The numerical code solves for the conservation of mass and momentum (the Stokes equation) on a Eulerian grid to calculate the velocity and pressure fields 1∂vi∂xi=0, and 2-∂p∂xi+∂τij∂xj=ρgi, where vi and xi are velocities and spatial coordinates, p the dynamic pressure (mean stress), τij the deviatoric stresses, ρ the density (constant), and gi the gravitational acceleration (g1 = 0; g2 = 9.8 ms-2). Temperature is solved by considering the energy conservation on the Eulerian grid, 3ρCpDTDt=κ∂2T∂xi2, where Cp is isobaric heat capacity, DDt is the total time derivative, T is temperature, t is time, and κ is the thermal conductivity coefficient. Additional heat production, such as radioactive heating and shear heating, is not activated in the presented experiments due to the geometrical constraints of the model setup and related boundary conditions that affect the diffusion of such secondary heat production.

The pressure and temperature fields calculated from the governing equations are interpolated onto the Lagrangian markers based on a linear distance-weighted scheme (Gerya, 2019). The Lagrangian markers store all material properties and advect through the Eulerian grid based on a fourth-order Runge–Kutta interpolation of the calculated two-directional Eulerian velocity field.

The numerical code employs a visco–elasto–plastic/brittle rheology, where viscoelasticity is implemented by a Maxwell-type expression. Elasticity plays a key role in capturing short-term stress accumulation and release, which is crucial for fault and fold behavior. The Maxwell model allows the simulation of the immediate elastic response and long-term viscous flow, ensuring that important transient phenomena such as fault reactivation and seismic activity are accurately represented during both extension and convergence. The strain rate of a Maxwell body under stress consists of viscous and elastic components, 4ε˙ij=12ητij+12GDτijDt, where G is the elastic shear (100 GPa for all materials here), and η is the effective viscosity. First-order finite differences in time are used to represent the objective co-rotational time derivatives of the viscoelastic stresses as follows: 5DτijDt=τij-τijoldΔt.

The effective viscosity η is calculated from the non-Newtonian dislocation, ηdisl, creep equation, 6ηdisl=0.5⋅1AD⋅σII(1-n)⋅exp⁡QRT, where 7σII=12τij2, and R, AD, n, and Q are the gas constant, the pre-exponential factor, the power law constant, and the thermal activation energy, respectively. Elastic behavior is achieved by updating the effective viscosity in response to an elastic time step (Maxwell time; Δte = 1000 years) and the stress history (Gerya and Yuen, 2007; Moresi et al., 2007, 2003). The updated viscoelastic deviatoric stresses are defined by 8τij=2ηε˙ijz+τijold(1-Z), where 9Z=Δte⋅Gηdisl+Δte⋅G.

The effective viscosity is multiplied by this viscoelastic factor (Z) to obtain a numerical viscosity ηnum to be used for solving the set of equations as follows: 10ηnum=ηdisl⋅Z=ηdisl⋅Δte⋅Gηdisl+Δte⋅G.

Plastic failure occurs if the second invariant of the viscoelastic stress tensor exceeds the yield stress, σy, following a pressure-dependent Drucker–Prager criterion: 11σy=p⋅(1-λ)⋅sin⁡φ+c⋅cos⁡φ, where p is the pressure (mean stress), and c, φ, and λ, are the cohesion, friction angle, and the fluid pressure ratio of the bulk material, respectively. The components of stress (σxx is the normal stress component, and σxy is the shear stress component) and the viscosity are then updated as 12σxxnew=σxxσyσII, and if σII>σyield,σxx, and if σII≤σyield,13σxynew=σxyσyσII, and if σII>σyield,σxy, and if σII≤σyield,14ηnum=σy2ε˙II, if σII>σyield, where 15ε˙II=12ε˙ij2.

The viscosities, including the viscoelastic effect and the plastic failure, are calculated on the Lagrangian markers and interpolated onto the Eulerian nodes using a distance-weighted scheme. To ensure numerical stability, they are capped by lower and upper cutoffs of 10¹⁷ and 10²⁵ Pas, respectively. Given the numerical time step of Δte = 1000 years, material undergoing deformation at viscosities below 3.16 × 10²¹ Pas can be considered predominantly viscous, while deformation at viscosities above 3.16 × 10²¹ Pas is to a significant part elastic and thus reversible. Elastic relaxation time varies between ∼ 1 year and 1 million years, depending on the viscosity of the material, which results in Deborah numbers of 10⁻⁷–0.1 for a deformation period of 10 million years.

The model domain is defined by a box of 500 km width and 60 km height (Fig. a). The Eulerian grid consists of 1001 × 121 nodes, with a nodal resolution of 500 × 500 m. The initial marker distribution defines, from bottom up, (1) a 30 km thick crustal basement layer, given the depth of basement crustal detachment (Vergés et al., 2011; Kendall et al., 2020); (2) a mechanically weak salt horizon emplaced between 100 km < x < 450 km; (3) a 3 km thick Paleozoic sequence based on the stratigraphy of the Fars Arc; and (4) a 25 km thick low-density and low-viscosity sticky-air layer to simulate a free surface, allowing for the vertical growth of the evolving fold-and-thrust belt (Crameri et al., 2012). The thickness of the salt layer varies in different models in order to examine its impact on the structural evolution. Some experiments include three inherited basement faults located at x = 100, 200, and 350 km (top of the basement), which dip at an angle of 50° at their top towards the hinterland (Mouthereau et al., 2006). These weak zones may either have a listric or planar geometry. The rheological parameters used in the experiments are provided in Table . Strain weakening is implemented by a linear decrease in the values for the frictional angle (φ) and cohesion (c) between a lower and upper strain threshold as defined by the second invariant of the strain tensor εII0=0.1 and εII1=1.

