American Mineralogist, Volume 61, pages 788-80j, 1976

Geophysical constraints on radial and lateral temperature variations in the upper mantle

SEeN C. Sor-or',roN

Department of Earth and Planelary SciencesM as sac huse t t s I ns t itut e of T e chnol og y

Cambridge, Massachusetts 02 139

Abstract

Temperatures in the upper mantle may be inferred from measurements of physical proper-t ies which are strongly dependent on temperature and by identi f icat ion of seismic discontin-u i t ies w i th phase t rans i t ions o f measurab le equ i l ib r ium boundar ies . Tempera ture a t the top o fthe low-ve loc i ty zone, equated w i th the onset o f inc ip ien t me l t ing , i s genera l l y l l00 ' + 100"Cfrom a wide variety of evidence. The extensive melt ing detectable beneath mid-ocean r idgesimplies temperatures above l250oC in the shal low asthenosphere under spreading centers.Below a thermal boundary layer at the top of the asthenosphere, associated with convectionon a scale secondary to plate motions, geotherms in the asthenosphere fol low nearly adiabaticgrad ien ts and in te rsec t the o l i v ine-sp ine l t rans i t ion a t a tempera ture o f 1300" + 150" C. Theo l iv ine-sp ine l t rans i t ion is e leva ted about 100 km in subducted ocean ic l i thosphere , imp ly inga 1000'C temperature contrast between slab and normal mantle at 250 km depth. Systematicthermal dif ferences between stable ocean basins and continental shields are necessary but arenot l ikely to extend deeper than 200 km. Lateral temperature variat ions of perhaps 200'C dopersist deeper than 200 km and are probably associated with convective f low in the astheno-sohere

Introduction

The temperature d is t r ibut ion in the ear th is in-t imate ly re lated to the dynamics of i ts in ter ior and isfundamental to a proper in terpretat ion of much ofthe data f rom sol id-ear th geophysics, geochemist ry .and petro logy. Di rect observat ion of the temperaturedist r ibut ion is l imi ted to measurement of temperatureand i ts spat ia l der ivat ives in the upper f lew k i lometersof the ear th 's crust . This paper is a synthesis of themany indi rect observat ions, most ly geophysical , thatprovide in format ion on the radia l and latera l var ia-t ions of temperature in the upper mant le.

Temperatures in the upper mantle may be esti-mated us ing two types of in ference chains: ( l ) theident i f icat ion of se ismic d iscont inui t ies wi th phasetransi t ions whose equi l ibr ium boundar ies can bemeasured in the laboratory, and (2) the measurementof physical propert ies which are st rongly dependenton temperature. The f i rs t c lass of constra ints inc ludesthe locat ion o l the boundar ies of the low-veloc i tyzone, in terpreted as the onset of par t ia l mel t ing, andof the d iscont inui t ies mark ing the breakdown of theol iv ine and spinel phases of (Mg,Fe)rSiOo. The sec-

ond class includes information on the depth depen-dence of thermally-activated properties such as elec-t r ica l conduct iv i ty , se ismic d iss ipat ion, and v iscosi ty .

Both types of constraints are brought together inthis paper to develop a self-consistent picture of up-per mant le temperatures. The p ic ture is c loselyrelated to recent ideas about the structure and evolu-t ion of the l i thosphere and the convect ive f low pat-tern within the asthenosphere.

Phase boundaries as geothermometers:the low-velocity zone

The seismic low-veloc i ty , low-Q zone has t radi t ion-ally been identif ied by seismologists and others as theasthenosphere (e.g. , Press, 1959). The top of the low-veloc i ty zone probably marks the locus of the sol idusof mant le mater ia l in the presence of smal l amountsof a free fluid phase (Kushiro et al., 1968;, Lambertand Wyl l ie , 1968; Ringwood, 1969), and thus const i -tutes a geothermometer if the phase diagram formant le mater ia l is assumed to be known. Var iat ionsin the depth to the top of the low-velocity zone repre-sent lateral differences in temperature and perhapscomoosi t ion.

GEOPHYSICAL CONSTRAINTS ON TEMPERATURE VARIATIONS IN THE UPPER MANTLE 789

Euidence Jbr incipient melting

Several l ines of ev idence support the hypothesisthat the low-velocity zone is generally in a state ofinc ip ient mel t ing, a term proposed by Ringwood(1969 ) t o d i s t i ngu i sh t he sma l l amoun t ( - l 7o ) o fmel t ing associated wi th the lower ing of the sol idus byfree HrO or COz from the greater amount of melting(5-307o) thought necessary to produce most basalticmagmas:

( l ) The deta i led d is t r ibut ions of ve loc i ty and Q ofP and S waves in the upper mant le requi re that somesort of shear-relaxation process operate in the low-veloc i ty zone. The rat ionale for th is conclus ion hasbeen summarized by Anderson and Sammis (1970)and by Solomon (1972), and inc ludes the f ,o l lowing:the sharp gradients in veloc i ty and Q- 'at the top andbot tom of the zone, the much larger var iat ion inmodulus and in losses for shear than for compres-sion, and the apparent frequency dependence of Q-'in the upper mant le. A smal l amount of par t ia l mel t -ing wi th in the low veloc i ty zone can readi ly accountfor these observat ions (Walsh, 1969).

(2) The temperature at the base of the l i thosphereis in excess of the sol idus for per idot i te wi th smal lamounts of HrO or CO2 (Wyl l ie , 197l ; Green, 19736Mysen and Boet tcher , 1975). The data used to estab-l ish th is resul t are d iscussed in a la ter sect ion.

(3) There are numerous geochemical and petro lo-g ical grounds favor ing some HrO and COz in themant le at asthenosphere depths. These inc lude hy-drous minerals in u l t ramaf ic nodules and other rocksbel ieved to be der ived f rom the mant le (Oxburgh,1964; Kushiro et a l . , 1967; McGetchin et a l . , 1910Merr i l f e t a l . , 1972), CO,- f i l led inc lus ions in o l iv ine-bear ing nodules thought to be mant le-der ived (Roed-der , 1965); the presence of and oxidat ion state ofgases g iven of f dur ing volcanic erupt ions (Eaton andMurata, 1960; Hol land, 1962; Nordl ie , l97 l ) , themechanism of emplacement of d iat remes (Shoemakeret al., 1962; McGetchin and Silver, 1972), the veSicu-lar i ty of young basal ts erupted on the ocean f loor(Moore, 1970), and the exper imenta l mel t ing re la-t ions for cer ta in types of basal ts (Bul t i tude andGreen, 1967; Green, 1973a).

