-68

Owens WH and Rutter EH 1978 The development of magnetic susceptibility anisotropy through crystallographic preferred orientation in a calcite rock Phys Earth Planet Inter 16 215-222

Park JKmiddot1983 Paleomagnetism for geologists Geosci Can 4 180-188

Rathore JS 1979 Magnetic susceptibility anisotropy in the Cambrian Slate Belt of North Wales and correlation with strain Tectonophysics 53 83-97

Rathore JS 1985 Some magnetic characteristics of sheared zones J Geodyn 2 291-301

Rathore JS and Henry B 1982 Comparison of strained magnetic fabrics in Dalradian rocks from the southwest Highlands of Scotland J Struc Geol 4 373-384

Rees AI 1965 The use of anisotropy of magnetic susceptshyibility in the estimation of sedimentary fabric Sedimentolshyogy 4 257-271

Rees AI 1968 The production of preferred orientation in a concentrated dispersion of elongated and flattened grains J Geol 76 457-465

Rochetle P 1987 Metamorphic control of the mineralogy of black shales in the Swiss Alps toward the use of magnetic isograds Eanh Planet Sci Lett 84 446-456

Rochette P 1988 Relation entre deformation et metamorshy

f

bull

phisme Alpin dans les schistes noirs Helvetiques Iapport de la fabrique magnetique Geodin Acta 2 (in press)

Rochette P and Vialon P 1984 Development of planar and linear fabrics in Dauphinois shales and slates (French Alps) studied by magnetic anisotropy and its mineralogical conshytrol J Struct Geo 6 33-38

Schwarz E 1974 Magnetic fabrics in massive sulfide deposits Can J Earth Sci 11 1669-1675

Schwartz EJ 1975 Magnetic properties of pyrrhotite and their use in applied geology and geophysics Geo Surv Can Pap 74-59 24 pp

Singh J (now Rathore J) Sanderson DJ and Tariing DH 1975 The magnetic susceptibility anisotropy of deformed rocks from North Cornwall England Tectonophysics 27 141-153

Smith GM and Banetjee SK bull 1987 The dependence of weak field susceptibility on applied magnetic field Phys Earth Planet Inter 46 71-76

Stott GM and Schwerdtner WM 1981 A structural analyshysis of the central part of the Shebandowan metavolcanicshymetasedimentary belt Ontario Dep Mines Toronto Final Repbull Onto Geosci Res Rep No 5349 44 pp

Strangway DW 1970 History of the Earths Magnetic Field McGraw-Hili New York NY 168 pp

Tarling DH 1983 Paleomagnetism Chapman and Hall London 379 pp

Tullis TEbull 1976 Experiments on the origin of slaty cleavage and schistosity Geo Soc Am Bull 87 745-753

Tullis TE and Wood DS 1975 Correlation of finite strain from both reduction bodies and preferred orientation of mica in slate from Wales Geol Soc Am Bull 86 632-638

Urrutia-Fucugauchi J and Odabachian Y 1982 A Bibiograshyphy of Magnetic Susceptibility Anisotropy of Rocks Inshystituto de Geofisica Universidad Nacional Autonoma de Mexico Mexico 42 pp

Uyeda S Fuller MD Belshe JC and Girdler RW 1963 Anisotropy of magnetic susceptibility of rocks and minershyals J Geophys Res 68 279-291

Van den Ende C 1975 On the origin of anisotropy of magshynetic susceptibility in Permian Redbeds from the western part of the Dome de Barrot (S France) In GJ Borradaile et al (Editors) Progress in Geodynamics North-Holland Pub Co Amsterdam pp 176-189

Voight W and Kinoshita S 1907 Bestimmung absoluler Wene von Magnelisierungszahlen insbesondere fUr Krisshytalle Ann Phys 24 492-514

Wagner JJ Hedley FG Steen D Tinkler C and Vaugnat M 1981 Magnetic anisotropy and fabric of some progresshysively deformed ophiolitic gabbros J Geophys Res 86 307-315

Weast RC and Astle MJ (Editors) 1978 CRC handbook of Chemistry and Physics 59th edn CRC Press Palm Beach Fla

20

II

Wing-Fatt L and Stacey FD 1966 Magnetic anisotropy of laboratory materials in which magma flow is simulated Pure AppJ Geophys 6478-80

Wood DS Oertel G Singh J and Bennett HF 1976 Strain and anisotropy in rocks Philos Trans R Soc London Ser A 283 27-42