The initial temperature field is characterized by a linear temperature increase with depth, starting from 0 °C at the interface between rock and sticky air and reaching 600 °C at the bottom, which is in agreement with a constant geothermal gradient of 20 °km-1 inferred from paleothermal data (Aldega et al., 2018) and a relatively thick lithosphere (∼ 200 km) beneath the Zagros (Jiménez-Munt et al., 2012; Priestley et al., 2012; Tunini et al., 2014). Applying a linear geotherm is a reasonable simplification for the uppermost ∼ 50 km of the continental lithosphere (Hasterok and Chapman, 2011; Goes et al., 2020). Each Eulerian cell initially contains 16 randomly distributed Lagrangian markers carrying rock information and properties. If the finite spatial domains of a specific node become empty of any Lagrangian marker, the previous interpolated parameters are applied for solving the system of equation of this particular node.

The numerical experiments simulate the deformation of the NE margin of the Arabian Plate during Permian–Triassic rifting and Oligocene–recent continental collision. Tectonic quiescence affects the thermal state and, consequently, the rheological behavior of the rocks. However, we assume that the temperature field reached a steady state by the onset of the collision phase to simplify the model setup. This implementation allows us to effectively capture the relevant thermal conditions, while maintaining focus on the critical dynamics of the extension and collision phases. The velocity boundary conditions are prescribed in a way to simulate the tectonic inversion of the rifted margin, including the initial extension and subsequent convergence. During the rifting phase, an outward horizontal boundary velocity of vx = 5 mmyr-1 is applied on the right side of the model domain, while the left boundary is kept fixed in horizontal direction (Fig. a). The bottom boundary has zero vertical velocity, and the top boundary has an incoming vertical velocity of vy = 0.6 mmyr-1, ensuring the conservation of the volume within the model domain (Fig. a). On all boundaries, free-slip conditions (zero shear stress) are prescribed. The finite Eulerian domain impedes elastic bending of the lower boundary, affecting the resulting surface taper angles compared to the ZFTB (Mouthereau et al., 2006; McQuarrie, 2004). The extension phase is applied for a period of 5 Myr, resulting in a total extension of 25 km. During this period, the rift basin is allowed to be filled with syn-rift deposits (equivalent to the Dashtak and Dehram formations). Following the extension phase, 4 km of sediments representing the depositional environment during the tectonic quiescence and subsidence period are added onto the existing stratigraphy (Fig. b). These sediments represent the Khami and Bangestan groups and the Gurpi and Pabdeh formations (Fig. ). The Late Cretaceous ophiolite obduction episode has affected only some parts of the Arabian margin, namely the Kermanshah, Neyriz, Hajiabad, and Oman regions. We have not included the Late Cretaceous deformation in our modeling, as it accounts for just a few percent of the observed shortening in the ZSFB (e.g., Saura et al., 2011).

Crustal shortening in the experiments is simulated by imposing a horizontal velocity of 1 cmyr-1 at the bottom and the left side of the domain. The right side acts as a partial backstop by allowing the basement part of the crust to escape the model but prevents the sedimentary cover from exiting. For the lower part of the right boundary (basement), different horizontal velocities between 0 and 1 cmyr-1 are tested (Fig. b). This arrangement permits us to vary the degree of basement involvement and to study the development of thin-skinned and thick-skinned tectonics in the model. The compressional phase ran for 15 Myr, accommodating a total shortening of 25 % (i.e., 125 km), This amount offsets the 25 km extension during the extensional phase and the 20 % shortening during the collisional phase, comparable to estimates for the SE Zagros (McQuarrie, 2004; Motamedi et al., 2012; Pirouz et al., 2017; Najafi et al., 2021).

The surface processes of sedimentation and erosion during the evolution of the models are simulated by applying diffusion of the rock–air interface. We used the following diffusion equation: 16∂hs∂t=K∂2hs∂x2, where hs is the surface topography, t is time, K denotes a diffusion constant (K = 10⁻⁶ m2s-1), and x is the horizontal coordinate. The left and right sides of the surface line prescribe free-slip boundaries.

The reference model (Model 1) has an initial 2 km thick salt horizon with a power law viscous rheology (Tables  and ). The basement exhibits three inherited listric fault zones and is shortened at the same rate as the sedimentary cover during convergence. The extensional phase is characterized by the development of half-graben basins forming along the listric basement faults that are filled by syn-extensional deposits (Figs. a–c and S1 in the Supplement). The second invariant of the strain-rate tensor shows that the fastest deformation occurs along the pre-existing weak zones. During extension, all three inherited faults are simultaneously active and without any recognizable preference. Normal fault deformation along the basement faults propagates upward into the post-salt strata, inducing typical half-grabens and the bending of the hanging wall (Fig. c and S1).