I t is expected that any HrO in the mant le would bepresent as a free fluid phase or dissolved in a sil icatemel t below the depth in the mant le at which amphi-bole and perhaps phlogopi te are stable phases (Kush-i ro et s l . , 1968; Lambert and Wyl l ie , t968) . Such anexpectat ion is consistent wi th the depth to the low-veloc i ty zone and wi th independent est imates of tem-perature at that depth (see below). Whether COz

would be concentrated in a fluid or a solid phase atmant le depths appropr iate to the low veloc i ty zone isa matter of some uncertainty (Green, 1972; Irvingand Wyl l ie , 1973; Newton and Sharp, 1975), thoughas long as some HrO is present then this uncertaintydoes not affect the discussion here.

The oceanic lithosphere

Thermal models for the oceanic l ithosphere, to-gether with experimentally determined phase rela-t ionships for probable mant le composi t ions, predictthat the solidus deepens with l ithospheric age (Wyll ie,

l97 l ; Forsyth and Press, 1971). The depth to the topof the low-velocity zone beneath oceans, interpretedas the depth to the solidus, can be located by severaldifferent seismic techniques and appears to deepensystematically with sea-floor age in the manner pro-posed (Leeds et q l . , 1974; Forsyth, 1975).

The occurrence of a low-velocity zone is normallydemonstrated in a refraction experiment by a timeoffset in the travel t ime versus distance curve for f irstarrivals and/or a distance range over which first-arr iv ing s ignals have low ampl i tudes, and in a sur-face-wave experiment by direct inversion of surface-wave phase or group velocities. For both types ofexperiments, there is a trade-off between the depthextent of the low-velocity zone and the velocitywi th in the zone. The bot toms of low-veloc i ty zonesare therefore never located with much reliabil i ty. Thetop of a low-velociry zone (for P waves) can often bereasonably well located by a refraction experiment,but for inversion of surface-wave dispersion there isusually another trade-off between (S wave) velocityin the l id above the low-veloc i ty zone and depth tothe top of the zone. If the l id velocities are themselveslower than normal , as in many tectonic areas, there isan addi t ional ambigui ty in choosing where the l idstops and the low-veloc i ty zone begins.

A summary of est imates of l i thospher ic th ickness,as defined by the depth to the low-velocity zone,beneath oceans is given in Figure L The most exten-sive data come from surface-wave phase velocities"regionalized" into zones of different ages (Leeds elal., 1974; Weidner, l9'74; Forsyth, 1975). Dis-agreement among the different determinations do notnecessarily imply different thickness-age relationsamong the several oceans sampled, but more l ike lyrepresent the sensitivity of the estimated l ithosphereth ickness to assumpt ions made in the invers ion. Seis-mic refraction experiments at ridge crests (Francisand Porter , 1973; Orcut t e t a l . , 1975) and in o lderoceanic l i thosphere (Asada and Shimamura, 1975)

790 SEAN C SOLOMON

R e f r o c t i o n , M A R I o n d E P R ( F r o n c i s o n d P o r t e r , I 9 7 3 ; O r c u t t e l o l . , 1 9 7 5 )

- - - )= - - - - - . 1 Foco l mechon i sms , MAR

Sur foc€ nor " " , Nor "o /

( F o r s y t h , 1 9 7 5 )

O c e o n i c L i t h o s p h e r e t

50

EJ

6

oo

Io

F

t o o

t 5 0

lend confidence to the general trend displayed by thesurface wave results, except for the results of Leeds e/a l . (1914) on sea f loor o lder than 100 m.y. , s incerevised (Leeds, 1975) and in much better agreementwith refraction results. The implications of Figure Ifor temperature in the oceanic upper mantle are dis-cussed below.

The continental lithosphere

Seismic data on the thickness of the continentall i thosphere are more abundant than for oceanic re-g ions, but cannot be neat ly categor ized as monotonicfunctions of only one parameter. Reliable determina-tions of depth to the continental low-velocity zone

are summarized in Figure 2, with the results grouped

roughly (after Knopoff, 1972) into tectonically activeregions, stable continental platforms, and Pre-

cambrian shields. The great majority of the datacome from North American profi les.

The thicknesses shown for tectonically active areas

are all from the western United States, though por-

tions of east Africa appear to be similar (Knopoff,

l 2t oJas , n . y .

Frc . I Se i sm icde te rm ina t i onso focean i c l i t hosphe re th i ckness ,equa tedw i t h thedep thbe lowsea leve l t o t he topo f t he l ow-ve loc i t y

zone Estimates from inversion of surface-wave phase velocities for various sea-floor age intervals are from Leeds e, al. (1974) for lhe

Paci f ic , Weidner (1974) for the At lant ic , and Forsyth (1975) for the Nazca plate. Ridge-crest refract ion exper iments by Francis and Porter( I 973 ) on the mid-A t lant ic r idge and Orcut t et a l . (197 5) on the East Paci f ic Rise fo u nd the top of the asthenosphere wi th in the oceanic

c rus t The long re f rac t i on l i neo f AsadaandSh imamura (1975 )was in thewes te rnPac i f i cbas ineas to f Honshu .Thedashedcu rve i s f r om

the r idge model ofSolomon and Jul ian (1974) f i t ted to d istor t ions in the propagat ion di rect ions of te leseismic P waves f rom r idge-crest

earthquakes

1972). Such regions are characterized by very pro-nounced low-velocity zones extending upward toshallow mantle depths, sometimes to the base of thecrust. Refraction profi les give l ithosphere thicknessesof 30 to 70 km for such regions, a result generallysupported by inversion of phase velocity (Biswas andKnopoff, 1974) and Q-t (Lee and Solomon, 1975) forLove and Rayleigh waves over similar paths.

