Journal of Structural Geology - دانشگاه تهران · The mechanical evolution of transpression zones aﬀected by fault interactions is investigated by a 3D elasto-plastic

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Journal of Structural Geology

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Mechanical evolution of transpression zones affected by fault interactions:Insights from 3D elasto-plastic finite element models

Seyed Tohid Nabavia,∗, Seyed Ahmad Alavia, Soheil Mohammadib, Mohammad Reza Ghassemic

a Faculty of Earth Sciences, Department of Geology, Shahid Beheshti University, Tehran, IranbHigh Performance Computing Laboratory, School of Civil Engineering, University of Tehran, Tehran, Iranc Research Institute for Earth Sciences, Geological Survey of Iran, Tehran, Iran

A R T I C L E I N F O

Keywords:Fault interactionPure-shear-dominatedTriclinic transpressionVertical and lateral extrusionDiscontinuous heterogeneous flowFinite-element method

A B S T R A C T

The mechanical evolution of transpression zones affected by fault interactions is investigated by a 3D elasto-plastic mechanical model solved with the finite-element method. Ductile transpression between non-rigid wallsimplies an upward and lateral extrusion. The model results demonstrate that a, transpression zone evolves in a3D strain field along non-coaxial strain paths. Distributed plastic strain, slip transfer, and maximum plastic strainoccur within the transpression zone. Outside the transpression zone, fault slip is reduced because deformation isaccommodated by distributed plastic shear. With progressive deformation, the σ3 axis (the minimum com-pressive stress) rotates within the transpression zone to form an oblique angle to the regional transport direction(∼9°–10°). The magnitude of displacement increases faster within the transpression zone than outside it.Rotation of the displacement vectors of oblique convergence with time suggests that transpression zone evolvestoward an overall non-plane strain deformation. The slip decreases along fault segments and with increasingdepth. This can be attributed to the accommodation of bulk shortening over adjacent fault segments. The modelresult shows an almost symmetrical domal uplift due to off-fault deformation, generating a doubly plunging foldand a ‘positive flower’ structure. Outside the overlap zone, expanding asymmetric basins subside to ‘negativeflower’ structures on both sides of the transpression zone and are called ‘transpressional basins’. Deflection atfault segments causes the fault dip fall to less than 90° (∼86–89°) near the surface (∼1.5 km). This results in apure-shear-dominated, triclinic, and discontinuous heterogeneous flow of the transpression zone.

1. Introduction

Fault steps or stepovers are sites of localized deformation where astraight planar fault surface is interrupted by discontinuities. This de-finition refers to geometric segmentation (Fossen and Rotevatn, 2016).In this sense, fault steps are zones of slip transfer between discontinuoussub-parallel fault segments in which segments interact through theirassociated stress field and any hard-linkages. Various non-planar frac-tures and fault geometries observed in nature and studied both theo-retically and numerically (e.g., Rodgers, 1980; Segall and Pollard,1980; Aydin and Schultz, 1990) are segmented/stepping, ramped, in-tersecting/branching, splayed, and curved (Ritz et al., 2012, 2015; Ritz,2013). Fault steps localize either contraction or extension as a functionof their manual geometries (right- or left-stepping) and fault kinematics(left- or right-lateral) (Christie-Blick and Biddle, 1985; Woodcock andFischer, 1986; Ramsay and Huber, 1987; Reches, 1987; Crider, 2001;Storti et al., 2003; Cunningham and Mann, 2007; Mann, 2007). Strike-slip systems (e.g., Misra et al., 2014; Misra and Mukherjee, 2015;

Mukherjee, 2015a,b; Dasgupta and Mukherjee, 2017) can also produceimportant vertical displacements. Pop-up structures and transpressionaldeformation are local zones of uplift at contractional steps along strike-slip fault segments (Fig. 1). Contractional or restraining steps occuralong transform boundaries, intraplate and intracontinental strike-slipfaults and transpressional settings. In these settings, transpression zonesdevelop in contractional sectors between overlapping en-échelon faultsegments (Biddle and Christie-Blick, 1985; Woodcock and Schubert,1994; Richard et al., 1995; Storti et al., 2003; Crider, 2015).

Transpressional deformation in contractional steps is commonlyaccommodated by doubly plunging and highly curvilinear folds, shearindicators, boudinage, flanking reverse or oblique-slip faults (flankingstructures reviewed in Mukherjee and Koyi, 2009; Mukherjee, 2013,2014a, 2014b, 2015a,b), uplift, block rotation, subsidiary extensionalstructures, extrusion, and exhumation (e.g., Upton and Craw, 2014)(Fig. 1). Such deformation patterns and features have been observed inmany field studies (e.g., Sanderson et al., 1991; Alsop et al., 1998;Holdsworth and Pinheiro, 2000; Tavarnelli et al., 2004; Wakabayashi

https://doi.org/10.1016/j.jsg.2017.11.003Received 16 August 2017; Received in revised form 2 November 2017; Accepted 5 November 2017

∗ Corresponding author.E-mail addresses: [email protected], [email protected] (S.T. Nabavi).

Journal of Structural Geology 106 (2018) 19–40

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et al., 2004; Carosi et al., 2005; Wakabayashi, 2007; Waldron et al.,2007, 2010; Crispini et al., 2009; Mukherjee and Koyi, 2010; Sylvester,2012; Massey and Moecher, 2013; Talbot, 2014a, 2014b; Nabavi et al.,2017b, 2017c; Zanchi et al., 2016; Massey et al., 2017; Zhang et al.,2017), scaled analogue (Richard et al., 1995; Schreurs and Colletta,1998, 2002; McClay and Bonora, 2001; Czeck and Hudleston, 2004;McClay et al., 2004; Leever et al., 2011; Mitra and Paul, 2011; Dooleyand Schreurs, 2012; González et al., 2012; Ghosh et al., 2014; Barcoset al., 2016; Frehner and Schreurs, 2016) and numerical (Willemseet al., 1996; Ramsay and Lisle, 2000; Duan and Oglesby, 2005; Davisand Titus, 2011; Davis et al., 2013; Landgraf et al., 2013; Strijker et al.,2013; Dasgupta et al., 2015; Lozos et al., 2015; Frehner, 2016a, 2016b;Nabavi et al., 2016, 2017a, 2017e) studies of strike-slip and obliqueconvergence systems.

Transpression is characterized by simultaneous simple shearingparallel to the shear zone boundaries (i.e., strike-slip component) to-gether with coaxial flow shortening orthogonal across the shear zoneboundaries and stretching parallel to them (Harland, 1971; Sylvesterand Smith, 1976; Sanderson and Marchini, 1984; Fossen et al., 1994;Braun and Beaumont, 1995; Dewey et al., 1998; Mukherjee and Koyi,2010; Fernández et al., 2013; Díaz-Azpiroz et al., 2014, 2016; Frehner,2016a, 2016b; Nabavi et al., 2017c). Strain partitioning (with bothspatial and temporal end members) (Curtis, 1997) is common in thesetectonic settings leading to oblique displacement that has importantconsequences in tectonic interpretation (Jones and Tanner, 1995;Curtis, 1997; Ellis and Beaumont, 1999; Tikoff and Teyssier, 1994;Teyssier et al., 1995; Druguet et al., 2009; Carreras et al., 2013;Philippon et al., 2015; Díaz-Azpiroz et al., 2016; Philippon and Corti,2016). Transpression zones are common in such tectonic setting instrike-slip fault systems, orogenic belts, and plate boundaries; they re-sult from oblique convergence where convergence motion vectors areoblique to the boundaries between deforming crustal plates (Díaz-Azpiroz et al., 2016; Frehner, 2016a; Mookherjee et al., 2016; Nabaviet al., 2017a, 2017c; Philippon and Corti, 2016). The angle of obliqueconvergence (depending on the kinematic vorticity number, Wk)quantifies the relative plate motion of a system (Fossen and Tikoff,1993; Fossen, 2016) (Fig. 2). A convergence angle perpendicular(α = 90°, Wk = 0) (Fig. 2a: i–iii) or parallel (α = 0°, Wk = 1) (Fig. 2c:i–iii) to the deformation zone boundary fault results in coaxial pure-shear contraction (or orthogonal convergence) and non-coaxial simple-shear (i.e., an ideal shear zone) (Ramsay, 1980; Mukherjee, 2012;Talbot, 2014a), respectively. These end-member strain states lead toplane strain (2D) deformation. Transpression (convergent strike-slip)occurs when the far-field shortening vector is at an oblique angle α tothe deformation zone boundary faults (i.e., 0° < α < 90°) (Fig. 2b:i–iii) (Harland, 1971; Sylvester and Smith, 1976; Sanderson and