Zavoyskiy VN 1982 Use of magnetic susceptibility tensor for solving problems in structural geology Izv Akad Nauk SSSR Earth Phys Ser 18 217-223

18

II

Goldstein AG bull 1980 Magnetic susceptibility anisotropy of mylonites from the Lake Char Mylonite Zone SE New England Tectonophysics 66 197-211

Graham lW 1954 Magnetic susceptibility anisotropy an unexploited petrofabric element Bull Gool Soc Am 65 1257-1258

Graham lWbull 1966 Significance of magnetic anisotropy in Appalachian sedimentary rocks In lS Steinhard and Tl Smith (Editors) The Earth beneath the Continents Gooshyphys Monogr Am Geophys Union 10 627-648

Hamano Y and Yom ida K 1982 Magnetic anisotropy and porosity of Antarctic chondrites Mem Natl Inst Polar Res Tokyo 25 281-290

Hamilton N 1963 Susceptibility anisotropy measurements on some Silurian siltstones Nature 197 170-171

Hamilton N and Rees AI 1970 The use of magnetic fabric in paleocurrent estimation In SK Runcorn (Editor) Paleogeophysics Academic Press New York NY pp 445-464

Hamilton N and Rees AI 1971 The anisotropy of magnetic susceptibility of the Franciscan Rocks of the Diablo Range Central California Geo Rundsch 60 1103-1124

Hamilton N Owens WH and Rees AI 1968 Laboratory experiments on the production of grain orientation in shearing sand l Goo 76 465-472

Hargraves RB 1959 Magnetic anisotropy and remanent magnetism in hemo-ilmenite from ore deposits at Allard Lake Quebec l Goophys Res 68 293-309

Heider Fbull Dunlop DJ and Sugiura N 1987 Magnetic properties oC hydrothermally recrystallized magnetite crystals Science 236 1287-1290

Henry B 1983 Interpretation quantitative de lanisotropie de susceptibilite magnetique Tectonophysics 91 165-177

Henry B and Daly L 1983 From qualitative to quantitative magnetic anisotropy analysis the prospect of finite strain calibration Tectonophysics 98 327-336

Hirt AM Lowrie W bull Clendenen WS and Kligfield R 1988 The correlation of magnetic anisotropy with strain in the Chelmsford Formation of the Sudbury Basin Ontario Tectonophysics 145 177-189

Hrouda F 1976 The origin of cleavage in the light of magnetic anisotropy investigations Pbys Earth Planet Inshyter 13 132-142

Hrouda F 1979 (reponed 1977) The strain interpretation of magnetic anisotropy in rocks of the Nizky lesenik Mounmiddot tains (Czechoslovakia) Sb Gool Ved (Uzit Geofyz) 16 27-62

Hrouda F 1980 Magnetocrystalline anisotropy of rocks and massive ores a mathematical model study and its fabric implications l Struct Geo1bull 2 459-462

Hrouda F 1982 Magnetic anisotropy of rocks and its apmiddot plication in geology and geophysics Geophys Surv 5 37-82

Hrouda F 1986 The effect of quanz on the magnetic ani sotropy of quartzite Studia Geophys Geod 30 39-45

Hrouda F bull 1987 Mathematical model relationships between

the paramagnetic anisotropy and strain in slates Tectonophysics 142 323-327

Hrouda F and Chlupacova M bull 1980 The magnetic fabric in the Nasavrky massif Cas Mineral Goo 25 17-27

Hrouda F and lanak F 1971 A study of the hematite fabric of some red sediments on the basis of their magnetic susceptibility anisotropy Sediment Geol 6 187-199

Hrouda F and Janak F 1976 The changes in shape of the magnetic susceptibility ellipsoid during progressive metashymorphism and deformation Tectonophysics 34 135-148

Hrouda F and Jelinek V in prep Resolution of ferromagmiddot netic and paramagnetic components of magnetic anishysotropy using combined low-field and high-field anishysotropy measurements I

Hrouda F Chlupacova M and Rejl L 1971 The mimetic fabric of magnetite in some foliated granodiorites as indio cated by magnetic anisotropy Earth Planet Sci Leu 11 381-384

Hrouda F Chlupacova M and Rejl L bull 1972 Changes in magnetite content and magnetite fabric during Cenitization as investigated by petromagnetic methods Neues Jahrb Mineral Abh 117 61-72