After compression for 5 Myr, the cover sequence mainly deforms between the right backstop and the salt pinch-out at x ≈ 150 km (Fig. d and S1). The basement fault closest to the backstop has experienced a significant amount of reverse motion and has caused a large step of several kilometers in the salt décollement geometry. Faulting of the sedimentary cover mainly develops where the syn-rift strata are the thinnest, i.e., in front of the basement thrusts. Strain localization occurs along the basement faults, and in the case of the frontal fault (x ≈ 120 km), it cuts across the strata overlying the salt layer (Fig. d and S1). Towards the backstop, the deformation in the basement and the cover sequence is decoupled along the weak salt horizon.

As convergence progresses (10 Myr), the basement fault at x ≈ 300 km undergoes inversion and creates a ramp–flat–ramp geometry (Fig. e and S1). Basement fault propagation deforms the syn-extensional strata and forms harpoon-like anticlines within the sedimentary cover. The syn-tectonic sedimentation concentrates within multiple structural basins between the developing anticlines. The salt layer decouples the deformation between the basement faulting and the sedimentary cover folding, allowing for more amplification within the sedimentary cover. Strain rates indicate intense deformation within the basement, which particularly localizes along the inverted normal faults, as well as the basal décollement level. The strain-rate pattern starts to gradually diffuse below ∼ 26 km depth, indicating the transition from brittle to ductile deformation in the lower crust (Fig. f and S1).

Patterns of the second invariant of the stress tensor after the extensional phase and after full convergence indicate an increase in stress with depth down to ∼ 30 km (y = 50 km), which is where the brittle-to-ductile transition begins (Fig. a and d). The lower part of the basement displays low stresses, given its lower viscosities and ductile nature (Fig. b and e). Viscosity plots furthermore indicate the position of the low-viscous décollement and basement thrusts.

Figure c illustrates the vertically averaged viscosity of the non-Newtonian salt horizon after an extension of 25 km, which is influenced by the temperature and strain rate (Table ; Li and Urai, 2016). During the extension and the formation of half-grabens along pre-existing faults, the strain-rate and temperature increase in these areas. Consequently, these regions exhibit the lowest viscosities (10¹⁸ Pas), corresponding to the locations of the basement faults (Fig. c). In areas without strain localization within the cover sequence, the viscosity shows larger values (10¹⁹–10²⁰ Pas). After an extension for 5 Myr, the half-graben basins are covered by post-rift deposits prior to the onset of convergence. After 15 Myr, the intensity of thin-skinned folding within the sedimentary cover increases (Fig. f). The development of long-wavelength folds is influenced by the reactivation of basement faults, which exert a significant impact on the deformation of the upper crustal region. The frontal basement fault is influenced by the salt pinch-out and overthrusts the post-rift strata, whereas the other two faults undergo a transition to a ramp–flat–ramp configuration. In the post-rift sediments, new shear zones are formed along the continuation of the pre-existing faults. These faults have been displaced due to the presence of basal salt, leading to deviation from their original dip. Strain rates indicate that the continuity of the salt décollement is disrupted due to the offset introduced by the inherited faults (Fig. f). The largest viscosities of salt are found in the anticlines with long wavelengths that form in the areas between two pre-existing faults (Fig. f). In contrast, lower viscosities are observed in areas where the strain rate reaches its maximum, specifically at the tip of the basement faults where the salt layer is thin.

Figure  shows the effect of the thickness of the salt layer on the deformation. In the absence of a salt layer (Model 2; Fig. a), no mechanical decoupling occurs between the sedimentary cover and the basement. The extension phase is dominated by the pre-existing faults and their geometry, and the majority of the deformation accumulates along the pre-existing normal faults. After convergence for 15 Myr, long-wavelength and basement-cored anticlines develop in the sedimentary cover. The anticlines form asymmetrically and with a low internal deformation of the sedimentary sequence (Figs. b and S2). The folding style within the sedimentary cover is determined by the pre-existing faults, resulting in the development of thrust faults that propagate upward through the overlying rocks. Basement faults cut the sedimentary cover and reach the surface without any significant deviation from their initial orientation. Furthermore, backthrusts form in the hanging wall as conjugates to the reactivated inherited faults. Strain-rate patterns reveal that the entire crustal package deforms uniformly, without mechanical decoupling along the different lithological layers.

Increasing the salt layer thickness to 4 km (Model 3) does not significantly affect the structural development during the extension phase compared to the reference model (Figs. c and c). However, a thicker salt layer hinders the extensional faults from fully cross-cutting the salt after a full extension (Figs. c and S3). During shortening, a thicker salt layer acts as a more efficient décollement, impeding small-scale deformation in the sedimentary cover relative to the reference model (Fig. d; compare to Fig. f). The sedimentary cover develops décollement folds cored by a thickened salt. The cover is pushed over the frontal basement fault on the left, which, upon reactivation, results in a salt-cored fault-propagation fold at x ≈ 210 km. Furthermore, the increased amount of salt allows for vertical breakthroughs and diapir formation.