Marchini, 1984; Sylvester, 1988; Fossen and Tikoff, 1993; Ghosh,2001), and non-coaxial 3D strain develops (Vitale and Mazzoli, 2010,2015; Fossen and Cavalcante, 2017). In this case, the transpressionstrain ellipsoid is oblate and lies in the flattening field (Sanderson,1984, 2014; Sanderson and Marchini, 1984; Tikoff and Fossen, 1993;Fossen et al., 1994; Dewey et al., 1998; Fossen and Tikoff, 1998; Díaz-Azpiroz et al., 2014; Vitale and Mazzoli, 2015; Mookherjee et al., 2016;Nabavi et al., 2017c; Fossen and Cavalcante, 2017). The angle betweenthe infinitesimal contraction and the convergence vectors are 0° and 45°for orthogonal contraction and simple shear, respectively. Transpres-sion can have either a monoclinic or a triclinic kinematic symmetry,depending on the orientation of the pure shear axes with respect to thesimple shear axes. Two types of transpression and two types of trans-tension zones have been introduced based on the kinematic vorticitynumber (Wk) and the convergence angle (α) (Fossen and Tikoff, 1993;Fossen et al., 1994; Tikoff and Teyssier, 1994, 1999; Casas et al., 2001;Bailey et al., 2004, 2007; Mukherjee, 2012): (i) simple shear (wrench)-dominated (1>Wk > 0.81, α < 20°); (ii) pure-shear-dominated(Wk<0.81, α>20°).

Obliquely convergent orogens such as the Zagros Mountains Range(Mohajjel and Fergusson, 2000; Sarkarinejad and Azizi, 2008;Sarkarinejad et al., 2013; Ruh et al., 2015) and Alborz Mountains Range(Allen et al., 2003; Landgraf et al., 2009; Ballato et al., 2013; Nabaviet al., 2017c) are typically modeled as transpressional systems. Somenatural cases of transpression zones associated with contractional faultsteps are the Mecca Hills region of the San Andreas fault system,southern California (Sylvester and Smith, 1976), the Cerro de la Mica,Atacama fault system, northern Chile (McClay and Bonora, 2001), theGargano Promontory, southern Italy (e.g., Brankman and Aydin, 2004),the Monte Cornetto di Folgaria, Southern Alps, northeastern Italy(Zampieri et al., 2003), the Mount Diablo, San Andreas fault system,San Francisco Bay area (Wakabayashi et al., 2004), the Mt. Kumeta-Rocca Busambra, western Sicily, Italy (Barreca and Maesano, 2012), theKolah-Ghazi Mountains, south of Isfahan (Nadimi and Konon, 2012),and the Kuh-e-Hori, SE Iran (Nabavi et al., 2016, 2017a).

Analytical, analogue, and numerical models have been used tobetter understand transpressional deformation zones. There also aremany numerical studies of transtensional settings such as oblique riftsand pull-apart basins. In contrast, such models, especially those in 3D,have rarely been used to understand brittle-ductile transpression zones.Our previous numerical analysis of two dimensional transpressionzones within contractional steps has given important insights into theevolution of the stress distribution and strain localization withintranspression zones (Nabavi et al., 2017a). That analysis suggested thattranspression zones generate heterogeneous and non-coaxial strains. Inaddition, important factors influencing the strain field are: (i)

Fig. 1. 3D sketch of the transpressional basins, which is consistent with the results obtained in the present study.

S.T. Nabavi et al. Journal of Structural Geology 106 (2018) 19–40

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convergence angle, (ii) step geometries, and (iii) overlap-to-separationratio. In this study, we extend our previous study (Nabavi et al., 2017a)into the three-dimensional displacement-based, non-linear finite-ele-ment (FE)-models using the commercial FE-package ABAQUS™ to studythe role of fault interactions in the evolution of transpression zones, anapproach that also includes two dimensional problems.

Three-dimensional numerical modelling decodes fault interactionsand their influence on complexities that arise from non-linear evolutionof transpression zones. The main sources of nonlinearities in the modelare frictional sliding on the fault segments (e.g., Vernant and Chéry,2006a, 2006b; Maerten, 2010; Soliva et al., 2010; Maerten et al., 2016;Zeumann and Hampel, 2016), and inelastic material behaviour or, largedeformation beyond the linear elastic regime, changing strains andboundary conditions, or any combination of these factors during themodelling of deformation. These parameters might work coevallyduring deformation. Early numerical analysis of transpression betweencontractional fault steps (e.g., Nabavi et al., 2016, 2017a) as two-di-mensional discontinuities in an isotropic, linear elastic medium gavefirst-order insights into the evolution of stress and strain distribution,accumulation of displacements and interaction between adjacent fault/fracture segments. We apply here various factors, such as overlappingfault step, oblique convergence angle, fault slip, and thickness thatcontrol the evolution of 3D stress, strain, traction vectors, and dis-placement paths within transpression zones. We monitor the evolutionwith time of oblique convergence together with increasing

displacement on the fault segments. Another novelty in our analysishere is that (i) we remove the ‘confined transpression’ boundary re-striction, and (ii) use non-rigid deformation zone boundaries that differfrom all previous transpression models.

We mainly address: 1) How do the displacements, stresses andstrains evolve in the step between adjacent fault segments and how dothese differ from the deformation outside the transpression zones?, 2)How do the total inelastic strains (i.e., permanent deformation) andcoefficient of sliding friction on the fault segments influence the evo-lution of transpression zones?, 3) How does the displacement field varywith structural position in the transpression zones?, 4) How do theimplications of our 3D FE-models improve understanding of the de-velopment of hard linkage between adjacent fault steps. The outcome ofthis study is compared to earlier analogue and mechanical modellingstudies and a natural example.

2. Model setup

2.1. Geometric configuration

The model (Fig. 3) comprises two rectangular blocks with theiredges parallel to the axes of a Cartesian coordinate system. The XZplane is horizontal, with the X axis parallel to the strike of the faultsegments, and the Y axis is vertical (Fig. 3a and b). The blocks fric-tionally slide along fault segments. In brief, these blocks are collectively

Fig. 2. The kinematic regime of transpression zone. The angle of obliquity α is the angle between the far field contraction and the deformation zone boundary. a) α = 90° for purecontraction causes vertical thickening and homogeneous pure shear in the deforming zone. Flow is confined to the YZ plane. b) 0° < α < 90° in oblique convergence, which causeshomogeneous transpression in the deforming zone. The shear plane parallels the XZ plane. c) α = 0° for far-field homogeneous simple shear motion. The shear plane parallels the XZplane.


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called ‘active’ blocks (Fig. 3a). The dimensions of the model are scaledto natural examples of continental oblique-slip systems(70 × 70 × 15 km3) (Fig. 3c). The model block has two pre-definedfault segments or slip surfaces, where displacement is allowed parallelto the fault planes in both horizontal and vertical directions and can actas oblique-slip faults in the analysis (Fig. 3b). The pre-defined faultsegments have a length along strike of 50 km. The fault segments, alsoknown as principal displacement zones (e.g., Dooley and Schreurs,2012), are vertical (i.e. 90° dip) in cross-section and their ends aredefined by rectangular tip lines (YZ section in Fig. 2). In the presentstudy we model two fault segments with an overlap of 30 km and aseparation of 10 km (Fig. 3c). Incorporating fault segments with rec-tangular tip lines, as in the models discussed here, offers some criticalinsights into the variations in the three dimensional stress and strainverified in the transpression zone.