The aseismic continental platforms, typified bymidwestern North America but also including largeportions of most continents (Knopoff, 1972), arecharacterized by a definite low-velocity zone, but onethat is deeper and less pronounced than in areas ofrecent tectonic activity. Lithospheric thicknesses l iein the range 80 to 140 km, wi th perhaps 120 km agood representative figure (Biswas and Knopoff,1974; Lee and Solomon, 1975),

The older shield regions have very modest low-velocity zones, if any. Surface-wave dispersion andsome refraction profi les in shields can be fitted bymodels with no low-velocity zones (Brune and Dor-man, 1963; Knopoff, 1972; Alexander and Sherburne,

S h i e l dT e c t o n i c

C o n t i n e n t o lL i t h o s p h e r e

P l o i f o r m

GEOPHYSICAL CONSTRAINTS ON TEMPERATURE VARIATIONS IN THE UPPER MANTLE

Ftc. 2. Seismic determinat ions of cont inental l i thosphere th ickness, equated wi th the depth to the top ofthe low-velocity zone. Each box represents the thickness determined from one refractioh profile; an Swithin the box designates an ,S-wave profile. The range of lithosphere thicknesses obtained from inversionof surface wave phase veloci ty (Knopoff , 1972; Biswas and Knopoff , 1974) and at tenuat ion (Lee andSolomon, 1975) are shown as sol id (where preferred) to long dashed and short dashed l ines, respect ively.Tectonic refract ion prof i les inc lude ClT204 (Johnson, 1967), ClTl09 through ClTl '12 (Archambeau ela l ,1969), STAN3 (Kovach and Robinson, 1969), U526 (Anderson and Jul ian, 1969), NTS N3, NTSNE l , and NTS E l ( Ju l i an , 1970 ) , SDL-UT-BR l (Mass6e t a t . , 1972 ) , HWA and HWB (W igg ins andHelmberger, 1973), and SHRI4 (Helmberger and Engen, 1974) Plat form refract ion prof i les inc lude ER2(Green and Ha les , 1968 ) , NC l , YUKON4 , UTAHI , NTS NE I -W P la i ns , and NTS E l -W. P la i ns ( Ju l i an ,1970), and the Mexico prof i le of Shurbet (1972). Shield refract ion prof i les inc lude YLKNFI0 andHUDSBYI0 ( Ju l i an , 1970 ) , t he Ea r l y R i se mode l o f Mass6 (1973 ) , and SMAKI (S impson e t a l , 1974 \ ,the last ofwhich found no low-veloci ty zone necessary (arrow at bot tom of f igure).

'791

E

o

F

1972). For such regions the temperature profi le maybe everywhere subsolidus, and the usual identi-f ication of the top of the low-velocity zone as the baseof the l ithosphere loses its uti l i ty.

Spreading centers: the anhydrous solidus

Throughout most of the low-velocity zone theamount of mel t present is l ike ly to be smal l , on theorder of I percent, and controlled by the HrO andCO2 abundances in the asthenosphere. The melt frac-t ion wi l l be appreciable ( - l0 percent) only when thetemperature is close to the anhydrous solidus (Wyll ie,1971 ;Green , l 97 l ) , a cond i t i on res t r i c ted to reg ionsof upwelling from deep within the asthenospheresuch as beneath mid-ocean ridges. When the fractionof melt exceeds a few percent, the shear modulus issubstantially reduced from the value for solid mate-r ia l or for inc ip ient mel t ing (Walsh, 1969). I f theincrease in melt fraction occurs over a narrow tem-perature interval reasonably well approximated by

the anhydrous sol idus (Wyl l ie , 1971), the seismic lo-cation of this melt-fraction boundary can be used asanother geothermometer.

Such a melt-fraction boundary has been inferredbeneath the mid-Atlantic ridge on the basis of twotypes of seismic measurements: very low Q for shearwaves propagating through the region of extensivemel t ing enclosed by the boundary (Solomon, 1973)and severe distortion of the propagation directions ofteleseismic P waves from ridge-crest earthquakes be-cause ofthe pronounced velocity gradients across theboundary (Solomon and Julian, 1974). The zone ofextensive melting is roughly 40 to 60 km in half-widthin the north Atlantic and from several km to severaltens of km in thickness, in agreement with the degreeof melting (-30 percent) and the magma segregationdepth (15-25 km) inferred flor ocean-ridge mantlefrom the chemistry of sea-floor basalts (Kay et al.,1970). As predicted by most thermal models forspreading centers, the width of the extensively molten

SEAN C. SOLOMON

zone appears to scale approximately with the spread-ing rate (Solomon and Jul ian, 1974).

Other constraints on upper mantle temperatures

The identif ication of the top of the low-velocityzone with the mantle solidus permits a determinationof temperature at the base of the l ithosphere in eachof the regions mentioned above . In this section, suchan exercise is combined with a number of independ-ent techniques for estimating temperatures in the up-per 100 to 200 km of the mantle to present a coherentpicture of temperatures in the shallow asthenosphere.Most of the emphasis in this section wil l be on oce-anic regions, with a discussion on continent-oceandifferences reserved for later.

Figure 3 summarizes the various constraints onoceanic mantle temperatures. The locus of the solidusis sketched from Figure l. The location of the an-hydrous sol idus is taken f rom Solomon and Jul ian(1974). Temperatures at various depths on bothboundaries are taken from the experimental phase

diagram of Green (1973b) on pyro l i te p lus 0.2 per-

cent HrO; somewhat lower temperatures would beindicated if the generally similar phase diagrams ofMysen and Boettcher (1975) or of Milhollen et ql.

(1914) on peridotite plus HrO were employed. Otherentries in the figure are discussed in turn.

Laua temperatures

Temperatures measured on erupting lavas, if nocooling process other than adiabatic decompressionhas operated on the lavas between magma segrega-tion and eruption, are within perhaps 50' to 100'C ofthe temperature of the source of the magma beneaththe point of eruption. Measured temperatures in lavafountains and lava lakes in Hawaii range betweenabout 1060' and I190'C (Aul t e l a l . , 196l ' K inoshi taet al., 1969). Identifying the magma source with thebase of the l ithosphere beneath Hawaii (Eaton andMurata, 1960) gives a temperature at the top of theasthenosphere of 1200' + l00oc, probably some-what higher than beneath nonvolcanic regions.