To investigate the impact of the rheology of the salt on the style of deformation, we considered two models with linear viscosity for the salt layer and compared the results with that of the reference model. For Models 4 and 5, we chose linear viscosities of 10¹⁸ and 10²⁰ Pas, respectively, which are roughly equal to the lowest and largest viscosities observed in the reference model (Fig. c and f). After an extension for 5 Myr, the low-viscosity Model 4 leads to the formation of symmetric ridges along the half-grabens and footwalls (Figs. a and S4). The majority of the deformation is accommodated by the salt layer and the inherited faults. After compression for 15 Myr, the pattern of folds within the sedimentary cover diverges from that of the reference model, as it displays an inclination towards the hinterland (Figs. b and S4). Based on the strain rates, deformation is accommodated across the décollements.

In Model 5, with higher salt viscosity, the structural pattern after an extension for 5 Myr resembles that of the reference model (Figs. c and c). Strain rates reveal significant deformation occurring within the basement, localizing along the pre-existing weak zones. After shortening for 15 Myr, the style of folding shows significant differences from Model 4 (Figs. b, d and S5 in the Supplement). Several forethrusts develop above the imbricated basement blocks and backthrusts are generally absent. Strain rates indicate that the décollement remains laterally connected across the different basement blocks, whereas it is interrupted in the model with low linear viscosity (compare Fig. b and d).

Figure  presents the vertically averaged strain rate within the salt layer across models with different décollement rheology. The influence of a power law rheology on strain rate is characterized by a non-linear, accelerating response to stress. As stress levels increase, the strain rate increases more rapidly compared to a linear rheology, where the strain rate maintains a constant, linear relationship with stress. The mean strain rate in a salt layer with a power law rheology exceeds that in a salt layer with linear rheology, as illustrated.

Figure  shows two models, namely one with planar basement faults (Model 6) and one without prescribed basement faults (Model 7). After an extension for 5 Myr, the basement faults maintain a constant dip angle, resulting in the formation of conjugate normal faults rooting in the lower extent of the pre-existing faults (Figs. a and S6). Similar to the case with listric faults (Fig. c), the second invariant of the strain-rate tensor indicates high concentration of deformation through the development of fractures within the sedimentary layers above the salt horizon, specifically at the back of the footwall of the faults (Figs. a and S6). After compression for 15 Myr, multiple overturned forward- and backward-verging folds develop within the sedimentary cover at x ≈ 350 km (Figs. b and S6). These folds originate in relation to the activation of thrusts in the underlying basement. Notably, the planar faults play a pivotal role in the formation of backthrust faults. The principal strain rate is concentrated within vulnerable zones such as the salt layer, planar faults, and the newly formed backthrust faults within the basement (Figs. b and S6). Basement faults cross-cut the salt décollement to form bypass thrusts.

In the absence of inherited faults (Figs. c and S7), no zone of significant strain accumulation is formed during the extension phase. The maximum strain rate accumulates primarily along the fractures caused by the extension, while the basement is decoupled from the overlying sedimentary strata. After a shortening for 15 Myr, the basement has undergone an intense deformation by thrusting (Figs. d and S7). Near the backstop wall (x = 350–500 km), it is deformed into pop-up structures caused by conjugate thrusts, while forward-verging thrusts dominate towards the foreland. The overlaying sedimentary sequence is mainly shortened by décollement folding/faulting between x = 200–350 km. A large pop-up structure (x ≈ 230 km) without mechanical decoupling between the basement and the sedimentary cover develops in front of the salt pinch-out (Figs. d and S7). The strain rates indicate that at the late stage of shortening, a thin-skinned style of deformation is taking place in front of the salt pinch-out and the associated basement thrust.

The effect of basement involvement during convergence is implemented by varying the horizontal velocity of basement rocks exiting the right-side boundary, vx_b (Fig. b). All of the previous models exhibit a rigid backstop over the entire right side that prevented the basement material from leaving the model domain (vx_b = 0), resulting in 100 % involvement of the basement in the deformation. In this section, we show a set of models in which the basement is allowed to exit the model domain with a velocity that is a varying fraction of that on the left boundary (Fig. ). The basement will experience a slower rate of shortening with respect to the cover. As a result, the degree of thin-skinned deformation will increase.

With a basement involvement of 75 % (vx_b = 0.25 ⋅ vx), the two faults located on the right side of the model transform into flat–ramp–flat structures (Model 8; Figs. a and S8). Above the basement blocks, the sedimentary cover undergoes thrusting, and the cover sequence overthrusts the frontal fault zone by ∼ 50 km. If the basement shortening rate is 50 % of the cover shortening rate (vx_b = 0.5 ⋅ vx), the faults situated on the right side of the model remain continuous and undergo significant displacement (Model 9; Figs. b and S9). After a convergence for 15 Myr, the fault on the right side partly exits the model domain. Additionally, strain rate indicates that most deformation localizes within the salt layer, the pre-existing basement faults, and faults within the sedimentary cover. With a basement involvement of 25 % (vx_b = 0.75 ⋅ vx), the fault on the right side almost entirely left the model domain, and the other two faults experience lesser degrees of involvement, roughly displaying 100 % of tectonic inversion (Model 10; Figs. c and S10). In comparison to the previous cases, deformation in the sedimentary cover is more distributed laterally and does not depend as strongly on the location of basement faults. Furthermore, the salt layer remains connected and forms a nearly horizontal décollement horizon (Fig. c). In the case where the basement exits the model domain with the same velocity as the bottom boundary (vx_b = vx), inherited basement faults are not reactivated, and the sedimentary cover deforms in a thin-skinned tectonic style (Model 11; Figs. d and S11). The second invariant of the strain-rate tensor demonstrates that the salt horizon acts as a décollement layer with basement steps that developed during the rifting phase. The resulting thin-skinned fold-and-thrust belt exhibits a flat surface taper, given the weak salt rheology (Fig. d).