2.2. Material properties

Elasto-plastic rheology (a solid-like, Prandtl material) describes thebehaviour of material that involves both elastic and plastic deformationcomponents. Stress and elastic strain increase until a critical stressreached, called the yield strength, beyond which the deformation isplastic (Mohammadi, 2003). The rheology of the upper crust is elasto-plastic, which means that stresses increase with strain up to a certainlimit, where failure occurs and plastic deformation starts. Plasticmodels can predict the initiation and development of fractures or faultsthat can be readily implemented in different numerical models (Ramsay

and Lisle, 2000; Mohammadi, 2008, 2012).The depth to which oblique convergence extends is typically re-

stricted to the brittle-ductile thickness of the crust. Linear elastic ma-terial properties have been used to model deformation at shallowcrustal level (e.g., Crider and Pollard, 1998). The choice of elasticrheology, however, ignores the permanent deformations observed inrocks (e.g., fractures, faults, and folds). In this study, the model block isassigned an isotropic, elasto-plastic rheology (upper part of the crust)assuming the average material properties of sandstone. Young's mod-ulus (E), Poisson's ratio (ν) and density (ρ) are taken as 55 GPa, 0.25,and 2600 kg/m3 (based on Carmicheal, 1982; Pollard and Fletcher,2005; Mukherjee and Mulchrone, 2012; Goteti et al., 2013), respec-tively for the elastic component, whereas for the plastic component, ayield strength of 890 MPa is used (based on Carmicheal, 1982). This isbased on a compressive experiments on sandstone deformed at a con-fining pressure of 500 MPa (see Carmicheal, 1982). The pre-definedfault segments are assigned a constant coefficient of sliding friction of0.51 (Pollard and Fletcher, 2005).

2.3. Displacement-based boundary conditions

Oblique convergence is modeled by imposing a given displacement(Fig. 3a) at the boundaries. A total oblique convergence of 20% (14 kmshortening) with a convergence angle of 45° is imposed onto the modelblock. Imposing displacements, instead of traction, allows formulating amodel that is consistent with field observations and obviates the need toinfer stresses. This boundary condition is consistent with the common

Fig. 3. Setup of the three-dimensional FE-model. a) Three-dimensional block diagram of the model showing the imposed loads and boundary conditions. Oblique contraction imposed inthe ‘active’ block containing two pre-defined fault surfaces. b) Vertical section through the model showing the vertical geometry of the faults. c) Horizontal section through the modeldisplaying the definition of fault separation (S) (=10 km) and fault overlap (O) (=30 km). ‘O’ is positive for overlapping faults. d) Discretization of the model into 11,567 three-dimensional 8-node elements. Average material properties of sandstone are assigned to the model blocks. RP-1 and RP-2 are reference points of applied displacement-based boundarycondition.


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observation that the central parts of fault segments evolve in an overallplane strain deformation. However, this constraint does not include thetranspression zone between contractional fault steps, which evolve ingeneral three dimensional displacement fields. In addition to the dis-placement boundary condition, a body force corresponding to the ac-celeration due to gravity (9.81 m/s2) acts on the model blockthroughout the deformation. For the FE-analysis, the model block isdiscretized into 222,000 continuous, three-dimensional, linear, hex-ahedral finite elements (i.e., C3D8R) (Fig. 3d). These elements are re-commended for simulations involving deforming contacts in FE-ana-lysis. Upon imposing the far-field displacement boundary conditionsand gravity, the stiffness of each finite element is calculated using 8-node Gaussian integration during each increment of the deformation(Bathe, 1996; Mohammadi, 2003, 2008, 2012). We use the 3D FE-modelling software package ABAQUS™ (ABAQUS/CAE; FE-commercialprogram ABAQUS™ tutorial version 6.14–2, 2014; www.simulia.com/)to simulate stress and strain features recorded in the transpression zone.Due to the continuum nature of the FE-analysis, the model presentedhere cannot precisely simulate the brittle failure of rocks characteristicof shallow crustal levels. However, by using the orientation of theprincipal stresses and strains that develop in the model transpressionzone, it is possible to show and predict the most probable orientation ofbrittle structures that could develop during deformation.

3. Results and discussion

We propose a transpression model configuration with two right-stepping, en-échelon fault segments interacting under oblique con-vergence (α = 45°) to produce a transpression zone within the con-tractional fault configuration. In this Lagrangian model, meshes deformalong with the crustal block. During oblique convergence, materialtrapped between the two fault segments deforms in a ductile fashion,and the deformation preferentially localizes in the model within thecontractional fault step between blocks separated by en-échelon faultsegments. Deforming material is allowed to shorten (or lengthen), andshear vertically and horizontally, while slip is possible along the de-formation zone boundaries (i.e., both fault segments). Given the chosenobliquity angle, the model develops a pure-shear-dominated trans-pression zone. The deformed model geometry reproduces many of thefirst-order geometric features of natural transpression zones and pop-upstructures such as the regional doubly plunging anticline, reverse andhigh-angle sinistral-oblique-reverse faults, flower (or Y-shaped) struc-ture, uplift and exhumation, local folding, and basins associated withoblique convergence and frictional slip on the fault segments. Thisoverall conformity of the results of the models in this work with theanalogue studies and natural transpression zone examples, gives in-sights into predicting and analyzing the evolution of three-dimensionaldeformation and displacement fields in transpression zones. Upon im-posing the total oblique convergence (20%) in an incremental manner,the model block evolves under a combination of slip (discrete de-formation) on the fault segments and distributed deformation withinthe ‘active’ block. The ‘active’ block overall undergoes oblique con-traction, shortens, and thickens in both the horizontal and vertical di-rections, respectively, with rotation around horizontal and verticalaxes. It is important to note that uplift and subsidence develop in themodels as a result of the amount of the oblique convergence, and thatprocesses such as sedimentation, and isostatic response (as inMukherjee, 2017) do not contribute. This is a simplification, as theseprocesses are known to affect uplift and subsidence.

3.1. Modeled stress fields

Changes observed in the slip behaviour of each modeled fault arecaused by transient changes in the crustal stress field related to thegrowth and shrinkage of the surface load (Hampel and Hetzel, 2006;Turpeinen et al., 2008). The results show that the mean and maximum

principal stresses increase (compression increases) inside the step be-tween the fault segments compared to the region outside the step(Fig. 4a and b). In other words, the contractional quadrants of the innerfault segment tips are located inside the step, resulting in local highstresses and strains in this part. Under simple shear conditions (fracturemode II or III), strike-slip faulting can propagate through the specifiedprocess zone. In contrast, the complex stress and strain trajectoriesassociated with an oblique-slip setting such as transpression zonesprevent it from extending through the specified and single process zone.

The orientation and magnitude of the minimum compressive stress(σ3) can be used to understand the overall evolution of the three di-mensional stress field in the transpression zone, and we compare thespatial variation of stresses within (Fig. 5a) and outside (Fig. 5b) therelay zone. Note that σ3 represents the stress at the end of each incre-ment of deformation. Within the transpression zone, the interaction ofthe stress fields near the tip lines of the fault segments results in acomplex three dimensional stress field. The σ1 and σ3 axes within thetranspression zone are initially parallel and normal to the imposedoblique convergence direction, respectively. With progressive de-formation of the model block, the σ3 axis rotates within the transpres-sion zone forming an oblique angle (∼9°–10°) to the regional transportdirection and the transpression zone boundaries. Therefore, the or-ientations of the σ3 axis are strongly dependent on the structural po-sition within the transpression zone. Outside the transpression zone, theσ3 tensor is sub-normal to the regional transport direction (with onlyslight deviation of ∼4° with respect to sub-normal state, Fig. 5b); it isalso sub-parallel to the maximum extensional finite strain (S1). Alter-natively, the σ1, the minimum extensional finite strain (S3), and theconvergence direction sub-parallel each other outside the transpressionzone. The sub-parallelism between incremental and finite strain axesand also their negligible deviation outside the transpression zone sug-gests coaxial flattening, and not necessarily plane strain deformation.The magnitude of stress generally increases as deformation intensifies(Fig. 5).