Mineralogical geothermomelers and geobarometers

The magma temperatures of several ocean-floorbasalts have been calcuiated by Frey et at. (1974) withtwo indepbndent techniques. Using the Kudo andWeill (1970) plagioclase thermometer as refined byMathez (1973) to account for the non- ideal so l id-solution behavior of plagioclase, Frey et al. obtainedplagioclase crystall ization temperatures on four sam-ples of 1230 to 1250'C. Scheidegger (1973) obta ined

higher temperatures withoi.rt the Mathez refinement.Frey et al. also obtained temperatures in the range1170 to 1220"C on three samples from the olivine-l iqu id equi l ibr ia data of Roeder and Emsl ie (1970).

As pointed out by Frey et al., their determinations fitwell with the I atmosphEre l iquidus temperatures ofr idge basal ts (1190' to 1250'C) measured by Ti l ley e lal. (1972). These temperatures are in good agreementwith magma segregation at l5 to 25 km depth (Kay e/al., l97O) and the temperatures indicated beneath ther idge crest in F igure 3.

Pyroxene geothermometry (Boyd, 1973) onmantle-derived ultramafic xenoliths offers consid-erable promise for providing estimates of the localgeotherm at the time the xenoliths were brought fromdeep in the l ithosphere or asthenosphere to near thesurface. The technique is not without some uncer-tainties and corrections yet to be worked out (e.9.,

Boet tcher , 1974; Wi lsh i re and Jackson, 1975), but isuseful at present to corroborate other estimates oftemperature.

Pyroxene geotherms for several regions designatedas oceanic have been constructed by MacGregor(1914) and MacGregor and Basu (1974) and by Mer-

c ier and Carter (1975). The data most readi ly appl iedto a known oceanic environment are those from xe-nol i ths in Hawai ian a lkal i basal ts . The Hawai ian geo-

therms of both Merc ier and Carter (1975) and Mac-Gregor and Basu (1974) (the latter after shift ing to l5percent lower pressures as an approximate correctionfor Fe and Ca to MacGregor's (1974) geobarometerbased on AlrO, solubil ity in orthopyroxene) indicatetemperatures in excess of I 100'C below about 90 kmdepth, in adequate agreement with other estimates.

Oceanic heat fow and topography

The variation of oceanic heat f low and bathymetrywith sea-floor age is well matched by thermal modelsfor the oceanic l ithosphere based on a spreading platewith an isothermal lower boundary (McKenzie,19671,Sleep, 1969; Sclater and Francheteau, 1970; Sclater e/al., 197l: Parsons and Sclater, 1975). The fit of mod-els to observations provides constraints on both thethickness and the temperature at the base of such aplate. A recent analys is (Parsons and Sclater , 1976) ofthe probable values of these parameters gave ll7 Il5 km and 1560 + 390oC, respect ive ly . The uncer-tainties are probably even larger than the formalerrors given, since uncertainties in several physicalparameters, notably thermal conductivity, were notincluded. That the plate thickness determined fromthermal models exceeds the depth to the low-velocity

GEOPHYSICAL CONSTRAINTS ON TEMPERATL]RE VARIATIONS IN THE UPPER MANTLE

^ , /ase , m. ) / ,FIc. 3. Var ious independent est imates of temperature in the oceanic asthenosphere. Discussion of est imates and sources of data are given

in the text ; o is e lectr ical conduct iv i ty , and z is shear stress.

793

EI

oo

zone is to be expected, since the upper part of aconvective boundary layer at the top of the astheno-sphere probably moves with the overlying l ithosphere.The temperature at 120 km depth, which scales ap-proximately as the heat f low in old ocean basins, ishigher than most other estimates in Figure 3, but thevar ious uncer ta int ies over lap.

Viscosity

Viscosity is one of several physical properties thatare extremely sensitive to variations in temperature.Thus, although the viscosity in the asthenosphere isvery diff icult to measure with much precision, even arough estimate can be a useful constraint on temper-ature.

Limits on the viscous drag coefficient acting on thebase of l i thospheric plates have been obtained bycomparing the l ithospheric stress field calculatedfrom plate tectonic driving force models (Solomon elal., 1975; Richardson et al., 1976) with the intraplatestress inferred from midplate earthquake mechanisms(Sykes and Sbar, 1973) and in situ measurements. Thebest f it of calculated and observed directions of orin-

cipal stresses arises when viscous drag acts to retardplate motion and when the shear stress r at the baseof the l ithosphere.l ies in the range (.001 to .01) opu,where oa is the compressive stress near spreadingcenters and u is the absolute plate velocity in cm/yr(Sofomon et al., 1975; Richardson et al., 1976).Tak-ing op = 200 bar (Morgan,1972; Ar tyushkov,1973)and u = 8 cm/yr for oceanic plates (Solomon et al.,1 9 7 5 ) g i v e s 2 ( . r { 2 0 b a r .

Given the shear stress and an estimate of the strainrate, the compilation by Kohlstedt and Goetze (1974)of creep measurements in dry olivine may be used toestimate the temperature at the base of the l itho-sphere. The strain rate e depends on the thickness ofthe shear zonE beneath the l ithosphere but is unlikelyto exceed 3 X 10-14 sec-'. An extrapolation of theKohlstedt-Goetze creep relations to lower strain ratesthan measured (ignoring pressure effects) gives 7 :

l l00 '+100'C for r = 2-20 bar and e : 3 X 10-14sec-1. The formal error in temperature is based on afixed constitutive relation and the given stress rangeand strain rate and so underestimates the total uncer-tainty, particularly on the low-temperature side. In-

P l o g i o c l o s e T h e r m o m e t r y ,L i q u i d u s T t l l 7 5 - 1 2 5 0 " C L o v o : l O 5 O - l 2 O 0 " C

L o w V p , O - . . -

_Lzsq._____)

s ^ , .i {os

Py roxene Geo fhe rmome t r -= - -

lO5O"T. i lOO"C

_---- -sa-_

i = i otoo, ?35.. /--/

O c e o n i c T e m p e r o t u r e s o _ t o _ t f ) _ t , _ t o c e o n r c T o p o g r o p h y ,T . t S O O o C H e o t F l o w 3 l 5 O O t 4 O O " C

SEAN C, SOLOMON

cipient melting wil l lower the temperature estimatefurther, but the results of Auten et al. (1974) suggestthat the reduction may be small.

