Finite Strain and Their Relation to Tectonic Deformation Byusing Normalized Fry Method in Ber Bahr...

AARJMD VOLUME 2 ISSUE 3 (AUGUST 2015) ISSN : 2319 - 2801

Asian Academic Research Journal of Multidisciplinary

www.asianacademicresearch.org

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A Peer Reviewed International Journal of Asian

Academic Research Associates

AARJMD

ASIAN ACADEMIC RESEARCH

JOURNAL OF MULTIDISCIPLINARY

FINITE STRAIN AND THEIR RELATION TO TECTONIC DEFORMATION BY

USING NORMALIZED FRY METHOD IN BER BAHR ANTICLINE NORTH OF

MOSUL CITY –IRAQ

AHMED A. H. AL-MOADHEN1; MUSTAFA R. S. AL-OBAIDI

2

1Department of Geology, College of Science, University of Baghdad

2Department of Geology, College of Science, University of Baghdad

Abstract

Iraq is one of the countries that are exposed to tectonic activity due to its location. Zagros-

Tours belt is located in the collision area between the Arabian plate and Iranian- Turkish

plates. For the first time in the High Folded Zone- North of Iraq, the principal strain axes has

been analyzed and this related to tectonic deformation of beds. This zone is one of the most

important tectonic zone in Iraq. Different strained beds are present in this zone; Sandstone

and limestone beds being the dominant type in the N and NE of Iraq. These beds in the study

area are deformed and contain many faults and folds The calculated axial ratios (three

dimensional orientations of the strain axes) of strained beds are shown which is equivalent to

the log Flinn diagram normally used for plotting strain ellipsoids and according to the

stereographic projection method, the long axes of these ellipsoid are sub parallel to

measured fold axes and the short axes are approximately perpendicular to the axial planes

of folds in the area. The compensation of strain data (axial ratio layer parallel

shortening) between the study area and other areas has been done. These orientation of these

axes is related to the movement of the Arabian plate.

Keywords: Structural geology, Strain analysis, Fry Method, Ber Bahr Anticline, Iraq.




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1-2 Introduction

Folded strata must always have an heterogeneous strain state through the structure ( Ramsy

& Huber 1987) at any locality where the bedding has a constant orientation the strain may

be homogenouses , but the different lithologies are likely to have different strain. Under

this assumption the Fry method is one of the best methods for the analysis of deformed

ellipsoids. This method is based on the assumption that the initially uniform anticlustered

distribution distribution of points will change after deformation into a non-uniform

distribution.

Finite strain data can provide important information about the structure of a deformed

terrane, such as strain intensity gradients or distribution of strain in high folded zone in the

north part of Iraq. Many methods of finite strain determination exist, and are based either

on grain-location analysis (Fry, 1979; Erslev, 1988) or on grain-shape analysis (Rf/ɸ)

method of Ramsay (1967) and Dunnet (1969); Panozzo methods (Panozzo, 1983, 1984);

Feret diameters method of Lapique et al. (1988). These methods require different

parameters to characterize the shape or location of the quartz grains or other strain markers

(coordinates of the centers of mass, lengths of major and minor axes and their orientations,

or location of whole boundaries of grains). In fact, all of these parameters can be computed

from the whole boundary of a grain, if it is assumed to be an ellipse. This paper deals with

computation of the finite strain using the Normalized Fry method from thin sections of

sandstone of the Ber Bahr Anticline - North of Iraq.

The Ber Bahr anticline (Zawita anticline) located in the northern part of Iraq, it lies within

Dohuk Governorate, its covering an area of 195 square kilometers and the geographic

coordinates of the study area as follows : Northing 36°50´ – 36°58´ and Easting 42° 57´-

43°14´ (Figure 1).

1-3 Geological Setting

The exposed geological formations in study area range in age from Cretaceous to

Quaternary, these formations are Bekhmah , Shiranish, Kolosh, Khurmala, Gercus, Pila

spi, Avanah, Fatha and Injanah (Figure 2).

According to the tectonic map (Buday and Jassim,1984 ) (Jassim and Goff, 2006), study

area is located within the Unstable Shelf , represented by the High Folded (Figure 1). Ber

Bahr anticline is the continuation of Shaik Adi Anticline towards west. It has abnormal

trend, bence began with E-W direction, then swings to ENE-WSW and again to E-W. It

probably joins with Aqra Anticline, but because the probable area is built up by Pilaspi

Formation which is highly deformed, therefore it is difficult to decide whether the two

anticlines join, each other or not. The southern limb is steeper than the northern one, with

exposed Bekhme Formation in the core. The northwestern plunge is inundated by Dohuk

lake (Sisakian,1995).