3.2. Variation of slip along fault segments

The distribution of the deformation is determined by the rate ofdecrease of slip toward the end of the fault segments (i.e., towards thevertical tip line) (Fig. 6). The slip along the fault segment creates anoffset between ‘active’ blocks. Due to the gradual decrease of slip alongthe sliding surfaces, the transpression zone between the two faultssegments is expected to gradually increase its height (vertical dis-placement) towards the overlapping zone. This means that the com-pression component of the transpression zone is concentrated in thecentral area of the fault step. The slip decrease along fault segments canbe attributed to the accommodation of bulk shortening across adjacentfault segments. Furthermore, the slip along the fault segments decreaseswith increasing depth, so that distinct slip offsets are visible at depths of0–5 km and 5–15 km (Fig. 6). Fig. 6 illustrates these results with a viewof the fault surface after deformation. Results show about 5% (depth12 km) to 19% (near surface) of imposed displacement and deformationaccommodated by fault slip on pre-existing faults (Fig. 6). The resultsalso show that fault slip distributions in the elasto-plastic model arequite asymmetric. The lower portion of the fault can lock with in-creasing depth, while its upper portion slips at the plate displacementcondition. The maximum slip occurs near the center of the fault surfacenear the surface of the model.

3.3. Displacement and strain patterns within and outside the transpressionzone

Another feature resulting from the interaction between the modeledfault segments is the almost symmetrical rectangular pop-up structureor domal uplift (up-dip extrusion in Fernández and Díaz-Azpiroz, 2009;Díaz-Azpiroz et al., 2014; Barcos et al., 2016) along and across the


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transpression zone bounded by the overlapping faults (Figs. 7 and 8).Following an initially circular antiformal/domal area, this uplift orvertical extrusion (material particles displace upwards) becomes pro-gressively better defined with increased displacement. This typicallygenerates doubly plunging arrangements of folds that produce four-waydip closure (a periclinal structure) (e.g., Woodcock and Rickards, 2003)or synclastic antiform (terminology from Lisle and Toimil, 2007), oflimited strike extent. This doubly plunging fold structure grows in allthree dimensions and its long axis rotates with the oblique convergence

in time. The obliquity of the hinge line of the antiform with respect tothe fault strike decreases with increasing fault overlap so that its trendssub-parallel the fault for the largest overlaps. On the other hand, theuplift, which is evident as vertical separation or fold amplification(Frehner, 2014, 2016a) in Fig. 7, is one source of off-fault deformationthat is more prevalent in transpression zones with large slip gradients(e.g., Cooke et al., 2013; Herbert et al., 2014).

For transpression, the resulting fold axis deviate from being per-pendicular to the convergence direction and the orientation of the fold

Fig. 4. a) Maximum principal stress distribution in the oblique convergence system affected by the contractional fault step. Here, dimension is 70 × 70 × 15 km. b) Maximum principalstress along the middle part of whole model (Fig. 5a) within contractional fault step. Here, dimension is 70 × 10 × 15 km. The compressive (positive values) and tensile (negative values)zones are specified.


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axis in map view is a function of the convergence angle (e.g. Titus et al.,2007; Fossen et al., 2013; Frehner, 2016a) (Fig. 8). The angle betweenthe fold axis and the X reference-axis increases from pure shear (0°) tosimple shear. The fold axes are commonly curved in transpressionzones. Fold amplitude and wavelength increase and decrease, respec-tively, with strain (i.e., the fold tightens), such that the transpressionzone within the contractional step suffers convex upward hetero-geneous thickening (Fig. 8a). The directions of maximum compressivestress and fold axes are nearly perpendicular to each other. Ad-ditionally, the transpression zone stretches along the X-axis (lateralextrusion) (e.g., Dias and Ribeiro, 1994; Jones et al., 1997; Fernándezand Díaz-Azpiroz, 2009; Massey and Moecher, 2013; Massey et al.,2017) in addition to uplift along the Y-axis (vertical extrusion as to-pographic relief), and it also rotates about the Y-axis ca. 30° (Fig. 8b).

Although the geometry of both fault segments is symmetric, theresulting plastic strain is not. The results (Fig. 9) show that the region ofthe model experiencing the largest plastic strain (damage) is located inthree parts within the transpression zone, one in the central part of

transpression zone, and the other two coinciding with the tips of thefault segments (Fig. 9a). These plastic zones are the preferred sites forthe nucleation and growth of early reverse and sinistral-oblique-reversefaults (as conjugate step-up shears) similar those observed in experi-mental studies of oblique convergence and contractional steps/bends ofstrike-slip systems (e.g., McClay and Bonora, 2001; Cooke et al., 2013).With continued convergence, the plastically deformed volume thickensand rapidly widens along the X-, Y-, and Z-axes (Fig. 9b). Strain loca-lization (that can generate shear bands, Barnichon and Charlier, 1996;Barnichon, 1998) takes place within the transpression zone at thebottom of the model. The plastic strain is distributed throughout thestep, with its greatest values in the center of the transpression zone thatdecreases outward from the step. A sharp transition occurs between thesignificant plastic strains within the step to very low plastic strainsimmediately outside the contractional fault step. Hence, slip transfer isgreater across the transpression zone and contractional fault step thanin transtensional zones and releasing fault steps, this is due to the stressstate and plasticity in this zone (e.g., Nevitt and Pollard, 2017).

Fig. 5. Azimuth vs. magnitude plots for σ3 a) within, and b) outside the transpression zone. Outside the transpression zone, σ3 vectors initiate normal to the regional transport direction.With progressive deformation, the vectors rotate towards obliquity to the regional transport direction. Different colors represent data from five selected increments of deformationrepresenting 0.1 (red), 0.25 (blue), 0.5 (green), 0.75 (orange), and 1 (dark blue) of total regional oblique convergence. Three data were collected at each selected increments. (Forinterpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)


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According to the spatial variation of plastic strain through thetranspression zone, two pairs of high-angle sinistral-oblique-reversefaults, that is called “sidewall faults” (e.g., Sylvester, 1988; Mann,2007), can be identified bounding the transpression zone. Indeed, theorientation of stress and strain principal axes are compatible with theactivity along the oblique-reverse fault systems that fan outward fromthe overlapping step. This result is approximately coincident with theresults of scaled analogue modelling (e.g., McClay and Bonora, 2001;Dooley and Schreurs, 2012; Cooke et al., 2013). At the final stages ofthe 45° oblique convergence, deformation and plastic strain affects theentire model. Distributed plastic strain beyond each fault segment ef-fectively lengthens the faults, allowing slip magnitudes to increase to-ward the transpression zone.

According to Sanderson and Marchini (1984), vertical stretchinglineations should predominate in transpression zones. However, variousfield and analytical studies indicate that lineations can be either hor-izontal or vertical under monoclinic transpression, or even show in-termediate plunges within triclinic transpression zones, depending onthe angle of convergence. The results of this work show that the

maximum tensile principal stress (Fig. 10) is well developed throughthe transpression zone. In addition, less well-marked lineations appearoutside the transpression zone so that they may even remain unnoticed.On the other hand, the model show a progressive increase in the dip ofplanar fabrics (foliations) towards the transpression zone, and are ap-proximately vertical along its central plane (Fig. 10). Hence, the strainellipsoid varies in orientation throughout the step, depicting the het-erogeneous nature of deformation (e.g., Goteti, 2009; Goteti et al.,2013). Generally, stretching lineation and the major principal strainaxis are perpendicular to the shear direction and parallel to the trans-pression zone for pure shear-dominated transpression zones. Char-acteristic sub-horizontal to shallow plunging lineations and sub-verticalfoliations agree with simple-shear-dominated deformation in centralparts of the transpression zone (Fig. 10) with respect to the pure shear-dominated deformation in surrounding.