Hrouda F Janalc F and Rejl L 1978 Magnetic fabric and ductile deformation of rocks in zones of progressive reshygional metamorphism Ger Beitr Goophys 87 126-134

Hrouda F Jelinek V and Zapletal K 1985a Use of magshynetic propenies of rocks in ore and petroleum geophysics (in Czech) Res rep Goofyz Brno pp 54-75

Hrouda F Siemes H Herres N and Hennig-Micbaeli c 1985b The relationship between the magnetic anisotropy and the cmiddotaxis fabric in a massive hematite ore J Geophys bull 56 174-182

International Critical Tables 1929 McGrawmiddotHiIl New York NY

Ising G 1942 On the magnetic propenies of varved clay Ark Mat Astron Fys 29A 1-37

Jelinek V 1981 Characterization of the magnetic fabrics of rocks Tectonophysics 79 T63-T67

Karlin R Lyle M and Heath GR 1987 Authigenic magmiddot netite formation in suboxic marine sediments Nature 326 490--493

Kean WF Day R Fuller M and Schmidt VA 1976 The effect of uniaxial compression on the initial susceptibility of rocks as a function of grain-size and composition of their constituent titanomagnetites J Geophys Res 81 861-874

Khan MA 1962 Anisotropy of magnetic susceptibility of some igneous and metamorphic rocks J Geophys Res 67 2873-2885

KJigfie1d R Lowrie W and Dalziel I 1977 Magnetic susshyceptibility anisotropy as a strain indicator in the Sudbury Basin Ontario Tectonophysics 40 287-308

KJigfield R Lowrie W and Pfiffner OA 1982 Magnetic propenies of deformed oolitic limestones from the Swiss Alps the correlation of magnetic anisotropy and strain Eclogae Geo He1v 75 127-157

Kneen SJ 1976 The relationship between the magnetic and

19

strain fabrics of some hematite-bearing Welsh Slates Earth Planet Sci Lett 31 413-416

Lamarche G and Rochette P 1987 Microstructural analysis and origin of lineations in the magnetic fabric of some Alpine slates Tectonophysics 139 285-293

Lapointe P Morris WA and Harding KL 1986 Interpreshytation of magnetic susceptibility a new approach 10 geoshyphysical evaluation of the degree of rock alteration Can J

Earth Sci 23 393-401 March A 1932 Mathematische Theorie der Regelung nach

der Korngestait bei afrmer Deformation Z Kristallogrmiddot 81 285-297

Means WD 1977 A deformation experiment in transmitted light Earth Planet Sci Lett 35 169-179

Nagata T 1966 Magnetic susceptibility of compressed rocks J Goomag Geoelectr 18 73-80

Nagata T 1970 Anisotropic magnetic susceptibility of rocks under mechanical stresses Pure App Goophys 78

110-122 Nye JF 1957 The Physical Properties of Crystals Clarendon

Press Oxford 322 pp Oertel G 1983 The relationship of strain and preferred

orientation of phyllosilicale grains in rocks-a review Tectonophysics 100 413-447

Owens WH 1974 Mathematical model studies on factors affecting the magnetic anisotropy of deformed rocks Tectonophysics 24 115-131

Owens WH and Bamford D 1976 Magnetic seismic and other anisotropic properties of rock fabrics Philos Trans R Soc London Ser A 283 55-68

Owens WH and Rutter EH 1978 The development of magnetic susceptibility anisotropy through crystallographic preferred orientation in a calcite rock Phys Earth Planet Inter 16 215-222

Park JKmiddot1983 Paleomagnetism for geologists Geosci Can 4 180-188

Rathore JS 1979 Magnetic susceptibility anisotropy in the Cambrian Slate Belt of North Wales and correlation with strain Tectonophysics 53 83-97

Rathore JS 1985 Some magnetic characteristics of sheared zones J Geodyn 2 291-301

Rathore JS and Henry B 1982 Comparison of strained magnetic fabrics in Dalradian rocks from the southwest Highlands of Scotland J Struc Geol 4 373-384

Rees AI 1965 The use of anisotropy of magnetic susceptshyibility in the estimation of sedimentary fabric Sedimentolshyogy 4 257-271

Rees AI 1968 The production of preferred orientation in a concentrated dispersion of elongated and flattened grains J Geol 76 457-465

Rochetle P 1987 Metamorphic control of the mineralogy of black shales in the Swiss Alps toward the use of magnetic isograds Eanh Planet Sci Lett 84 446-456