Between Ber Bahr and Swara Tika Anticlines there is long, narrow and deep syncline, in

its trough even the Mukdadiyah Formation is preserved. The axis of the syncline is




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truncated by thrust fault with E-W direction and has brought the Pilaspi Formation in

contact with Injana and Mukdadiyah Formations. The thrust fault is truncated by small

fault of NE-SW trend, the displacement is about 200-300m (Sisakian,1995).

Figure 1 : Tectonic map of Iraq (after Buday and

Jassim1984).

Figure 2: Geologic map of study area (Sisakian,1995).




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1-4 Methodology

Strain analysis quantifies strain magnitude and/or orientation of distortion in rocks between

microscopic to regional scales. The basis of strain-measurement techniques involves

measuring strain markers to obtain principle strain axes orientations and axial ratios. In

case strain markers are passive, which means they have similar rheological properties as

the host rock and deform in the same manner as the whole rock, then the total strain in the

sample can be characterized. Non-passive strain markers have rheological properties which

are contrast those of the host rock, and thus provide only a minimum estimate of total bulk

strain (Bannister,2004).

1-4-1 Normalized Fry method:

Fry method is the fastest and visually more considered the most attractive method for

finding two-dimensional strain and was developed by Norman Fry at the end of the 1970s

(Fossen, 2010). This method of strain analysis is a type of center-to-center method, it uses

the distances between grain centers as a basis for measuring strain. Specifically, this

method is a graphical approach uses the distribution of the centers of initially spherical

strain markers to determine a strain ellipse for the rock (Fry 1979; Ramsay and Huber

1983; Figure 3). A Fry plot is produced by plotting the location of strain-marker centers

which used as a function of distance from every other strain-marker center (Figure 4).and

this can be done manually by plotting each grain center on a sheet of tracing paper

overlying a photomicrograph of grains; if the grain centers plotted again and the overlay

is moved incrementally, the shape of a strain ellipse eventually appears. The ellipse is in

the form of a void in the center of the Fry plot, which defines the strain ellipse with an

axial ratio (Rs). The orientation of the strain ellipse is mainly measured by using the rake

of the long axis from the baseline (Φ) in the principle plane of strain. This method is the

most effective with strongly anti-clustered, basicly spherical strain markers of an equal

sizes that are strained homogenously (Fry 1979; Dunne et al. 1990; Crespi, 1986). The

occurrence of such strain markers is not usually common in nature. So to compensate for

this problem, developed the normalized Fry method Erslev (1988). This modification

accounts for natural variations in the sizes and sphericity of strain markers. This method

generates plots with agreater definition of the central void.

Six field-oriented samples of Sandstone were collected from Injana , Fatha and Gercus

Formation from both limbs of the fold (Figure 5 ). All the samples have been cut into

three mutually perpendicular slabs in anticipation of a future 3D strain analysis: (1)

bedding normal/parallel to strike (PTS); (2) bedding normal/in the dip plane (IDP); and (3)

bedding parallel (PTB). Slabs were notched to preserve the field orientation of the sample

during professional thin section preparation. Large-format thin sections were used to

provide ample surface area for choosing representative areas for analysis (Figure 6

illustrates the spatial relationship between these slabs(Digital photomicrographs were taken

of each thin section through a 4X objective lens with the upper and lower polars set

parallel using a Sony 1080 digital camera to produce 9.1 megapixel images (Figure 7).




276

Figure 4 : The construction of a fry plot. (A) the position of an overlay centered on point1

with all other points located relative to point 1. (B) The overlay centered over point 2 and

all points located relative to point 2 . (C) The final diagram once every point has been used

as the center for the overlay . The central void defines the shape and orientation of the

strain ellipse (Ramsay and Huber 1983)

Figure 3 : Diagram showing how the distance between grain centers change with direction

when strain develops. (A) unstrained grains, (B) strained grains. (Ramsay and Huber,

1983)




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Figure 5 : Sample 4 -Southern limb in Ber Bahar anticline.