The early models of transpression zones described monoclinic flows,resulting in either strike- or dip-parallel lineations depending on theangle of convergence and magnitude of deformation (e.g., Sandersonand Marchini, 1984; Fossen and Tikoff, 1993). The oblique lineations

Fig. 6. Slip distribution along the fault segment 1's surface as the vertical section. This model is the middle part of whole model and its dimensions are 70 × 10 × 15 km.

Fig. 7. Model result showing vertical displacement (Uy) of the transpression zone.


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recorded in many natural transpression zones cannot be explained bymonoclinic models, and were modeled instead by transpression flowwith triclinic symmetry (e.g., Jiang and Williams, 1998; Lin et al., 1998;Czeck and Hudleston, 2003, 2004; Jones et al., 2004; Iacopini et al.,2007, 2010; Jiang, 2007; Fernández and Díaz-Azpiroz, 2009). The re-sults of this work indicate that the lineations are oblique in the trans-pression zone, both to the zone boundaries (i.e., fault segments) and tothe horizontal plane. These results can provide a realistic test for nat-ural cases. With time evolution of oblique convergence due to in-creasing displacement, opposing displacement on the adjacent fault

segments results in a complex displacement field within the overlappingzone and around it, as shown in a fringe plot of displacement compo-nents along all three reference axes (Fig. 11). Contours on the deformedvolume show how the strike of displacement vectors parallels the ob-lique convergence direction around the transpression zone, and thosevectors are rotated within in the transpression zone. The steep dis-placement gradient at the tips of fault segments result is the strongestvariation in the displacement pattern in the transpression zone(Fig. 11).

The same sense of slip along the fault segments warps and tilts the

Fig. 8. Uplift/Vertical and lateral extrusion, and also rotation of fold axis with respect to undeformed state (grey meshed block) within the resulting transpression model. This model is themiddle part of whole model and its dimensions are 70 × 10 × 15 km.

Fig. 9. a) First plastic zones in the transpression zone affected by fault interaction in timestep 0.13, where stress state exceeding yield strength. b) Extended plastic zone withintranspression zone in timestep 0.3. Time-step is 0.01 in this modelling from 0.00 to 1.00.


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overlapping contractional step by rotating vertical and horizontal axes.This superposition of distortion and rotational deformation results in acomplex three-dimensional displacement field within the transpressionzone. Fig. 11 illustrates modelling results of particle paths and the or-ientation of the oblique flow apophyses within the transpression zone.The rotational component increases along strike from the lateral limitsof the model inwards towards the transpression zone. Rotation of thedisplacement vectors during increasing oblique convergence suggeststhat the transpression zone evolves under an overall non-plane straindeformation. Away from the lateral sides of the model, vertical dis-placement increases along-strike of the primary fault segments towardsthe transpression zone. Outside the transpression zone and away thefault segments, the displacement field is almost constant and the overalldeformation conforms to plane strain. Near the fault segments andwithin the transpression zone, the displacement vector field is morevariable with strong gradients in the orientation and magnitude of thedisplacement vectors, with distinct shapes of the deformation ellipsoids.Directional derivative azimuth (0°–360°) was plotted by measuring theangle between the displacement vectors and the transpression zoneboundaries (Fig. 12). The area of slow displacement (oblique to thetranspression zone, where displacement is attributed to sigmoid-I and–II transpressional faults or Y-shears; Mathieu and de Vries, 2011;

Mathieu et al., 2011) rotates counterclockwise during the deformation.This rotation affects the extruded material within the transpressionzone. The counterclockwise rotation resulting from the model for aright-stepping fault system is consistent with the rotations shown byanalogue models (e.g., McClay and Bonora, 2001; Dooley and Schreurs,2012). Unlike some other fault types (e.g., brittle rotational faults;Mukherjee and Khonsari, 2017), the fault segments do not rotate butinstead accommodate the rotation of the material between them by slipgradients.

Fig. 12a shows the evolution of the finite displacements within thetranspression zone at five selected increments of deformation corre-sponding to time steps 0.1, 0.25, 0.5, 0.75, and 1. At the onset of theimposed deformation, the displacement vectors are everywhere obliqueto the transpression zone boundaries. The results of this work show howthe overall transport direction outside the transpression zone is sub-parallel to the imposed regional oblique convergence (Fig. 12b).However, the displacement vectors within the transpression zoneevolve along distinct paths. With the evolution of oblique convergencein time, the magnitude of displacement increases faster within thetranspression zone than outside it. Moreover, the evolution of the finitedisplacements outside the transpression zone increases the deviation ofdisplacement vectors (from 10° to 50°) to the transpression zone

Fig. 10. Maximum tensile principal stress trajectories within the transpression zone. This model is the middle part of whole model, 70 × 10 × 15 km.

Fig. 11. Displacement field result from oblique convergence and within the contractional step (transpression zone).


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boundaries from time step 0.1 to 0.5. After that, the angle between thedisplacement vectors to the transpression zone boundaries decreasesfrom time step 0.75 to 1 (from 47° to 35°) (Fig. 12b). Plots on Fig. 13bshows a curved path from time step 0.1 to 1 as upward convexity. Thiscontinuous reduction in deviation angle of displacement vectors couldbe due to the temporal evolution of oblique convergence and simple-shear-dominated deformation outside the transpression zone. Opposingdisplacement gradients on the adjacent fault segments define a coun-terclockwise vertical axis rotation of the model transpression zone. Thecounterclockwise rotation predicted by the model for a contractionalright stepping is consistent with the rotations predicted by field andanalogue studies (e.g., McClay and Bonora, 2001; Mitra and Paul, 2011;Dooley and Schreurs, 2012).

Fig. 13 depicts the displacement time series for the present model-ling, and shows a rapid increase in displacement at time step 0.13,when the first plastic strain zones and oblique-reverse faults developed

in the contractional step, and are then followed by a non-linear increasewith continued oblique convergence. According to the higher con-centration of plastic strain within the contractional step and thetranspression zone, the amount of vertical displacement (Uy) is largerthan that of horizontal displacements (Ux, Uz). This pattern of dis-placement in a time series has also been demonstrated by Armaş et al.(2017) in their analysis of the Bucharest's ground displacement dy-namics as a possible transpressional system.

The models explored in this work are based on the Sanderson andMarchini (1984) and Fossen and Tikoff (1993) models of transpression.However, those models assume homogeneous strain and produce a “flattopped” mountain range. Both the present work and natural cases oftranspression zones, displacements, fault slips, and shortening are likelyto partition across and along strike the deformation zone. This workshows that the particles move along curved paths (Fig. 14), an unlikelysituation in some of the previous models of shear zones (e.g., Mukherjee

Fig. 12. Azimuth vs. magnitude plots for surface displacement a) within, and b) outside the transpression zone. Outside the transpression zone, the model block evolves in an overallplane strain deformation. Within the transpression zone, displacements suggest a complex three dimensional displacement field. Data shown with different colors, are from five selectedincrements of deformation representing 0.1 (red), 0.25 (blue), 0.5 (green), 0.75 (orange), and 1 (dark blue) of total regional oblique convergence. Eight data were collected at eachselected increment. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)


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and Mulchrone, 2013; Mulchrone and Mukherjee, 2015, 2016). Curvedflow paths in shear zones are most likely in shear zones with curvedboundaries (e.g., Mukherjee and Biswas, 2014; Zibra et al., 2014).These paths are almost parallel to the fault segments and their sheardirection in the center of the model can be attributed to the effect ofsimple-shear-dominating the deformation or partitioning so that thepaths are at distinct angles to the fault segments and shear direction.Hence, the displacement partitions into various amounts of extrusion(as doubly plunging folds) and heterogeneous strain throughout thetranspressional system.