The mechanical strength of fold-and-thrust belts and the partitioning of strain during their growth has been a topic of interest for many decades (Chapple, 1978; Davis et al., 1983; Stockmal et al., 2007; Tavani et al., 2015). During continental collision and the emergence of mountain belts, plate convergence rates usually decrease stepwise, given the increasing strength of the affected plate boundary (Wortel et al., 2009). Weak zones within the deformed rock layers play a crucial role in shaping the structural evolution of fold-and-thrust belts. In the case of the Zagros, numerical experiments demonstrate that the sub-horizontal salt horizon and inherited weak basement faults significantly influence the partitioning of strain. Regardless of whether the viscous décollement can fully decouple the upper and lower crust mechanically, the basement exerts a strong influence on the overall structural evolution of the Zagros fold-and-thrust belt. This must be considered when constructing structural cross sections.

All experiments with prescribed weak zones within the basement show intense inversion along these inherited structures (e.g., Fig. ). A particular experiment is Model 7, where no basement faults were prescribed (Fig. c and d). The structural style observed in Model 7 is driven by the low rheological strength of the salt layer, which decouples basement shortening from the overlying layers, resulting in thin-skinned deformation of the cover sequence (Fig. d). This weak salt layer promotes the formation of fault-propagation folds and conjugate thrusts (pop-ups), rather than a clear structural vergence, as observed by a large pop-up structure at x ≈ 230 km. The topography of the top of basement is likely caused by a critical wedge geometry defined by the viscous strength of the lowermost modeled crust.

In fold-and-thrust belts with local weak zones in the form of décollement layers and reactivated inherited faults, strength may vary across-strike. For example, the reference model (Model 1) displays a stress distribution with maximum values in the brittle part of the basement, which is cross-cut by hinterland-dipping faults (Fig. a). To illustrate across-strike variations in strength, three vertical stress profiles are shown representing different segments of the evolving fold-and-thrust belt. (i) At x = 150 km, basement faults and a salt décollement are absent, and the strength profile exhibits a simple form with a brittle (y ≈ 15–40 km) and ductile (y ≈ 40–60 km) part (Fig. b). (ii) The second profile at x = 320 km cross-cuts both salt décollement (y ≈ 18 km) and a basement fault (y ≈ 40 km) that strongly affect the strength profile (Fig. c). While the salt horizon shows very low stresses of only a few megapascals, stresses across the basement fault are reduced to ∼ 150 MPa, in contrast to maximum stresses of ∼ 600 MPa around the brittle–ductile transition. (iii) Close to the backstop at x = 460 km, maximal stresses increase to ∼ 800 MPa at y ≈ 40 km (Fig. d). At y ≈ 18 km, the salt décollement displays an effective decoupling horizon, and an additional weak zone at y ≈ 27 km is defined by flat ramp of a basement sliver stack. To infer the force acting across the fold-and-thrust belt related to the reference model, the differential stress profiles at each x coordinate are integrated over the vertical distance. For the reference model after a convergence for 15 Myr, values range between ∼ 7–15 TNm-1, where the lowest values coincide with the occurrence of basement faults (Fig. c). In general, there is no clear trend observable that would refer to a weakening or strengthening related to deformation, as crustal thickening (strengthening) goes hand in hand with basement thrusting (weakening).

Figure  shows the temporal evolution of the average force (e.g., the average value of Fig. e for the reference model) for a variety of models to identify key parameters that affect the stress state of continental collision zones. All models show similar boundary forces during the extension phase of ∼ 4 TNm-1 (Fig. ), except for Model 7 without pre-existing basement faults, which exhibits values of ∼ 4.2 TNm-1 (Fig. b). Similar force values during the extension for models with planar and listric inherited basement faults indicate that none of the tested fault geometries would preferably localize. During the convergence phase, boundary forces quickly increase, and most of the models show a general increasing trend from ∼ 6–8 TNm-1 to ∼ 10–12 TNm-1 over a 15 Myr time span (Fig. ). A minor increase and decrease in force are observed related to the absence (Model 2) and increased thickness of the salt horizon (Model 3), respectively, while the strength (viscosity) of the salt has no detectable effect (Fig. a). The absence and geometry of basement faults display a significant importance during convergence, in contrast to the extension phase, where planar preexisting faults increase the necessary boundary force by ∼ 1–2 TNm-1, and no faults lead to another increase of ∼ 1–2 TNm-1 during the first 10 Myr of convergence (Fig. b). More important is the effect of basement involvement in crustal shortening, with decreasing involvement resulting in decreasing boundary force (Fig. c). This illustrates the importance of an effective décollement level that is able to decouple an upper crust with distributed deformation from a basement that is underthrust towards the suture, where it deforms more intensely (Tavani et al., 2015; Pfiffner et al., 2002). A similar pattern of boundary force evolution was also observed from analogue models, however, with more acute variations for specific internal deformation of the compressed sand pile (McBeck et al., 2018).

