Determination of Magnitudes and Orientation of the Paleostress of Bekhme Structure in Shaqlawa area, Northerneastern Iraq

This study presents the determination of the paleostress magnitudes and orientation of Bekhme Structure in Shaqlawa area, northeastern Iraq. Paleostress analysis of slip-fault measurements is performed using Right dihedral, Lisle diagram, and Mohr Circles methods. Depending on Mohr Circles, Bott law, and vertical thickness, the magnitudes of the paleostress at the time of the tectonic activity were determined. Firstly, Georient Software was used to estimate the orientation of the paleostresses (σ1, σ2, and σ3). Secondly, using the rupture – friction law, taking into account the depth of the overburden and the vertical stress (σv),the magnitudes of the paleostresses were calculated (σ1=4500 bars, σ2=1900 bars and σ3=700 bars). The high magnitudes of the principal stress axes may be attributed to the active tectonic events which led to the deformation of the area during the Cretaceous and Tertiary periods. The study area shows that the poles of the measured faults lie in the reactivated area of Mohr circles. This indicates the instability of the study area. The study area is estimated to have high importance, due to the possibility of the existence of deposited hydrocarbons. FoldThrust belt marks the deformation fronts of the major orogeny that forms from the collision of the Arabian Plate with the Turkish and Iranian Plates.


Introduction
Behkme Structure lies in Shaqlawa area, northeastern Iraq. It runs along NW-SE trend, with a symmetrical anticline, where the southwestern limb is steeper than northeastern limb, with doubly plunging anticline. The southeastern plunge is affected by strike slip faults and the northwestern plunge is an en-echelon of Aqra Structure that is separated by thrust fault, extending parallel to Zagros Belt and located within the High Folded Zone in the Unstable Shelf of Iraq. The length of the structure is about (30) Km and the width is about (5) Km. It is located between latitudes (36° 37ʹ -36° 48ʹ North) and longitudes (44° 00ʹ -44° 23ʹ East), as illustrated in Figure-1. There are many structural studies which have been carried out on the High Folded Zone of Iraq and dealt with the orientation and magnitude of the paleostresses [1][2][3][4][5][6]. Generally, the state of paleostress in the rocks is anisotropic and is defined by stress ellipsoid axes, which characterizes the magnitudes of the principal stresses [7,8]. Most authors who are concerned with fault slip data aim to determine the principal stresses orientation. However, the main aim of the present study is to determine the structural model of the paleostress (orientations, magnitudes, and stress Ratio) and understand the dynamics of the study area.

Geological Setting
The study area belongs to the unstable shelf represented by the High Folded Zone [10,11]. Bekhme Structure exposes a large number of lithostratigraphical divisions. The exposed formations range in age from Late Jurassic (Sargalu Formation) to Late Pliocene (Bai-Hassan Formation). These formations were ordered, from the oldest to the youngest as: Sargalu, Naokelekan, Barsarin, and Chia Gara Formations [12]. The age of these formations ranges from Late Jurassic to Early Cretaceous. They comprise well bedded limestone and marly limestone, which contain a large number of Ammonite Fossils. The thickness of these formations is about (150) m.
Balambo-Sarmord Formation has an age of Early Cretaceous. It consists of dolomitic limestone and marly limestone. The thickness of the formation is about (80) m. Qamchuqa Formation belongs to the Early Cretaceous age. It consists of brown, hard, and bedded to massive limestone and dolomite.
Right dihedral method was used to determine the trend of principal stresses axes (σ1, σ2, and σ3) of the studied area, as follows. The maximum principal stress (σ1) and intermediate principal stress (σ2) were horizontal and the minimum principal stress (σ3) was sub-vertical. The dip of these faults was to the north east and south west directions in all fields of the study area (Plates -1 and 2; Figure-3). The determination of the principal stress axis orientations was performed according to an earlier study [16].

2: Determination of the Paleostress Magnitudes Using Mohr Circles
The magnitude of the vertical stress (σv) can be determined through estimating the lithostatic load and one of the principal stress axes. At the time of the tectonic event, the depth can be determined, as well as the average density of the overlying rocks. Additional information on the value of one principal stress can be obtained using the following equation [17,18,19]: The vertical stress σv = ρgz where: ρ: is the crustal density (kg/m³) . g: is the acceleration of gravity (m/s²). z: is the paleodepth (m).
Mohr circles and Lisle diagram were used to represent the state of stress (Figure -4). Mohr Plotter Software was used to determine paleostress magnitudes. The angles (α, β, γ) were measured between the perpendicular plane (N) on the fault plane and the direction of the principal stress axes (σ1, σ2, and σ3), respectively, of all faults. To determine stress ratio (R) value of all faults, Bott equation was applied [20]. R = tan θ Im -I² n / n-n³ where: R: is the ratio of the principal stress. θ: is the pitch angle. (I, m, n): are cosine values of the angles (α, β, γ), respectively, as shown in Table -1.