Our modelling results indicate that horizontal and vertical dis-placement of material within the transpression zone causes obliquefrictional simple shear (Fig. 15) along the surfaces of fault segments, asseen by the asymmetric distribution of shear stress/strain, so that thesimple shear direction is oblique to the strike of the transpression zoneboundary (Fig. 15). The initial dip of the fault segments is 90° and weexpect the result to be a monoclinic transpression zone, after the zoneboundary has deformed and deflected the tips of fault segments(Fig. 16). Deflection at fault segments caused the fault dip to fall to lessthan 90° (∼86–89°) near the surface (∼1.5 km) (Fig. 16). Hence, noneof the three-dimensional elastic and plastic stress and strain tensorswithin the transpression zone, are aligned with the axes of the co-ordinate system after the very beginning of deformation. The resultingtranspression zone is only a few degrees (∼1–4°) away from themonoclinic case. However, this results in a pure-shear-dominated tri-clinic transpression zone. According to these results, the model extru-sion is symmetric although, the angle between the extrusion direction

and the dip of the transpression zone (angle ν in Fernández and Díaz-Azpiroz, 2009) locally deviates from 0° (ν≠0°) at depths of 0–1.5 kmand 0° (ν = 0°) at depths of 1.5–15 km. In addition, since the verticalextrusion varies in relative intensity from point to point along thetranspression zone, the implication is that ν locally deviates from 0°.Therefore, there is an acute angle between the oblique simple shear andthe vertical extrusion direction, i.e., 0° < ζ < 90°. The relative ob-liquity of the simple shear component creates obliquely plunginglineations. Transpression with an oblique simple shear direction is alsodescribed by Robin and Cruden (1994), Dutton (1997), Jones andHoldsworth (1998), Lin et al. (1998), and Czeck and Hudleston (2003)among others. The results of this work demonstrate that the trans-pression zones are highly sensitive to slight variations in their con-trolling parameters, a problem recently addressed on statistical groundsby Davis and Titus (2017).

Our results from modelling sinistral transpression indicate that theprincipal stress and strain axes will undergo a counterclockwise rota-tion of 20–45° with progressive deformation. In the modeled trans-pression zone, the principal stress axes rotate counterclockwise aheadof each fault segment. In addition, the magnitude of stress and straincomponents decreases outwards from the central part of the trans-pression zone. This shows that deformation distributes over severalplanes with different orientations. Hence, the rotation of the strainprincipal axes and the variation in their magnitudes reflects the het-erogeneous nature of deformation, which ranges from approximatelysimple shear to non-coaxial flattening strain. Fig. 16 shows the archi-tecture of the fault segments that illustrates the curved nature of the

Fig. 13. Displacement time series of model elements. a) Uy, b) Ux,Uy for the present transpression zone FE-modelling.

Fig. 14. Curved path of material flow along the transpression zone.


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primary sidewall oblique-slip faults and the change in their geometriesalong strike with upward convex positive flower or Y-shaped structurein cross-section as the width of the deformation zone decrease withdepth and confining pressure (Figs. 17b and 18a–c). The angles definedby the curved faults, reflect the oblique convergence in en-échelonoblique-slip features and, are gentler compared to those shown by pop-

up structures resulting from the steps in pure strike-slip faults (as hasbeen observed in analogue modelling of Naylor et al., 1986, Richardand Cobbold, 1990; Richard et al., 1995; Dooley et al., 1999; McClayand Bonora, 2001; Cooke et al., 2013). Fig. 17 shows oblique shorteningbalanced by lateral and vertical extrusion at the transpression zone. Inaddition, the transpression zone is longer than the separation between

Fig. 15. Shear stress along a) fault segment 1, and b) fault segment 2 (bottom). The model is the middle part of the whole model and its dimensions are 70 × 10 × 15 km.

Fig. 16. The curved nature of the primary sidewall fault segments and the change in their geometries along strike after applying oblique convergence and deformation.


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the fault segments, so that zone located between the inward-ap-proaching walls creates a discontinuous heterogeneous flow (Fig. 17).

According to the initial constraints of our modelling strategy, weexpected the highest values of shear strain and dilation would occuralong the fault segments and in the areas immediately around them.However, the maximum shear strain and slip correspond to the faultstepping area, creating a stress and strain peak (Fig. 18). Elementswithin the overlapping zone undergo large stresses and strains. Fric-tional shear strain and contact slip along elements of fault segmentswithin overlap zone are basically higher than in the outer zone. Inaddition to these large shear strain values, low shear strain zones can befound far away from the fault stepping area, or in that area where thefirst stages of convergence occur (Fig. 18). These results show that mostof the elastic and plastic energy is concentrated in the transpressionzone (or the area limited by the two overlapping faults segments) andits adjacent regions, such as closer to the fault tips. The shear straindistribution along the fault segments, from surface to depth of theanalyzed model, is illustrated in Fig. 18a–c, which shows a flower-shaped strain localization region oblique to the fault segment. More-over, shear strain is not significant outside the transpression zone. Inother words, the slip on the inner side of fault segments does not an-nihilate or disappear because the faults are linked to each other and slipis transferred from one fault segment to the other. Furthermore, distinctmesh elements along the fault segments and transpression zone havedifferent responses. These complex responses are found due to stepgeometry, failures, and angle of convergence (or the orientation of faultsegments with respect to the maximum principal stress). Furthermore,distributed shear within the transpression zone adjacent to the slidingsurfaces is a sign of off-fault deformation.

The mechanical models may fill the gap between the complexity ofnatural structures and our theoretical understanding of them. Althoughthe models always simplify nature, they are realistic enough to uncoveressential features of the natural processes. The results presented in thisstudy are part of a broader spectrum of three-dimensional numericalmodels that we have developed to investigate the role of mechanicalinteraction between fault segments on the evolution of transpressionzones. The mechanical studies of oblique convergence settings allow usto determine and discuss different deformation parameters such asthree-dimensional geometry, stress and strain distribution, model re-storations, slip intensities, etc.

3.4. Kuh-e-Hori transpression zone, SE Iran

Transpressed volumes are characterized by pop-ups or domes (e.g.,Harding and Lowell, 1979; Harding, 1985; McClay and Bonora, 2001;Dooley and Schreurs, 2012; Pace and Calamita, 2014; Calzolari et al.,

2015; Maia et al., 2016; Cheng et al., 2017). Several parameters havebeen invoked to explain them; examples are convergence angle, stepgeometry, pre-existing faults, and local variation in fault segment dip.Pop-up-boundary faults display concave-downward geometries(McClay and Bonora, 2001; Dooley and Schreurs, 2012), consistentwith our modelling results (Fig. 1). Our model pop-up structure isbroadly rectangular in plan form, almost symmetrical, with a doublyplunging fold, such as the Kuh-e-Hori transpression zone, SE Iran(Fig. 19a–d) (sections AA′eFF′ in Fig. 17e of Nabavi et al., 2017a),Torcal de Antequera massif in the external Betics of southern Spain(Fig. 3a–b of Díaz-Azpiroz et al., 2014), as well as the Cerro de la Mica,Atacama strike-slip fault system in the northern Chile (Fig. 21 ofMcClay and Bonora, 2001). Hence, model and natural pop-ups are non-cylindrical folds due to non-cylindrical vertical extrusions along thetranspression zone. Note that doubly plunging folds can also be pro-duced by superposed deformations. Non-cylindrical folds are one of avariety of fold geometries expected to develop in transpressional andtranstensional settings (Fossen et al., 2013; Zulauf et al., 2017). Inaddition, pop-up structures are typically flanked by faults with oblique-reverse kinematics.