The shear stress and the viscosity at the top of theasthenosphere thus provide a useful l imit on temper-ature. Though determining these quantit ies in theearth and relating them to temperature and composi-tion in the laboratory need further work, the temper-ature at the top of most oceanic asthenosphere mustalmost certainly be less than 1200'C and perhaps Iessthan I100 'C .

Elect ri cal conduct iui t y

Electrical conductivity is another physical propertyhighly sensitive to temperature. The electrical con-ductivity of the upper mantle may be estimated byinversion of geomagnetic variation data (Banks,

1969; Parker, 1970), though at present the data arenot accurate enough to extract more than averagesover depth intervals of several hundred kilometers(Parker, 1970). The inferred average conductivity of0.1 O-rm- ' for the upper 400 km of the mant le im-p l i e s a t e m p e r a t u r e o f 1 8 0 0 ' C i f t h e c o n -ductivity-temperature relation for the most electri-

cally resistive olivine is used (Duba et al., 1974).This

is only an upper l imit on tcmperature, since the elec-

trical conductivity averages are dominated by the

most conductive regions both radially and laterally

and the mantle may be more conductive as a function

of temperature than olivine. Accounting for a small

amount of partial melt, for instance, could lower the

temperature estimate substantially (Chan el al., 1973:

Waff, 1974).

aSeismic attenuation can also be strongly dependent

on temperature. In a partially-melted asthenosphere;

the temperature sensitivity is due to a dependence on

the viscosity of the melt phase (Walsh, 1969; Solo-

mon, 1972). There are no experimental grounds for

assigning a temperature on the basis of a determina-

tion of Q at depIh, but some limits can be placed on

the magnitude of the lateral variation of temperature

within the asthenosphere from lateral differences in

the travel-time delays and attenuation of P and S

waves which travel through the asthenosphere. Fig-

ure 4 is a map of temperature variations in the North

American asthenosphere (after Solomon, 1972), con-

120

I l o l o o 9 0 8 0

Frc. 4. Lateral var iat ion of temperature ( 'C) in the asthenosphere of the Uni ted States, af ter Solomon

(1972). The value oI temperature beneath the point in Michigan is set at 1200"C, and al l other values

fol low f rom the assumpt ion that seismic-wave t ravel- t ime delay and at tenuat ion in the North American

asthenosphere are governed by a shear re laxat ion (Walsh, 1969). The re laxat ion t ime is taken to be

thermal ly act ivated wi th an act ivat ion energy of 57 kcal /mole. Temperatures correspond to a depth in the

middle of the low veloci ty zone, or perhaps 150 km.

I o

A s t hen osp hereT e m p e r o t u r e

.1238 tzsz \ tu^;f,-a1 /-

\ / { f ) ^ f ,A 1186

1 ' t toz

\ \egof r7 tzo1

\t 2 2 t \. t 2 : 4

l1ts 1206

GEOPHYSICAL CONSTRAINTS ON TEMPERATURE VARIATIONS IN THE UPPER MANTLE

structed by assuming that lateral variations in delaysand attenuation are due to regional differences in themelt volume and melt viscosity in the asthenosphere.The absolute level of temperature in the astheno-sphere is uncertain using these data, but lateral {iffer-ences of no more than 100' to 200'C are adequate toproduce viscosity variations large enough to accountfor the observed lateral variations in seismic proper-ties.

Phase boundaries as geothermometers: oliyine-spinel

Several seismic discontinuities deeper in the mantlehave been associated with particular mineralogicalphase transitions (Ringwood, 1970), most notablythe transition from the olivine to the spinel to the Bphase of (Mg,Fe)rSiOn (Ringwood and Major , 1970)at about 350 to 400 km depth, and the breakdown ofthe spinel phase to constituent oxides (Kumazawa e/al., 1914; Ming and Bassett, 1975) at about 650 km. Ifthe loci of these boundaries in temperature-pressure-composition space are known from laboratory ex-periments, then the depth of each such seismic dis-continuity may be converted to a temperature in themant le at that depth (Anderson. 1967). As a check on

such determinations, the vertical gradient in seismicvelocity, if sufficiently well known, may be comparedwith velocity profi les predicted from assumed miner-alogical assemblages and geotherms passing throughthe points indicated by phase boundaries (Anderson,1967; Graham, 1970; Forsyth and Press, l97l).

The 350 km discontinuity

The depths to the top of the olivine-spinel transi-tion as determined by several long refraction profi lesare given in Figure 5. The principal uncertainty inlocating the transition comes from a possible tradeoffbetween transition depth and the average velocity inthe overlying mantle. Thus, much of the spread inreported depths to the olivine-spinel transition is notreal. The three profi les reporting the shallowest tran-sit ion depth (Mass6 et al., 1972; Mass6, 1973; Simp-son et al., 1974), which all have an additional discon-tinuity 40 to 100 km below the first, were made inregions of pronounced lateral heterogeneity, and thusthe spherically-symmetric models fit to the profi lesare suspect (Julian, 1970). The two deepest reportedtransitions are from models HWA and HWB of Wig-gins and Helmberger (1973), since supplanted by

o6 a ,

o

4 o -

o

2 ;-oE:tz

250 300 3so 400 450Depth to f op o f t rons i t i on , k m

Ftc. 5. Seismic determinat ions of the depth to the top of the ol iv ine-spinel t ransi t ion. Each boxrepresents the th ickness determined f rom one refract ion prof i le; an,S wi th in the box designates an S-waveprof i le and the O designates the s ingle oceanic determinat ion (Frohl ich et a l . , 1975) Cont inental prof i lesinclude CIT204 (Johnson, 1967), CITl09 through I t2 (Archambeau et a| . ,1969), STAN3 (Kovach andR o b i n s o n , 1 9 6 9 ) , U 5 2 6 ( A n d e r s o n a n d J u l i a n , 1 9 6 9 ) , H U D S B Y l 0 , Y U K O N 4 , N T S N 3 , N T S N E l , a n dNTS E l ( Ju l i an , 1970 ) , SDL-UT-BR l ( dashed , Mass6 (1972 ) , HWA and HWB (W igg ins and He lmbe r -ger, 1973), the Ear ly Rise model (dashed) of Mass6 (1973), SHF. 14 (Helmberger and Engen, 1974), andSMAKI (dashed, Simpson et a l . , 1974). Dashed boxes are f rom prof i les crossing pronounced lateralheterogenei t ies. The conversion f rom depth (bot tom scale) to temperature ( top scale) fo l lows Ringwoodand Major (1970). The phase change elevat ion in the Tonga s lab is f rom Fig.6.