Figure 6 : (A) schematic diagram showing mutually perpendicular slabs cut

from field oriented samples. slabs are oriented parallel to bedding ( PTB),

bedding normal / parallel to strike ( PTS), and bedding / in dip plane ( IDP).

(B) slabs were prepared as oriented petrographic thin sections (Bannister,

2004).




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S limb Sample 4 PTB (4x) S limb Sample 4 IDP (4x) S limb Sample 4 PTS (4x)

N limb Sample 1 PTB (4x) N limb Sample 1 IDP (4x) N limb Sample 1 PTS (4x)

Figure 7: Thin sections of sandstone for samples (1 , 4) in northern and

southern limb showing the quartz grains distribution

1-4-2 EllipseFit v.3.1 software

Sandstone photomicrographs were analyzed using EllipseFit v.3.1 (© Frederick W.

Vollmer 2014). This program creates elliptical outlines and calculates grain centers of

individual grains from digitized locations of five points along grain margins (Figure 8).

More than Seven hundred grains were digitized on each photomicrograph to produce

statistically valid Fry plots. EllipseFit generates Fry plots from digitized grain data in

accordance with the methods outlined by Fry (1979).

Elongation is easily calculated from the difference in deformed and undeformed axial

lengths divided by the undeformed length (Eq. 1). Note that negative values are expected

for shortening and that multiplying results by 100 will yield a percentage change. The

undeformed length is determined by solving for the radius of a circle with an area equal to

an ellipse with axial ratio Rs (Figure 9 ). Substituting values from figure 7 into equation 1

and then simplifying in terms of Rs yields equation 2 (Bannister,2004)..




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Figure 6 : Screen shots from

EllipseFit v.3.1 (A). Parameters

for each digitized grain are

recorded in a data table. (B) Fry

graph setting (C) Fry plots

produced from the strain data.

Figure 8 : Screen shots from EllipseFit v.3.1 (a). Parameters for each digitized grain are

recorded in a data table. (b) Fry graph setting (c) Fry plots produced from the strain data.

Figure 9 : Example of a strain ellipse illustrating relationships between axial ratio (Rs),

undeformed circle radius (r), principle stress (σ1), deformed ellipse axes (a and b), ellipse

orientation (Φ), deformed and undeformed axis lengths (ld and lu), and area of each ellipse

(A). (A) Shape before deformation. (B) Shape after 25% strain (Bannister, 2004).




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1-5 Three-dimensional strain :

The finite spatial change in shape that is connected with deformation is completely

described by the strain ellipsoid. The strain ellipsoid is the deformed shape of an imaginary

sphere with unit radius that is deformed along with the rock volume under consideration.

The strain ellipsoid has three mutually orthogonal planes of symmetry, the principal planes

of strain, which intersect along three orthogonal axes that are referred to as the principal

strain axes. Their lengths (values) are called the principal stretches. These axes are

commonly designated X, Y and Z, but the designations √ʆ1, √ ʆ 2 and √ ʆ 3 , S1, S2 and S3

as well as e1, e2 and e3 are also used, where X represents the longest, Z the shortest and Y

the intermediate axis: X > Y > Z When the ellipsoid is fixed in space, the axes may be

considered vectors of given lengths and orientations. Knowledge of these vectors thus

means knowledge of both the shape and orientation of the ellipsoid. The vectors are named

e1, e2 and e3, where e1 is the longest and e3 the shortest, as shown in figure 10 .

Any strain ellipsoid contains two surfaces of no finite strain. For constant volume

deformations, known as isochoric deformations, these surfaces are found by connecting

points along the lines of intersection between the ellipsoid and the unit sphere it was

deformed from. For plane strain, where the intermediate principal strain axis has unit

length, these surfaces happen to be planar. In general, when strain is three-dimensional, the

surfaces of no finite strain are non-planar. Lines contained in these surfaces have the same

length as in the undeformed state for constant volume deformations, or are stretched an

equal amount if a volume change is involved. This means that: A plane strain deformation

produces two planes in which the rock appears unstrained. It also means that physical lines

and particles move through these theoretical planes during progressive deformation. The

shape of the strain ellipsoid can be visualized by plotting the axial ratios X/Y and Y/Z as

coordinate axes. As shown in Figure 11, logarithmic axes are commonly used for such

diagrams. This widely used diagram is called the Flinn diagram, after the British geologist

Derek Flinn who first published it in 1962. The diagonal of the diagram describes strains

where X/Y¼Y/Z, i.e. planar strain. It separates prolate geometries or cigar shapes of the

upper half of the field from oblate geometries or pancake shapes of the lower half. The

actual shape of the ellipsoid is characterized by the Flinn R-value.