The mechanics of fold-and-thrust belts has been investigated by means of numerical methods since the 1980s (e.g., Borja and Dreiss, 1989). Rapidly evolving computing capabilities led to a vast increase in geodynamic numerical modeling studies that provide an invaluable contribution towards our understanding of geotectonic systems (e.g., van Zelst et al., 2022; Gerya, 2022; Ismail-Zadeh and Tackley, 2010). Previous numerical models of fold-and-thrust belts have typically focused on thin-skinned tectonic systems, investigating parameters such as wedge and décollement strength, rheology, surface processes, and mechanical stratigraphy (e.g., Stockmal et al., 2007; Buiter et al., 2016; Simpson, 2011; Burbidge and Braun, 2002; Ruh et al., 2012). However, the inclusion of rifting prior to collision adds a new dimension that has often been overlooked in these studies. This approach allows for a more comprehensive understanding of tectonic evolution by examining how pre-collisional structural configurations influence later deformation patterns. Including rifting before convergence is crucial, as it sets the initial conditions that significantly impact structural evolution during collision (Buiter and Pfiffner, 2003; Ruh and Vergés, 2018; Granado and Ruh, 2019). This approach offers several advantages. It provides insight into structural inheritance, as rifting creates pre-existing weaknesses and fault systems that play a crucial role during subsequent compressional phases. Our model demonstrates how these inherited structures influence strain localization and deformation styles, providing insights into the evolution of complex geological features such as the Fars Arc. In the following, we discuss several numerical studies concerning tectonic systems that are similar to the one presented in this study to set our results into perspective and to identify generally applicable observations. We, furthermore, comment on the importance of implementing an extensional phase into the model setup.

Buiter and Pfiffner (2003) applied a two-dimensional, viscoplastic numerical model in order to evaluate the dynamics of tectonic inversion of a series of half-graben basins upon compression. They reported syn- and post-rift sediment uplift, accompanied by basement block rotation, and the emergence of newly formed shear zones in the post-rift sequence, originating from basin-bounding faults. Weak sediments at the basin base contribute to the generation of basement shortcut faults. Furthermore, their study illustrates the predominant development of back thrusts as conjugates to listric basin-bounding faults. The structural evolution observed in our models aligns with their research findings, demonstrating a similar pattern of strain localization within syn-rift and post-rift layers, mainly initiated by deformation along pre-existing underlying faults. Additionally, compared to their findings, our results indicate that the formation of back thrusts is mainly associated with the inversion of planar faults (Fig. ; Model 6).

Nilforoushan et al. (2013) presented two-dimensional thermomechanical experiments of thick-skinned fold-and-thrust belts with salt décollements. They demonstrated that the geothermal gradient and the mineralogy of the basement (ductile flow law) strongly affect the geometry and reactivation of inherited basement faults. Furthermore, they underlined the importance of a weak salt horizon at the base of the sedimentary succession for the mechanical decoupling and formation of a thin-skinned upper-crustal fold-and-thrust belt, resulting in the variability in the rate of shortening between the cover and the basement. Their findings corroborate the hypothesis of Molinaro et al. (2005) that in the ZSFB, greater shortening occurs within the cover compared to the basement. From our results examining the effects of the shortening rate of the basement on structural development, we observed the emergence of long-wavelength folds arising directly from the movements of faults within the basement (Fig. a–d). These findings align with natural occurrences and are corroborated by geological cross-sectional data, reinforcing the principal characteristics of the Fars Arc that are typified by folds of extensive wavelengths. This agrees with the suggestions by Mouthereau et al. (2006), who proposed that the early activation of basement deformation dictates the formation of the large-wavelength folds. Furthermore, Mouthereau et al. (2006) determined that the viscosity of Hormuz salt decreases significantly with increasing temperature, exhibiting Newtonian fluid behavior under low-stress and low-strain-rate conditions. In our results, the average viscosity of non-Newtonian salt is affected by both temperature and strain rate, where weak zones with the lowest strain rates and temperatures exhibit the largest viscosity values. The resulting values are larger than what was proposed for the Fars Arc resulting from critical wedge modeling (Mouthereau et al., 2006).

Ghazian and Buiter (2014) investigated the impact of salt for the southeast ZFTB by 2D thermomechanical models. Their findings revealed that the presence of a thick basal Hormuz salt effectively decouples overlying sediments from the basement and promotes the localization of deformation in the sediments. Our results align with these findings, demonstrating a significant influence of the salt layer on controlling topographic height and folding patterns (Figs.  and ). The deformation style in the basement and the cover sequence decouples along the weak salt horizon. As the salt thickness increases, this layer functions more effectively as a décollement, impeding deformation in the sedimentary cover sequence (Fig. ).

