Study of the Finite Strain of Bekhme Structure in Shaqlawa Area, Northeastern Iraq

Abstract


Introduction
Analysis of the finite strain provides a reliable key to understand the evolution of deformation field through the successive tectonic events, and considered very important technique of the structural studies to determine the stress field.The study region lies in Shaqlawa area Northeastern Iraq.Bekhme Structure is a symmetrical double plunging.It runs along NW-SE trend, is located between longitudes (44° 00ʹ -44° 23ʹ E) and latitudes (36° 37ʹ -36° 48ʹ N) , and covering an area about (150) Km². (Fig. 1).
Finite strain means as the instantaneous shape of a rock mass at any one time to its initial unreformed shape of the final strain at the time of measurement, it compares the initial and final configuration (Van der Pluijm and Marshak, 2004).Trend of the deformation ellipsoid was very important, specially in relationship of the solid sedimentary rock.The Finite Strain analysis refers to various methods of the finite deformation estimation exist, and were found fragment-site analysis (Fry,1979;Erslev,1988), as well as analysis of the fragments-shape (Rf/ɸ), method of Ramsay (Ramsay, 1967;Dunnet,1969;Panozzo,1983 and1984), method of ferret diameters (Lapique etal.,1988).Reflectance method (Al-Obaidi and Lisle, 1988;Al-Diabat,1999;Al-Muathen and Al-Obaidi, 2015;Al-Hachem and Al-Obaidi,2018).That methods require different coefficients to describe the shape, site of quartz mineral fragments and other deformation points ( lengths of maximum and minimum axes and their directions, or site of all the limits of the fragments, coordinates of the centers of mass).The main objective of this work is to estimate the fundamental strain axes and shape of the strain ellipsoids and determination finite deformation of sandstone beds in studied region using Fry method and Flinn diagram.

Materials and Methods
The studied region refers to the Folded Zone in an unstable shelf (Al-Khadimi et al.,1996;Numan,1997).Bekhme Anticline contains a large number of geological formations.The formations range in age from Upper Jurassic (Sargalu Formation) to Upper Pliocene (Bai-Hassan Formation).Below is a Summerized characterization of the important formations from the oldest to the youngest in age (Jasim and Goof, 2006): Sargalu, Naokelekan, Barsarin, and Chia-Gara Fns: The age of these formations ranges from Upper Jurassic to Lower Cretaceous.It comprises limestone and marly limestone, which include a big number of fossils.Balambo-Sarmord, Qamchuqa,  These thin sections were examined carefully under the microscope.Plates were digitized with Ellipse Fit Software.More than two hundred and fifty sand grains were digitized to obtain the strain ellipse from all thin sections (Figs. 3,4,5,6,and 7).
Elongation can be calculated from the difference between the new deformed (ld) and the original undeformed (lu) axial length divided by the undeformed length (Eq.1).Passive value indicates elongation, while the negative value is expecting for shortening (es) and that multiple results by (100) will yield a percentage alteration (Bannister, 2004;Fossen, 2012) es = Ld -Lu / Lu ……….Eq. 1 Where: Ld: is the deformed Length, Lu: is the undeformed length.

Flinn Diagram
The Finite strain alteration in shape and was bounded with deformation was characterized by the deformation ellipsoid.The deformation ellipsoid has three perpendicular surfaces of the heterogenous, the fundamental planes of strain, which intersecting along three perpendicular axes that belonged to the fundamental strain axes.These axes were designated (X, Y, Z), (X) was the biggest axis, (Y) the medium axis and (Z) the smallest axis, ( X>Y>Z) ellipsoid were fixed in space, the axes showed vectorial for given lengths and the directions.Knowing of theoe vectors by knowledge of both the shape and trend of the ellipsoid (Twiss and Moores, 2007;Waldron and Wallace, 2011).The strain ellipsoid included two planes of the non final strain.The stable volume deformations, known as isochoric strain, these planes are existed through connected marks along lines of the intersecting between the ellipsoid and circle of the unit, it was deformed .The lines included in these planes have same length at as in the undeformed state of stable volume strains, or were stretched an equal value if a volume alteration was interested, or the surface deformation produces two surfaces in which the rock shows unstrained (Ramsay and Huber, 1983).A graphic representation of 3-D strain states in deformation of the rocks, shape visualization through plotting ratio of the axial (Y/Z) against (X/Y) like axes of the coordinate, this chart was named diagram of Flinn (Rey,2011;Fossen, 2012).