By contrast, asymmetric subsidence basins commonly expand onboth sides outside the overlap of the transpression zone. These trans-pressional basins are generally long and narrow structural depressions,with oblique-slip faults and negative flower structures, and lie parallelto but outside the transpression zone and restraining bend/step (Figs. 1and 19c-d) (Nilsen and Sylvester, 1999a, 1999b). Natural examples ofthese transpressional basins are the Sahl-abad and Nehbandan sub-sidence basins that have developed as a result of the evolution of theKuh-e-Hori transpression zone in SE Iran (Fig. 19). The Kuh-e-Horitranspression zone is the result of interaction between the Esmail-abadand the West Neh right-lateral strike-slip fault segments so that thesetwo fault segments form a left-stepping geometry and create a con-tractional step (see Nabavi et al., 2017a for details). Depocentres ty-pically form adjacent to uplifted structural blocks and subside either byflexure caused by the tectonic load, or in response to the local extensionat the bend/step or intersection of strike-slip faults (Ingersoll, 2012).Similar to other basins in strike-slip zones, transpressional basins aregenerally smaller and more complex than other fault-related basinswith linear or curvilinear map form. Transpressional basins are char-acterized by high subsidence rates, asymmetrical distribution of facies,and multiple and complex unconformities (Ingersoll, 2012).

Generally, in this study, the transpression zone undergoes verticaland lateral extrusion (e.g., the unconfined monoclinic transpressionmodel of Jones et al., 1997; Fernández and Díaz-Azpiroz, 2009;Fernández et al., 2013; Díaz-Azpiroz et al., 2014). Transpression zonesin which the base is not confined are also subject to downward material

Fig. 17. Discontinuous heterogeneous flow model of the transpression zone. a) Initial, undeformed state. b) Deformed state showing the curved geometry of the faults bounding thetranspression zone.


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Fig. 18. a) Maximum principal strain distribution. This model is a section through the whole model. b) Minimum principal strain distribution. This model is a section through the wholemodel. c) Medium principal strain trajectories.


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displacement at depth as we have seen in early boundary conditions ofour model that the base of it was unconfined (not shown here). Joneset al. (1997) and Giorgis et al. (2009) presented an isostatically com-pensated model of transpression, where material is allowed to flow bothupward and downward to form topographic relief and crustal roots,respectively. Extrusion (vertical or lateral) strongly depends on theconvergence angle and the magnitude of shortening. For low con-vergence angles (simple-shear-dominated), lateral extrusion is alwayshigher than vertical extrusion. By contrast, contraction-dominated highconvergence angles always, drives more vertical extrusion than lateralextrusion. Moreover, the material in the transpression zones undergoes

syn-shearing volume loss. Ramsay and Graham (1970) in their classicwork dealt with the kinematics of shear zone flattening attributed tosyn-shearing volume reduction in the shear zone. Syn-shearing volumereduction can be considered as an important parameter for transpres-sion deformation (Le Pourhiet et al., 2014; Dasgupta et al., 2015).

For the model configuration and boundary conditions presented inthis study, the Von Mises equivalent stress is highest within the over-lapping fault step. For homogeneous transpression zones, the magni-tude of rotation decreases with increasing angle of convergence. Awayfrom the fault tips and out of the transpression zone, the strains aremore homogenous across wide areas; this encourages new normal and

Fig. 19. a) Regional overview of Iran; b) Simplified geological map of the northern part of the Sistan Suture Zone (after Fotoohi-Rad et al., 2009; Bröcker et al., 2013; Bayet-Goll et al.,2016). c) Google Earth™ image of the Kuh-e-Hori transpression zone from the map view. d) N-S topographic section of (Fig. 19c) that shows the Kuh-e-Hori transpression zone issurrounded by the Sahl-abad and Nehbandan transpressional subsidence basins on both sides of it.


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reverse faults to form in extensional and contractional regions, re-spectively. However, these faults can be partitioned in terms of strainand slip. The strain distribution for oblique-slip system and deep intranspression zone is produced by the addition of pure strike-slip anddip-slip displacements, resulting in different and widely varying me-chanisms.

Two zones can be identified in our model of strain distributionwithin transpression zones. Reverse fault mechanisms predominate inthe footwall and directly ahead of the fault segment tips. In the hang-ingwall and the central part of the transpression zone, strike-slip me-chanisms predominate. Furthermore, in this deformation system, strike-slip faulting is accompanied by oblique contraction driven by localizeddeep deformation resulting in positive flower/palm tree structures(Harding and Lowell, 1979; Stefanov and Bakeev, 2014, 2015), key-stone structures (Sylvester and Smith, 1976) or pop-up relay structures,which involve multiple fault branches. In addition, localization ofstrike-slip shear produces an increase in the kinematic vorticity numberwithin transpression zone relative to areas outside the zone. Therefore,a zone of normal faulting could develop in the subsidence regions be-hind the fault tips. Generally, contraction-dominated transpression wasaccommodated by a wider domain than simple-shear-dominatedtranspression; a process defined as “discrete partitioning” (Schulmannet al., 2003). Hence, slip partitioning results when the deformation isaccommodated by two or more faults with different mechanisms(McCaffrey, 1992; Jiang and Williams, 2001; Bowman et al., 2003). Innatural cases, however, slip partitioning can be more complex, withseveral domains of geological features contrasting in terms of straindistribution, location, scale, and time evolution.

In contraction convergence (α = 90°), the stress tensor is invariant(e.g., Upton and Craw, 2014, 2016). In transpression zones and obliqueconvergences zones, both stress and strain axes rotate. According to thepresent modelling, the temporal and spatial counterclockwise rotationof the principal axes of stress and strain can lead to contemporarystrike-slip and dip-slip faulting. In the transpression zone, the structuresaccommodate the oblique motion with deformation propagating fromsurface to depth as has been observed in the development of the firstplastic zones (Fig. 9). The transpression zone narrow with progressivedeformation. The simple-shear component in the transpression zone canbe accommodated by either individual slip planes or partitioned intopure-shear internal deformation as folding and strike slip on numerousfault segments. The modelling results reveal that oblique convergencenarrows contractional structures from wider transpression zones underoblique convergence settings, to either pure contraction settings orstrike-slip dominated systems. Moreover, deformation partition intranspression zones under oblique convergence is stronger than thatdue to pure contraction and simple shear deformation. This means thatregularly spaced oblique-reverse and strike-slip faults develop in theformer case. Indeed, deformation partitioning is limited in pure-shearor simple-shear-dominated transpression zones (Barcos et al., 2016).

Our modelling results show that the degree of partitioning is con-trolled by the convergence angle and slip along the fault segments. Thischaracteristic would result in oblique relationships between fold axialplane, as low angle counterclockwise rotation, and transpression zoneboundaries (e.g., Sanderson et al., 1980; Sanderson and Marchini,1984). The distribution of deformation depends upon the rate of de-crease of slip towards the end of the fault segments, and with increasingdepth, which is asymmetric (e.g., Duman et al., 2005; Khoshmaneshet al., 2015; Whipple et al., 2016; Nevitt and Pollard, 2017).

Determining the distribution of fault slip is important as it estab-lishes which parts of a fault segment are locked. The model results(Fig. 6, and Section 3.2) imply that the lower portion of the fault can belocked with increasing depth, while its upper portion slips at the platedisplacement condition. In dynamic models of crustal deformation(e.g., Aagaard et al., 2013), the locked, lower part of the fault accom-modates slip as quasi-static viscoelastic deformation throughout theearthquake recurrence time and, keeps pace with the dynamic slip of

the upper portion of the fault. This results in the cumulative slip beinguniform across the fault surface over an earthquake cycle. The amountof fault slip is affected by the magnitudes of the normal and shearstresses along the fault segment. In turn, changes in slip behaviourwithin the contraction step can be attributed to increased mean com-pressive stress within the step. Any increase in mean compressive stressreduces fault slip. Therefore, high Von Mises equivalent stress withinthe transpression zone causes significant plastic shear strain to developthere (e.g., Nevitt, 2015; Nevitt et al., 2017). Most major earthquakesoften take place in the seismogenic upper crust. Immediately below thatlevel, the localizing mid-crust, layer decouple a region where weak-ening would generate relatively ductile shear zone and that may asso-ciated with microseismicity (e.g., Gueydan et al., 2003, 2004). Micro-seismic clusters at depths ranging between 6 and 11 km below region ofactive extension (Rigo et al., 1996; Rietbrock et al., 1996) and less than20 km (∼10–20 km) in active contractional settings (Boese et al., 2012;Warren-Smith et al., 2017). It is possible to determine the stress transferonto surrounding fault segments to detect parts of the fault system thatare closer to failure, and to establish the relationships between faultgeometry and surface geomorphology needed to understand fault seg-mentation (e.g., Calais et al., 2010; Kaven et al., 2011; Elliot et al.,2016). Fault slip magnitude is mainly affected by the coefficient ofsliding friction within the crust and along the fault segments as well asby the depth of the fault tips and dips of the faults (e.g., Kim andSanderson, 2005; Abers, 2009; Hampel and Hetzel, 2012; Steffen et al.,2014a, 2014b, 2014c; Zeumann and Hampel, 2016).