Bauville and Schmalholz (2015, 2017) and Kiss et al. (2020) conducted 2D numerical experiments to investigate the transition from basement-involved thin-skinned to thick-skinned tectonics and the effects of tectonic inheritance on the development of nappe systems. The key parameters controlling this transition were found to be the viscosity ratios within the basement and between the basement and the sedimentary cover above it. Specifically, a higher ratio within the basement favors a thick-skinned deformation, while a higher ratio between the basement and cover leads to a thin-skinned deformation. As indicated by our study, 100 % participation of the basement in the deformation leads to thick-skinned deformation (Fig. ), while non-participation of the basement leads to thin-skinned deformation (Fig. ; Model 11). Their findings show that the tectonic and structural inheritance play a significant role in controlling the tectonic evolution and resulting structures in the fold-and-thrust belts. The geometry and magnitude of mechanical heterogeneities, like the varying basement–cover interface characterized by half-grabens and horsts, as well as the vertical alternation of sedimentary layers with different mechanical strengths, influence nappe formation. Their observations align with our findings that the presence of pre-rift salt and inherited faults, which serve as structural inheritances, influence the shape and geometry of the basin (Figs. , , and ). Moreover, their simulations and ours revealed that linear and power law viscous rheologies demonstrated similar features to those of more complex simulations, indicating the robustness of these findings (Fig. ; Model 4 and 5).

Eslamrezaei et al. (2023) used numerical discrete element models to investigate the impact of mechanical stratigraphy, décollement layers, and the number and thickness of cover sequences on the structural evolution and strain partitioning of thin-skinned fold-and-thrust belts. Their modeling outcomes revealed that weak décollements played a crucial role in decoupled deformation within the fold-and-thrust belt under continuous shortening. The study underscored that shortening was primarily accommodated by thrust-related folds, resulting in notable variations in structural styles. In alignment with our findings (Figs. , and ), the weak décollement layer, due to its characteristics, exhibited an inability to retain stress and undergo deformation, as evidenced by the increasing strain rate along the basal detachment (Fig. ). Their study's conclusions and our results emphasized that the structural style and decoupling in thin-skinned fold-and-thrust belts and the formation of structures, such as box folds and harpoon structures, are influenced by factors such as rheology, the number, and thickness of décollements (Figs.  and ).

An essential characteristic of the numerical experiments presented here is the implementation of a rifting phase prevailing crustal shortening. Earlier numerical studies on tectonic inversion demonstrated that strain-related weakening of the crustal basement during an extensional tectonic phase has an important effect on the localization of deformation during consequent convergence (Ruh and Vergés, 2018). Furthermore, the mechanical strength of sedimentary deposits filling rift-related basins has been shown to influence the structural evolution during tectonic inversion, where weak syn-rift deposits favor the development of hanging wall bypass structures (Granado and Ruh, 2019). In contrast, various studies mimic the extensional phase by prescribing inherited structures and geometric configurations comparable to rifted margins instead of conducting an extensional phase when investigating the tectonic inversion of fold-and-thrust belts (e.g., Buiter and Pfiffner, 2003; Nilforoushan et al., 2013; Bauville and Schmalholz, 2015; Kiss et al., 2020). However, the implementation of an extension phase allows for a dynamic formation of basement steps and graben geometry, based on the thermomechanical model characteristics such as the visco–plastic/brittle transition and the evolution of the salt decoupling along the basement top (Fig. a–c and a, b). Model 7 demonstrates that a certain type of strain localization is needed to form narrow shear bands similar to basement faults during extension (Fig. c). While other studies impose specific boundary conditions (Ruh and Vergés, 2018) or thermal variations (Ruh and Vergés, 2018), we introduced predefined geometries to localize extensional normal faults, controlling the position of basement deformation (Fig. b).

The tectonic style of the Fars Arc is characterized by a combination of thin-skinned salt-related folding and thick-skinned basement thrusting (i.e., Mouthereau et al., 2007a). The structure of the sedimentary cover is shaped by a series of detachment faults and fault-propagation folds involving several salt diapirs rooted in the Hormuz salt (e.g., Jahani et al., 2007; Motamedi and Gharabeigli, 2019; Vergés et al., 2024). In addition, at least three high-angle reverse basement faults (High Zagros, Surmeh, and Mountain Front faults) are constrained based on their seismicity, structural relief, magnetic anomalies, and abrupt topographic changes (e.g., Jackson and Fitch, 1981; Berberian, 1995; Talebian and Jackson, 2004; Mouthereau et al., 2007b; Teknik and Ghods, 2017; Karasözen et al., 2019). The dynamic importance of these faults is supported by our results, as numerical models without basement faults (Model 7 in Fig. ) display a marked difference in the structural style compared to geological observations in the Fars Arc. In the absence of basement faults in the models, deformation is concentrated only in the outer part of the arc in the form of an imbricate thrust system and a large mushroom anticline near the salt pinch-out. Furthermore, the importance of the Hormuz salt for the distinct structural style of the Fars Arc is corroborated by the numerical model without a basal salt layer (Model 2 in Fig. a and b). In that model, there are four basement-involved anticlines form across the entire belt, each with wavelengths of about 100 km, while in contrast, in the Fars Arc, the anticlines can be grouped into short-wavelength detachment anticlines and long-wavelength basement-involved anticlines (e.g., Mouthereau et al., 2006). In the model without salt, all structures verge towards the front without any back-thrusting. This type of fold and fault geometry is not representative of the observed structures in the Fars Arc (e.g., Motamedi et al., 2012; Najafi et al., 2014; Jahani et al., 2017). Observational evidence thus highlights the essential roles that the basement and the salt layer play in determining the deformation style of the belt.