Results
Many authors studied cohesion strength of the sedimentary rocks and they showed that the range of the cohesion strength magnitudes is between zero (0) bars (the rock is broken), with no stick between the two blocks of faults, and (100) bars [1], [2], [3], [4], [5], [14], [15], [22], [23], [24] and [25]. According to the compilations used by several authors, the internal friction angle (ϕ) for the sedimentary rocks is (45°) [1], [2], [3], [4], [5], [14] and [15]. Under the above determination, which is based on rupture friction analysis that depends on the stress ratio, the sliding friction angles and the vertical stress have directly resulted in the measurements of the magnitudes of the paleostresses. Two friction sliding line angles of thrust faults were measured experimentally in this study for fault surfaces. These measures showed values of angles where the average of the minimum friction sliding line angle was (25˚) from the origin of the smooth fault surfaces as limestone rocks, whereas the average of the maximum friction sliding line angle was (35˚) of rough fault surfaces as sandstone rocks.
Thrust faults measurements were obtained from two limbs of Bekhme Structure of the study area. The depth of the rocks was measured at the field and found to be equal to (3110 m). The acceleration of gravity (g) was equal to (9.8 m/ s²), whereas the average density of the sedimentary rock was estimated to be (2300) kgm/m³. Therefore, the vertical stress could be estimated to be (σ v = σ 3). Mohr circles were drawn depending on the stress ratio (R) magnitude (R=0.5) and the points (poles of the faults) were plotted depending on the angles (α, β, γ) on these circles. The plot poles in Mohr diagram should be found above the sliding line and beneath the failure envelope. The results obtained by the application of this method are summarized in Figure-5 and Table -   Thrust faulting in Bekhme structure involved a compression regime with (σ1), which was almost horizontal in the NE-SW trend, approximately perpendicular to the direction of Bekhme structure axis The extensional axis (σ3) was sub vertical and the intermediate axis (σ2) was horizontal in the NW-SE trend, approximately parallel to the direction of Bekhme structure axis, as shown in Figure -6. Figure 6-According to the study of faults solution in the lower hemisphere equal-area projection, the red color is an extensional field which contains (σ3) and the blue color is a contractional field which contains (σ1).

Discussion
The sedimentary rocks of the Mesozoic -Cenozoic Era (Sargalu and Bai-Hassan Formations) were studied to analyze the paleostresses based on fault slip data field analysis, Right dihedral method, Mohr circles, Bott equation, and Lisle graph. Mohr diagram showed that the poles of the thrust faults lie between the sliding lines and the failure envelope. It is clear that the poles of the fault planes were found by Mohr diagram to be associated with relatively low shear stress and high normal stress. This indicates that these faults do not have to slip under these conditions. However, the reality is opposite to this, due to the fact that the movement of these faults has already taken place. This contradiction may be due to several reasons. First, The effects of pore-fluid pressure, which reduces the magnitudes of the normal effective stresses, has not been taken into account, or there could be some error in the overburden thickness estimates. Second, the uplifting of the rock beds may change their orientations at a later stage.
The study results showed that the orientation axes of principal stress and their magnitudes are sufficient to reactivate faults. Magnitudes of the stress were not constant, and the stress ellipsoid was different. This difference may be due to the difference of the stress fields, the depth variation, and the possibility that the stress magnitudes were changed with time. The high magnitudes of the normal stresses may refer to the active tectonic events which led to the deformation of the area during the Mesozoic and Cenozoic Eras.

Conclusions
The style of the structural units in the Mesozoic and Cenozoic Eras is complex and appears to be controlled by a variation of mechanical stratigraphic units across Zagros Fold Thrust Belt. Magnitudes of the principal stresses were calculated depending on rupture-friction law and the known depth of burial. The maximum principal stress (σ1) was found to be (4500) bars, the intermediate principal stress (σ2) was (1900) bars, and the minimum principal stress (σ3) was (700) bars.These stress magnitudes are sufficient to produce reactivation in faults in the studied area. The study area is located within the unstable region, since the poles of the measured faults lie in the area of the faults reactivation in Mohr diagram. The stress ratio magnitudes on Lisle graph show mean values in the order of (R=0.5), which indicates that the state of the stress was flattening (σ1>σ2>σ3). The studied area was affected by a compression stress system during the Alpine Orogeny compression.