Fault overlap plays a prominent role in the evolution of displace-ment fields in transpression zone. The effects of fault overlap on thevertical deformation and rotation axes have been discussed by manyresearchers (e.g., Katzman et al., 1995; ten Brink et al., 1996). The faultseparation has a considerable effect on the size and shape of trans-pression (or pop-up structures with uplift) and transtension zones (orpull-apart basins with subsidence) between two fault segments. Whenfault overlap exceeds the fault separation, a sigmoidal- or rectangular-shaped transpression zone forms (e.g., Mitra and Paul, 2011; Dooleyand Schreurs, 2012). This zone is bounded by overlapping fault seg-ments that experience localized oblique convergence. Unlike kinematic,geometric, and theoretical models, the three-dimensional FE-modelsallow us to monitor the finite rotations at different structural levels; italso tracks incremental rotations at various structural positions in themodel transpression zone. In nature, the magnitude of rotation anddeformation may vary in much more complex manners and depends onsuch parameters as mechanical stratigraphy, elliptical fault surface,inclined boundaries, and anisotropy (e.g., Nabavi et al., 2017d). Ourmodel results suggest that even when the primary fault segments aresubjected to a particular convergence angle (45° in this study), atranspression zone evolves in a complex three-dimensional strain fieldthat is not consistent with the far-field strain. Our modelling results foroverlapping fault segments imply that the magnitude of horizontal andvertical rotations are higher in the transpression zone than outside it. Inaddition, the magnitudes of rotations increases as the oblique con-vergence matures. Fault interactions in an overlapping step geometrycan give rise to a broad variety of local structures that can be under-stood in terms of the variations in the stress and strain field predicted bythe model. Block rotation, thrust emplacement, multiple faulting, andmylonitisation apparently occur in regions of high compressive stressand plastic strain (i.e., within contractional fault steps and transpres-sion zones). The size and extent of the region with the largest stresschanges in the contractional step is smaller than in frictionless fault stepnumerical models (e.g., Brankman and Aydin, 2004; Steffen et al.,2014; Lejri, 2015; Lejri et al., 2015; Bagge and Hampel, 2016). This isdue to the effects of frictional faults, the magnitude of the increasedmean stress (positive mean normal stress), and of shear stresses. Theseresults are consistent with recent studies that point toward a complexdeformation patterns within transpression zones (e.g. Zibra et al., 2014;Maia et al., 2016; Nabavi et al., 2017b, 2017c).


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Our modelling results imply that plastic deformations and fracturingor faulting begins at the surface. Material strength increases with in-creasing depth due to the frictional component of the strength, whichincreases with lithospheric pressure or the mean stress. Hence, thematerial strength is lowest in the upper levels where plastic deforma-tion occurs first. Since the tensile strength of any material is less than itscompressive strength (Price, 1966; Price and Cosgrove, 1990), andsince the presence of tensile or compressive mean normal stress hasbeen observed in releasing and restraining steps, respectively (e.g.,Nevitt et al., 2014; Nabavi et al., 2017a), plastic strain localization andgeneration of brittle fractures is predicted to be more marked in re-leasing steps and transtensional zone than in restraining steps andtranspressional zones under similar conditions (e.g., Goteti et al., 2013;Ye et al., 2015). The rotational component is superposed on the de-formation field generated in oblique structures that exist in a broadvariety of orientations. Therefore, local structures develop oblique tothe transpression zone boundaries and the primary fault segments. Suchfeatures are very common in oblique convergence settings and havebeen extensively documented in natural examples (e.g., Díaz-Azpirozet al., 2014; Barcos et al., 2015). The model shows that deformationextends beyond the fault step, there is no oversimplified strain parti-tioning between pure- and simple-shear-domains, and strain gradientschange smoothly. This problems was widely discussed by Carreras et al.(2013) and Jiang (2014).

4. Conclusions

Many oblique convergence settings are characterized by regionalen-échelon oblique-slip fault segments that form a transpression zone.We have presented a three dimensional finite element model to analysethe role of fault interactions during the evolution of transpression zonesbetween adjacent fault segments. Slip profiles, stress distributions, andstrain localization patterns are described for the transpression zoneaffected by fault interaction as a function of the convergence anglebetween the far-field compression orientation and the strikes of faultsegments. The results show the mean and maximum principal stressincrease (i.e., the compression increases) inside the step between thefault segments relative to the region outside the step. With progressivedeformation of the model block, the σ3 axis rotates within the trans-pression zone to form an angle oblique to the regional transport di-rection (∼9°–10°) and the transpression zone boundaries. Outside thetranspression zone, the σ3 vectors are oriented sub-normal to the re-gional transport direction (with only slight deflection of ∼4°) and arealso sub-parallel to the maximum extensional finite strain.

Slip along the fault segment offsets ‘active’ blocks. As the slip alongthe sliding surfaces gradually decreases, the transpression zone betweenthe two faults segments is expected to gradually increase its height(vertical extrudes) towards the overlapping zone. The slip decreasealong fault segments can be attributed to the accommodation of bulkshortening along adjacent fault segments. Furthermore, the slip dis-tribution along fault segments decreases with increasing depth, so thatthe slip decreases at distinct steps between depths from 0-5 km to5–15 km. The fault slip distributions in the elasto-plastic model arequite asymmetric. The maximum slip occurs near the center of the faultsurface. The superposition of distortion and rotational deformationresults in a complex three-dimensional displacement field. With timeevolution of oblique convergence, the magnitude of displacement in-creases faster within the transpression zone than outside it.

Rotation of the displacement vectors with time of oblique con-vergence suggests that the transpression zone evolves under an overallnon-plane strain deformation. Another feature resulting from the in-teraction between the faults is the almost symmetrical domal uplift orvertical extrusion, that is one source of off-fault deformation, along thetranspression zone as a doubly plunging fold and ‘positive flower’structure. By contrast, commonly outside the overlap zone, expandingasymmetric subsidence basins develop on both sides of the

transpression zone that are called ‘transpressional basins’ with ‘negativeflower’ structures. Generally, the transpression zone undergoes lateraland vertical extrusion. After deformation the geometry of the zoneboundary changed and deflected the tips of fault segments. Deflectionat fault segments has caused the fault dip to decrease to less than 90°(∼86–89°) near the surface (∼1.5 km). Hence, none of the three-di-mensional elastic and plastic stress and strain tensors are within thetranspression zone, except at the beginning of deformation, are un-compatible with the axes of the coordinate system. This results in apure-shear-dominated, triclinic, and discontinuous heterogeneous flowmodel of transpression zone.

Acknowledgements

We thank Prof. Carlos Férnandez, Dr. Marcel Frehner, Prof. ArthurG. Sylvester, Prof. Christopher J. Talbot for their careful and con-structive reviews, comments, suggestions, and discussions that greatlyimproved earlier versions of this manuscript and help shaped the finalversion. This work forms part of the Ph.D. thesis of Seyed Tohid Nabaviat Shahid Beheshti University, Tehran, Iran. We thank reviewers Prof.Soumyajit Mukherjee and the honourable anonymous reviewer for theirattentive reading and constructive comments that improved themanuscript. Editorial and handling work by Prof. Ian Alsop is alsogratefully acknowledged.

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Journal of Structural Geology - دانشگاه تهران · The mechanical evolution of transpression zones aﬀected by fault interactions is investigated by a 3D elasto-plastic