Rochette P 1988 Relation entre deformation et metamorshy

f

bull

phisme Alpin dans les schistes noirs Helvetiques Iapport de la fabrique magnetique Geodin Acta 2 (in press)

Rochette P and Vialon P 1984 Development of planar and linear fabrics in Dauphinois shales and slates (French Alps) studied by magnetic anisotropy and its mineralogical conshytrol J Struct Geo 6 33-38

Schwarz E 1974 Magnetic fabrics in massive sulfide deposits Can J Earth Sci 11 1669-1675

Schwartz EJ 1975 Magnetic properties of pyrrhotite and their use in applied geology and geophysics Geo Surv Can Pap 74-59 24 pp

Singh J (now Rathore J) Sanderson DJ and Tariing DH 1975 The magnetic susceptibility anisotropy of deformed rocks from North Cornwall England Tectonophysics 27 141-153

Smith GM and Banetjee SK bull 1987 The dependence of weak field susceptibility on applied magnetic field Phys Earth Planet Inter 46 71-76

Stott GM and Schwerdtner WM 1981 A structural analyshysis of the central part of the Shebandowan metavolcanicshymetasedimentary belt Ontario Dep Mines Toronto Final Repbull Onto Geosci Res Rep No 5349 44 pp

Strangway DW 1970 History of the Earths Magnetic Field McGraw-Hili New York NY 168 pp

Tarling DH 1983 Paleomagnetism Chapman and Hall London 379 pp

Tullis TEbull 1976 Experiments on the origin of slaty cleavage and schistosity Geo Soc Am Bull 87 745-753

Tullis TE and Wood DS 1975 Correlation of finite strain from both reduction bodies and preferred orientation of mica in slate from Wales Geol Soc Am Bull 86 632-638

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Zavoyskiy VN 1982 Use of magnetic susceptibility tensor for solving problems in structural geology Izv Akad Nauk SSSR Earth Phys Ser 18 217-223

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Tullis TEbull 1976 Experiments on the origin of slaty cleavage and schistosity Geo Soc Am Bull 87 745-753

Tullis TE and Wood DS 1975 Correlation of finite strain from both reduction bodies and preferred orientation of mica in slate from Wales Geol Soc Am Bull 86 632-638

Urrutia-Fucugauchi J and Odabachian Y 1982 A Bibiograshyphy of Magnetic Susceptibility Anisotropy of Rocks Inshystituto de Geofisica Universidad Nacional Autonoma de Mexico Mexico 42 pp

Uyeda S Fuller MD Belshe JC and Girdler RW 1963 Anisotropy of magnetic susceptibility of rocks and minershyals J Geophys Res 68 279-291

Van den Ende C 1975 On the origin of anisotropy of magshynetic susceptibility in Permian Redbeds from the western part of the Dome de Barrot (S France) In GJ Borradaile et al (Editors) Progress in Geodynamics North-Holland Pub Co Amsterdam pp 176-189

Voight W and Kinoshita S 1907 Bestimmung absoluler Wene von Magnelisierungszahlen insbesondere fUr Krisshytalle Ann Phys 24 492-514

Wagner JJ Hedley FG Steen D Tinkler C and Vaugnat M 1981 Magnetic anisotropy and fabric of some progresshysively deformed ophiolitic gabbros J Geophys Res 86 307-315

Weast RC and Astle MJ (Editors) 1978 CRC handbook of Chemistry and Physics 59th edn CRC Press Palm Beach Fla

20

II

Wing-Fatt L and Stacey FD 1966 Magnetic anisotropy of laboratory materials in which magma flow is simulated Pure AppJ Geophys 6478-80

Wood DS Oertel G Singh J and Bennett HF 1976 Strain and anisotropy in rocks Philos Trans R Soc London Ser A 283 27-42

Zavoyskiy VN 1982 Use of magnetic susceptibility tensor for solving problems in structural geology Izv Akad Nauk SSSR Earth Phys Ser 18 217-223

20

II

Wing-Fatt L and Stacey FD 1966 Magnetic anisotropy of laboratory materials in which magma flow is simulated Pure AppJ Geophys 6478-80

Wood DS Oertel G Singh J and Bennett HF 1976 Strain and anisotropy in rocks Philos Trans R Soc London Ser A 283 27-42

Zavoyskiy VN 1982 Use of magnetic susceptibility tensor for solving problems in structural geology Izv Akad Nauk SSSR Earth Phys Ser 18 217-223