In the Flinn diagram, strain magnitude generally increases away from the origin. Direct

comparison of strain magnitude in the various parts of the diagram is, however, not

trivial.Strain ellipsoid represented on alog Flinn diagram




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Sample 1 Sample 2 Sample 3

Sample 4 Sample 5 Sample 6

Figure 10: The 3D strain ellipsoid for six sample of Northern and southern limbs showing

the strain axes

Figure 11: Strain ellipsoid represented on a log Flinn diagram. Using the Fry method , set

of ellipsoid fall in the biaxial positive field, the strain ellipsoids are determine from

sandstonebeds




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Figure 12 : The relationship between axial plane and the orientation of the principal axes of

the fry strains. long, intermediate and short axes show by circles , diamonds and triangles

respectively

Figure 13: Three dimensional strain axes and strain ellipsoids found by the Fry method

across the fold.




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PTB of N limb Sample2 IDP of N limb Sample2 PTS of

N limb Sample2

PTB of N limb Sample1 IDP of N limb Sample1 PTS of

N limb Sample1

PTB of N limb Sample3 IDP of N limb Sample3 PTS of N limb

Sample3

1-6 Results

Normalized Fry Method used For sandstone (18 thin sections) (Erslev,1988), which

quantifies anticlustering in distributions of clast centers, to estimate the strain ellipse for

each sample. The Normalized Fry Method is an improved version of the Fry Method (Fry,

1979; Ramsay and Huber, 1983), and allows more precise determination of bulk strain than

the older technique by correcting for the effects of variable sorting and packing (Erslev,

1988 (.

Strain ellipses were obtained for three mutually perpendicular sections for all six samples

from normalized Fry plots (Figure 13 and 14 ) generated by EllipseFit. Ellipse orientation

(phi), axial ratio (Rs), and calculated percent shortening for each ellipse are summarized in

table 1 and 2.

Ellipse orientations range from 0° to 80°. The average value for parallel to strike sections

is 69°, 19° for sections in the dip plane, and 36° for parallel to bedding sections. Strain

magnitudes are ranging from 0 % to 28% shortening. The majority of samples have strain

between 16% and 27% (table 1 ,2 ,3 ,4, 5 and 6), with an average of 20.7% shortening.

Figure 14: Fry Plots of Northern limb




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1-7 Comparison of Zgrous strain data to other orogens:

According to table 7, the study area is located in low tectonic deformation relative to the

other areas

Table 1: Ellipse orientation (phi), axial ratio (Rs),and percent shortening for ellipse of

sample1 in Northern limb .


sample 2 in Northern limb .

PTS section IDP section PTB section Sample 1 N- limb

1.75 cm 2.05 cm 1.65 cm A

1.15cm 1.75 cm 1.05 cm B

75 15 35 ᶲ

1.4186 1.894 cm 1.316 cm Lu

1.5217 1.171 1.523 Rs

-0.1889 -0.074 -0.202 es - Eq.1

-0.1893 -0.075 -0.2 es - Eq.2

18% 7.5% 20% es %


2.05 cm 1.6 cm 2.7 cm A

1.30cm 1.4 cm 1.7 cm B

65 20 35 ᶲ

1.576 1.142 cm 1.588 cm Lu

1.632 1.4966 1.7 Rs

-0.203 -0.064 -0.206 es - Eq.1

-0.203 -0.0641 -0.2063 es - Eq.2

20% 6.4% 20% es %




285


sample 3 in Northern limb .


sample 4 in Southern limb .