T e m p e r o i u r e o f t r o n s i l i o n , " C

O l i v i n e - S o i n e l T r o n s i t i o n

Tongo s lo b

SEAN C SOLOMON

SHR l4 of Helmberger and Engen (1974), in which anadditional discontinuity of about 500 km depth l iesbetween those at 360 and 620 km.

Excepting the outl ier determinations, the oli-vine-spinel transition appears to l ie at 360 t l0 kmdepth. This depth may be converted to a temperatureat that depth using Ringwood and Major's (1970)experimental high-pressure phase diagram for(Mg,FelSiOa at 1000'C, a Clapeyron slope for thereact ion of 30 bar l 'C, and an Mg/(Mg * Fe) molarfraction for the upper mantle of 0.89 (Ringwood andMajor , 1970). At 1000'C the t ransi t ion occurs at 100kbar pressure, so at 360 km depth the transitiontemperature is 1300 + 150'C. The uncer ta inty intemperature is calculated assuming a l0 km uncer-tainty in transition depth, a 0.03 uncertainty inMgl(Me * Fe) , and a l0 bar /oC uncerta inty in theClapeyron s lope. Anderson (1967) and Graham(1970) obta ined s l ight ly h igher temperatures us ingsomewhat different data.

tions in the upper mantle occur near subductionzones, and thermal models for the descending platepredict that the olivine-spinel transition wil l begreatly elevated within the cool slab relative to nor-mal mant le (e.9. , Turcot te and Schubert , 1971). Thishas been verif ied using the travel t imes of waveswhich have propagated through the slab (Fig. 6, afterSolomon and Paw U, 1975). The change in the meanP wave travel-time residuals with earthquake depthfor deep Tonga events observed at Australian sta-tions is more pronounced between about 250 and 350km depth than over other depth intervals (Fig. 6).This observation requires a higher velocity contrastbetween slab and normal mantle over that depthrange than over other s imi lar in tervals , and is mostplausibly explained as due to an elevation by 100 kmof the o l iv ine-spinel t ransi t ion in the s lab (Solomonand Paw U, 1975). Such an e levat ion impl ies a1000'C temperature contrast between slab and nor-mal mant le at about 250 km depth.

Some of the variation in the apparent depth to theolivine-spinel transition between neighboring conti- The 650 km discontinuity

nental profi les may be real (Julian, 1970). Variations For completeness, the several seismic determina-of l0 to 30 km in depth would require lateral temper- t ions of the depth to the inferred spinel-oxides transi-ature differences of l00o to 300'C or differences in tion are summarized in Figure 7. DeterminationsMgl(Mg + Fe) of 0.03 to 0.10 (Ringwood and Ma- from long refraction profi les and from P'P'jor , 1970). (PKPPKP) precursor t imes are both inc luded. The

The most pronounced lateral temperature varia- latter set of determinations are on the whole the more

D e p l h , k m

FIc. 6. (Lef t ) A schemat ic v iew of the exper iment used to detect an elevat ion of the ol iv ine-spinel phasechange in subducted l i thosphere. Isotherms (dashed), the phase t ransi t ion region (shaded), earthquakehypocenters (dots) , and a typical P-wave path are i l lustrated. (Right) Mean t ravel t ime residual versusearthquake depth for Tonga earthquakes recorded by Austra l ian stat ions at Charters Towers (CTA) andBrisbane (BRS), f rom Solomon and Paw U (1975). The arrows del imi t approximately the depth intervalover which the residual versus depth curves change most rapidly.

o-c)o

D i s t once

l i , 0l iv ine:;ll:lii!ir,+liiirri i!!1.?r.1'rli'ri

S p i n e l - O x i d e s T r o n s i t i o n

reliable, since the former depend on the integratederrors in the vertical travel t ime through the overlying,layers; however, the P'P' precursors are reflectionsoff a sharp velocity change confined to a depth inter-val less than 4 km th ick (Richards, 1972) and neednot mark the top of the t ransi t ion zone.

The depth to the spinel-oxides transition cannotyet be converted reliably to a temperature, since thedependence of transition pressure on temperature isnot known. Even the s ign of the Clapeyron s lope isuncertain (Jackson et al., 1974). Whether the spreadin transition depths has any reality is not yet demon-strable. Fitch (1975) reported higher than normal P-wave velocities at about 600 km depth within theTonga s lab, perhaps indicat ing upward d isplacementof the 650-km t ransi t ion. Solomon and Paw U (1975)found no evidence for such a displacement but werenot able to ru le i t out .

Synthesis and discussion

All of the constraints on temperature introducedabove may be combined to discuss some of the fea-tures of geotherms. A simple but important caution isthat there is no single geotherm with any physicalreality. nor even meaningful "oceanic" or "continen-

797

tal" geotherms. In oceans, it is clear that the l itho-spheric portion of the geotherm evolves with l itho-sphere age. In continents, it appears that thelithospheric l imb of the geotherm varies (moreslowly) with the age of the upper crust.

Neither wil l a single geotherm in the asthenospherebe adequate for either oceans or continents. Accord-ing to the arguments of Richter (1973), Richter andParsons (1975) and McKenzie and Weiss (1975), heatis transported through the asthenosphere by a con-vection pattern secondary to the pattern of plate mo-tions. The secondary convection has a horizontalscale comparable to the depth extent of this second-ary flow, probably about 600 km. Though the"mean" temperature profi le in the asthenosphere wil lbe very nearly adiabatic (McKenzie et al,, 1974),thegeotherm in any given location wil l depend onwhether the region is over an upwelling, mid-cell, ordownwelling portion of the secondary flow and wil lnot necessarily be stationary in time.