Results of Fry Method
Fifteen slides of S.St.rocks were used in Fry method for determination the deformation ellipse for each sample.Deformation ellipses are acquired by three orthogonal sections of all five samples from Fry plots, using Ellipse Fit Software.Ellipse trend (ϕ), ratio of the strain (Rs), and computted percentage shortening of all ellipse are briefed in Tables (1, 2, 3, 4 and 5).The deformation values of rock slides for PTS slide range (12.5 % -22.6%) shortening, with the average of ( 16.5% ) shortening, for PTB slide at range (11.5 % -22.7%) shortening, with the average of ( 15.4% ) shortening, and for PDP slide range (10.5 % -22.4%) shortening, with the average of (17.9%) shortening.

Flinn Diagram Results
Five directional samples of sandstone are collected from the study region belonging to Injana Formation in the southwestern limb of the Bekhme Structure.These types the fundamental strain axes (X, Y, and Z) were measured using Ellipse Fit Software.The (b and a ) magnitudes on the Flinn chart shows ellipsoid of the deformation , in general it is increase apath from the intial and appear deformation ellipsoid was lied above surface strain line (R>1), prolate geometries or cigar shape for high half of chart (Constrictional strain).This indicates the studied disrtict has been affected by the compression system of thestress in the southwest-northeast direction (Fig. 8).A suggestion model for this work is shown in (Fig. 9) which is presented for the prolate deformation determined from fragments of the sedimentary rocks.

Discussion and Conclusions
Analysis of the Strain results were shown that the general finite deformation is heterogeneous.The range of shortening (es) which were obtained from Fifteen oriented thin sections of sandstone, distributed across the SW limbthe of Bekhme Structure using method of Fry is between (10.5-22.7%)that leads the region was bounded within Non high strain and affected by fractures.All samples are plotted on Flinn diagram, and they fall above the plane strain line, prolate shape, this shape resulted from compression of folding and thrusting, the minimum axis of the deformation was perpendicular to the bedded surfaces and the maximum axis of strain was parallel to the bedding surfaces.Generally, the finite deformation indicates to the convoluted deformation history, but the development may be showed in simple model likely comprising of many points: a: before the tectonic perpendicular loading, b: during the tectonic compression (prior to folding) and c: high tectonic compression.The studied area was effected by folding and the thrusting of the tectonic deformation history during Alpine Orogeny compression.

Fig. 1 .
Fig. 1.Location of the studied area (Google Earth image, 2023) Akra-Bekhme, Shiranish formations: The age of these formations is Cretaceous.It comprises of carbonate rocks.Tanjero Formation: The formation age is Upper Cretaceous.It comprises of shale, sandstone, siltstone and claystone.Kolosh, Khurmala, Gercus Fns.: the age is Paleogene.They consist of sandstone, claystone and siltstone.Pila Spi Formation: The formation age was the Middle-Late Eocene.It comprises limestone and dolomite.Fat'ha Formation Middle Miocene.It consists of marl and claystone with an alternation of thickened limestone.Injana Formation: The formation age is the Late Miocene.It consists of sandstone, siltstone, marls and claystone.Muqdadiya Formation: The formation age is the Lower Pliocene.It comprises sandstone and pebbly increase in size upward.Bai-Hassan Formation Upper Pliocene.It consists of clastic sedimentary rocks (Fig.2).

Fig. 3 .
Fig. 3. PTS, PDP and PTB thin sections ellipses and their plates of sample 1, SW limb of Bekhme Structure

Fig. 4 .
Fig. 4. PTS, PDP and PTB thin sections ellipses and their plates of sample 2, SW limb of Bekhme Structure