PTS

section

IDP section PTB section Sample 4 S- limb

2.05 cm 1 1.7 cm A

1.35 cm 1 1.1 cm B

45 0 33 ᶲ

1.663 cm 1 1.367 cm Lu

1.518 1 1.545 Rs

-0.1884 0 -0.195 es - Eq.1

-0.188 0 -0.195 es - Eq.2

18% 0% 19% es %


2.65cm 1.25cm 1.4 cm A

1.65cm 1.05 cm 0.9 cm B

75 25 35 ᶲ

2.091 1.1456 cm 1.122 cm Lu

1.606 1.190 1.555 Rs

-0.210 -0.083 -0.197 es - Eq.1

-0.210 -0.0825 -0.197 es - Eq.2

21% 8.2% 19.7% es %




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PTS section IDP section PTB section Sample 5 S- limb

2.1 cm 1.15 cm 1.6 cm A

1.05 cm 1.05 cm 0.85 cm B

80 30 50 ᶲ

1.484 cm 1.0988 cm 1.1661 cm Lu

2 1.095 1.8823 Rs

-0.282 -0.0444 -0.271 es - Eq.1

-0.282 -0.0443 -0.271 es - Eq.2

28% 4% 27% es %



PTS section IDP section PTB section Sample 6 S- limb

1.65 cm 1.1 cm 1,65 cm A

1 cm 0.925 cm 1.15 cm B

75 25 30 ᶲ

1.2845 cm 1.0087 cm 1.377 cm Lu

1.65 1.1891 1.434 Rs

-0.221 -0.087 -0.164 es - Eq.1

-0.221 -0.0829 -0.164 es - Eq.2

22% 8% 16% es %




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Table 7 : The calculated magnitudes of the axila ratio for different studies in different

orogenies

1-8 Discussion and conclusion

The Calculated axial ratio are shown in figure 8 which is equivalent to the log flinn

diagram normally used for plotting strain ellipsoids . all classify as biaxial positive they

passes porlates indicators ( ∞ < R < 1 ). The calculated three dimensional orientations of

the axes show different relationship with folding (figure 12 and figure 13). The directions

of maximum axes are close in orientation of the axis of the fold from which the sample

was taken. The minimum axes is perpendicular to axial plain.

The comparison between the present fabric and strain results and other results in high

folded zone in Iraq is difficult because there has not been much research work entirely

devoted to the strain measurement .

The comparission between the present strain results and other results in other belts (table 7)

shows that the study area is located within low deformation. According to these results the

elongation is nearly parallel to fold axes . these results of strain analysis shown that the

regional finite strain os heterogeneous and generally increases northwards Never the less

the average orientation of e3 in a direction which is normal to the axial planes of folds

agree with that found by Hower & Davis (1981) and Salih & Lisle (1988(.In general the

final geometry is the end product of complex strain history, but the evolution may be

Orogens Axial ratio Rs Reference

NW-Zgrous in Iraq (study area ) 1.5 – 1.8 Authors

Glarus Thrust in Switzerland 1.5 -2 Ring et al. ,2001

Willard thrust of the Idaho -Wyoming- Utah fold-thrust

belt

2-4 Yonkee, 2005

Moine thrust in Scotland ˜ 50 Sanderson ,1982

Northern Appenines in Italy 5-10 Kligfield et al. , 1981

South walles 1.2-1.3 Salih and Lisle 1988

Orogens LPS ( layer-parallel

shortening )

Reference

NW- Zarous in Iraq (study area ) 16-27% Authors

The foreland parts of the of the Pennsylvania

salient of the Appalachian orogen,

13-20% Nickelsen, 1963, 1983;

Engelder, 1979; Gray and

Mitra, 1993; Faill and

Nickelsen, 1999

In exterior thrust sheets of the Idaho

Wyoming Utah salient of the Sevier fold-

thrust belt

5-30% Crosby, 1969; Gockley,

1985; Craddock, 1992;

Mitra, 1994; McNaught and

Mitra, 1996; Mukul and

Mitra, 1998; Yonkee

andWeil, 2009




288

PTB of S limb Sample 6 IDP of S limb Sample 6 PTS of

S limb Sample 6

PTB of S limb Sample 4 IDP of S limb Sample 4 PTS of S

limb Sample 4

PTB of S limb Sample 5 IDP of S limb Sample 5 PTS

of S limb Sample 5

viewed in simplified fashion as potentially consisting of three sequential steps 1) pre

tectonic vertical loading , 2) incipient tectonic compression (prior to folding) and 3) strong

tectonic compression accompanied by folding and thrust faulting (figure.15)

Figure 15: Fry Plots of Southern limb

Figure 16: Suggested origin of prolate strain, A-The initial compaction, B-Tectonic

strain associated with folding parallel to the axial plane of the fold, C-final prolate

resulting from super imposition




289

1-9 References

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Erslev, E.A., 1988, Normalized center-to-center strain analysis of packed aggregates:

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