Some schematic geotherms

Several oceanic geotherms consistent with the dis-cussion above are sketched in Figure 8. The materialupwelling beneath spreading centers wilI r ise more or

GEOPHYSICAL CONSTRAINTS ON TEMPERATURE VARIATIONS IN THE IJPPER MANTLE

600 650Dep t h t o t r ons i t i on , km

700

FIc. 7 Seismic determinat ions of the depth to the inferred spinel-oxides t ransi t ion Each box representsone determinat ion. Shaded boxes are est imates using P'P' precursors (Engdahl and Fl inn, 1969; Whit -comb and Anderson, 1970; Adams, l97l) , open boxes ( ,9 for S waves) are f rom refract ion prof i les,inc luding CIT2O4 (Johnson, 1967), CITl09 through I l2 (Archambeau et a l . , 1969), STAN3 (Kovach andRobinson, 1969), U526 (Anderson and Jul ian, 1969), HWA and HWB (Wiggins and Helmbergel 1973),the NTS east model (dashed) of Mass€ ( t974), SHR14 (Helmberger and Engen, 1974) and SMAKI(dashed, Simpson et al , 1974)

ao

' o

o-

o

D L- o-oI

=z

SEAN C. SOLOMON

(J

ol

ooEo

F

| 500

tooo

t u f - : ^ UPs " -a ' / oceontr

'

// ,",oceonll ' Y:r::':-----

Ridge/, ' : - , . ------ : : -----":,nt-/-"1

, : l/ Con t i nen to l; Pyroxene

i Geo lhe rmsO l - S p

i'l/,''4/,i ,;,i,i"",n7V,' ,''l' .i'") ' , , , 7 ' / ' ! /

H o w o i i . / , ' I / , / I ,i i i . / . :Pyroxene ,r/ , . / , i , ' t ' i1.r ' i

ceotherm(1./ ,,/y! /t .,1r. .! eronx

/ . , / / i , . ,1.,1 . ' s^itn' \ . . / t ' / ! . ' . t

/ . ' / / i i ' l ' s m i t h

l ' l / t i . / : . 1 - '

' ., ' / ., ',/' ' ./,,

I / i . zi . / ( -"*,\ - - / M i n g B o r

o loo 200 300 400D e P t h , k m

Ftc. 8. Some schemat ic geotherms. The pyrol i te sol idus wi th 0 2 percenl HrO and for anhydrous

condi t ions are f rom Green (1973b). The oceanic upwel l ing-r idge curve intersects the anhydrous sol idus at

the depths indicated in Fig. 3 and fo l lows an adiabat below The oceanic mid-cel l curve fo l lows an adiabat

upward f rom the ol iv ine-spinel t ransi t ion at 360 km depth (Fig 5) and intersects the sol idus at I 100'C

and 85 km depth. A curve for upwel l ing beneath a basin (Hawai i?) is a lso sketched. Several pyroxene

geotherms are included. Hawai ian geotherms I and2 are respect ively f rom MacGregor and Basu (1974)

and Mercier and Carter (1975). Geotherms are shown for the Lesotho k imber l i te (Boyd and Nixon, 1973),

the Frank Smith k imber l i te (Boyd, 1974), and the Ming Bar d iatreme (Eggler and McCal lum, 1974), and

approximately bracket other cont inental geotherms.

less adiabatically from some depth in the lower por-tion of the asthenosphere. To satisfy Figure 3, theoceanic upwelling-ridge geotherm is drawn to inter-sect Green's (1973b) anhydrous sol idus at 40 and 5km depth and follows an adiabat below 40 km.

Upwelling associated with the secondary scale ofconvection (Richter, 1973; Richter and Parsons,1975; McKenzie and Weiss, 1975) wi l l a lso occurunder ocean basins. An oceanic upwelling-basin geo-therm following the same adiabat as the ridge curvehas also been sketched. A thermal boundary layer ofuncertain thickness separates the adiabatic portion ofthe curve from the base of the l ithosohere. drawn to

intersect Green's (1973b) pyro l i te * 0.2 percent HrO

sol idus at I100'C (af ter F ig. 3) .Ocean basin regions situated over downwelling or

mid-cell portions of the secondary scale of convectionwill be characterized by a cooler geotherm below thelithosphere. A oceanic mid-cell-basin geotherm is

sketched in Figure 8 to follow an adiabat upwardfrom the olivine-spinel transition at 360 km depth(Fig. 5) and to in tersect Green's (1973b) pyro l i te *

0.2 percent HzO sol idus at I 100"C. The thermalboundary layer between the l ithosphere and that por-

tion of the geotherm with an adiabatic gradient may

be th icker than the boundary layer over an upwel l ing

GEOPHYSICAL CONSTRAINTS ON TEMPERATURE VARIATIONS IN THE UPPER MANTLE

adiabat, and the mid-cell gradient may actually besubadiabatic in the asthenosphere (McKenzte et al.,197 4) The oceanic upwelling and mid-cell geothermsare separated in Figure 8 by about l00oC, an accept-able value (McKenzie et al., 1974) but one for whichno independent information is available. The up-well ing, mid-cell, and downwelling (not shown) oce-anic geotherms meet at the bottom of a second ther-mal boundary layer located at the base of thesecondary flow.

Two pyroxene geotherms based on spinel lherzolitexenoliths in Hawaiian alkali basalts (MacGregor andBasu, 1974; Merc ier and Carter , 1975) are a lso in-cluded in Figure 8 and are adequate continuationsinto the l ithosphere of the basin geotherms sketchedin the asthenospheric portion of the figure.

An interesting aside is that if a stable basin regionsits atop a convective upwelling in the asthenosphere,there is no reason why the geotherm cannot be steep-er in the thermal boundary layer at the top of theasthenosphere than in the overlying l ithosphere. Thiswould give rise to a "kinked" geotherm such as thosereported for South African kimberlites (Boyd, 1973,1974; Boyd and Nixon, 1973; MacGregor and Basu,1974). As pointed out by many authors, such a k inkcannot be a steady-state feature. If the kink arises asin Figure 8, neither the flow pattern in the astheno-sphere (Richter , 1973; McKenzie et a l . ,1974) nor therelative position of the asthenosphere flow and theoverlying l ithosphere need be stationary for t imescomparable to the thermal equil ibration time of thel i thosphere ( -50 m.y. ) .

C ont ine nt - o ce an diffe re n ce s

It is now well known that continental and oceanicmantle must differ in temperature andlor in composi-tion at least to depths of about 200 km. The evidencesupporting this view includes the following: Themantle contribution to observed surface heat f lowappears to differ markedly between stable ocean ba-sins and continental shields (Sclater and Fran-cheteau, 1970), although this difference may be re-duced somewhat if corrections are made to thecontinental measurements to account for differentdegrees of saturation between in situ conditions andlaboratory conditions during conductivity determina-tions (Simmons and Nur, 1968) and for possiblepaleoclimatological effects (e.9., Horai, 1969). Thedepth to the low-velocity zone beneath stable conti-nents is greater than beneath ocean basins (Figs. Iand 2). Finally, pyroxene geotherms determined incontinental regions are typically cooler than those for

799

oceanic environments to at least 150 km depth (Mac-Gregor and Basu, 1974). Several continental pyrox-ene geotherms are shown in Figure 8, includingthose from the Lesotho (Boyd and Nixon, 1973) andFrank Smith (Boyd, 1974) kimberlites in South Af-rica and the Ming Bar diatreme in Montana (Egglerand McCallum, 1974). The data of Hearn and Boyd(1973) from Montana plot within or slightly abovethe field for Ming Bar. The South African kimberlitedata of MacGregor and Basu (1974), after shift ing tol0 to l5 percent lower pressures as a geobarometercorrection, plot in the range of Boyd's kimberlitegeotherms.

In a recent provocative paper, Jordan (1975) hasargued that thermal and/or compositional differ-ences between ocean basins and continental shields

must persist well below 200 km, to at least 400 kmdepth and probably greater. Jordan offered threemain arguments: (l) The ScS travel t imes from deepearthquakes to oceanic island stations are 5 sec laterthan the times to typical continental stations (Sipkin

and Jordan, 1975). This observation, together withmeasured differences in the phase velocities of long-period surface waves between continental and oce-anic paths, requires that systematic differences in Swave velocity between oceans and continents extendto at least 400 km depth. (2) The S wave travel t imesthrough the upper mantle computed from earth mod-els obtained by inversion of free-oscil lation periods

are several seconds greater than those obtained usingbody-wave travel t imes, most commonly recorded atcontinental stations. Since free oscil lations sample apredominantly oceanic earth, Jordan's inference isagain that the oceanic and continental structural dif-ferences must be deep. (3) Direct examination of theconstraints on temperature at depth beneafh con-tinents and oceans leads to the conclusion that oce-anic and shield geotherms do not intersect above 400to 600 km.

Each of these arguments, howevet, can be shownto be inconclus ive. Okal and Anderson (1975), us ingmultiple Sc,S arrival t imes, have shown that the verti-cal S-waile travel t ime is generally similar beneath oldoceanic and old continental regions, clearly implyingthat the is land stat ions used by Sipk in and Jordan(1975) do not overlie typical oceanic structure. More-over, differences in the oceanic and continental dis-persion curves for long-period surface waves do notby themselves require differences between oceanicand continental structure below 200 km (Dziewonski,

t97 t).The difference in the vertical S-wave travel t ime in

800 SEAN C. SOLOMON

the upper mantle between free-oscil lation models andbody-wave refraction models need not imply deepocean-continent heterogeneity. An equally plausibleexplanation, one expected on the basis both of solid-state theory and of attenuation data, is that thegreater travel t ime inferred from the longer-periodfree-oscil lation data arises from a mild frequency de-pendence of the shear modulus in the upper mantledue to a thermally-activated relaxation process suchas incipient melting or viscous grain-boundary relax-at ion (Nur, 1971; Solomon, 1972).

Jordan's (1975) th i rd argument is based ent i re ly onhis particular choice of oceanic and continental geo-therms. His conclusion that the thermal contrast be-tween shields and oceans must persist to 400 kmarose from selecting an oceanic geotherm too hot by100 to 200'C (see Figs. 3 and 8) and from basing hisshield geotherm on the MacGregor and Basu (1974)pryoxene geotherms, for which the authors admitteda l0 to l5 percent overestimate of pressures.

A more l ikely comparison of oceanic and continen-tal geotherms is given in Figure 8. The contineritalregions are cooler than the ocean basins to depths of150 to 200 km, and the shield geotherms may notintersect the mantle solidus at any depth. Systematiccontinent-ocean differences do not appear to extendbelow about 200 km on the basis of any of the ther-mal arguments considered in this paper. If the asthe-nosphere below 200 km is indistinguishable beneathoceans and cont inents then many ofJordan's (1975)other deductions on chemical layering in the mantleand on mantle convection are incorrect.

Conclusions

There is a wide variety of geophysical and miner-alogical data that loosely or t ightly constrain thetemperatures in the earth's upper mantle. Seismolo-gical geothermometers include the depth to the top ofthe low-velocity zone, interpreted as the onset ofincipient melting, the depth to the melt-fractionboundary associated with the anhydrous solidus, andthe depth to the top of the olivine-spinel transition.Other constraints include the temperatures of erupt-ing lavas, the parameters of l i thosphere cooling mod-els, and the measurement of thermally-activatedproperties of the mantle such as viscosity, electricalconductivity, and seismic attentuation. Pyroxene geo-thermometry provides results entirely consistent withall the other constraints and may eventually prove tobe the temperature-sensing technique with the bestdepth resolution.

The most probable value for the temperature at the

base of the l ithosphere, as defined seismically, isI 100'+ 100'C on the basis of all considerations. Thelithosphere is 90 to 100 km thick beneath old oceansand 50 or more km thicker beneath shields. Shieldsare about l00o to 200"C cooler than ocean basins at100 km depth, but the thermal contrast betweenstable continental and oceanic regions probably dis-appears by 200 km depth. Thermal gradientsthroughout most of the asthenosphere are nearly adi-abatic. Lateral temperature variations of up to per-haps 200'C persist at least to 400 to 600 km depthand are closely related to the convective flow patternin the asthenosphere. A major unsolved problem is torelate quantitrit ively the inferred .temperature varia-tions in the asthenosphere to a realizable flow model.

AcknowledgmentsI thank Buzz Craham for a critical review and Art Boettchgr and

Peter Wyllie for instructive discussion This research has beensupported by the Earth Sciences Section, National Science Foun-

dat ion, NSF Grant DES75- I 4812, and by the Advanced Research

Projects Agency, monitored by the Air Force Office of Scientific

Research under contract F44620-7 5C-0064.

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GEOPHYSICAL CONSTRAINTS ON TEMPERATT]RE VARIATIONS IN THE UPPER MANTLE