The results of the experiment with a 4 km thick basal salt layer (Model 3; Fig. c and d) demonstrate that a thicker salt layer interacts with the basement faults to form symmetrical anticlines containing salt cores and discordant diapirs. The topography of the Fars Arc cannot be solely attributed to the presence of a salt layer; the basement's role in structural development is also significant. As our results indicate, processes involving the basement should be considered an essential factor in reconstructing and assessing the geological development of the region. The models demonstrate that the basement faults ramp up through the upper part of the basement and eventually flatten along the Hormuz salt level at a depth of around 10 km (Model 1 in Fig. f). Similar structures of basement faults detaching along evaporitic levels in the middle of the sedimentary cover, or reaching the surface to cut the forelimbs of their hanging wall anticlines, are documented in the Fars Arc (Vergeìs et al., 2024), such as the Kangan, Asaluyeh, and Tabnak anticlines, located to the south of the cross section in the foreland vicinity and within the Mountain Front Fault (Berberian, 1995; Mouthereau et al., 2007b; Fig. b and c). These anticlines are characterized by a pronounced concentric surface geometry (Fig. a).

A well-studied example of syn-tectonic growth strata is the Dowlatabad syncline, located approximately 40 km northeast of the Persian Gulf coastline (Fig. a and b) and limited by the Sefid anticline to the north and the NW segment of the Pazan anticline to the south (Najafi et al., 2021). The Dowlatabad syncline is infilled by more than 2 km of syn-folding sediments. Numerical results from Model 3, which has a thick salt layer, compare well with the formation of the Dowlatabad syncline (Fig. a and b). (i) The forelimbs of the Pazan and Sefid anticlines were faulted by foreland-directed thrusts rising from the basal décollement; (ii) surface processes resulted in a smooth topography; and (iii) the surface has an asymmetric shape, while, at depth, the structure has the form of a box fold.

In the Zagros belt, there is a noted relationship between faulting patterns and the distribution of salt diapirs (Talbot and Alavi, 1996; Hessami et al., 2001; Bahroudi and Koyi, 2003; Sherkati and Letouzey, 2004; Sepehr and Cosgrove, 2004; Jahani et al., 2017). Our numerical results indicate that salt diapirism may be triggered at two distinct stages in the case of a thick (4 km) salt décollement. During the rifting phase, small-scale diapirs start to grow above the tip of normal faults, partially piercing the sedimentary cover (Model 3; Fig. c). This procedure can be considered a short-lasting and locally developed reactive diapirism stage (e.g., Jackson and Vendeville, 1994; Jackson and Hudec, 2017). More significantly, the growth of two salt diapirs is observed during the compression phase in the inner zone of the fold-and-thrust belt (Model 3 in Fig. d). In contrast to décollement folds, these salt bodies have pierced the overburden strata and show discordant contact with overlying sediments. The process involves the buoyant rise in underground salt when subjected to pressure from convergent tectonic forces. These early-growing diapirs, squeezed by further shortening, lead to the development of secondary salt welds. This type of shortened diapir has recently been documented in the High Zagros zone in a field-based study by Taghikhani et al. (2024) and has been already known in the SE Fars Arc (e.g., Callot et al., 2007; Jahani et al., 2007) and the Persian Gulf (e.g., Hassanpour et al., 2021, 2021; Snidero et al., 2020) through seismic interpretations. A well-exposed example of such a structure is the Hajiabad diapir, located in the inner part of the Fars Arc, where an 8 km long squeezed Hormuz salt diapir trends NW and dips towards NE (Fig. d). The salt-bearing evaporites have been shortened between the two flanks of the precursor salt wall, forming a secondary salt weld. Another well-exposed example in the inner Fars is the Kharman diapir (Fig. e), which is in good correlation with observations from Model 3. With numerical modeling, Fernandez and Kaus (2014) showed that pre-existing salt diapirs can significantly influence the pattern and growth of three-dimensional folds and fold patterns, accelerating fold formation and localizing deformation and highlighting the important role of diapirism in structural evolution during tectonic processes.

Figure a displays a seismicity map of the Zagros in the region of our profile. It shows events with magnitudes greater than ML = 4, between 2000 and 2023 from the International Seismological Centre (ISC) global database (http://www.ics.ac.uk, last access: 1 January 2023). We have excluded those events of the database with pre-fixed depths (usually set at 10 or 15 km) from the plot. Furthermore, a catalogue of small-magnitude earthquakes from Tatar et al. (2004) recorded by a local temporary network over a period of 7 weeks is plotted. A local network with close station spacing allows for more precise location of earthquakes, and Tatar et al. (2004) state that these events have horizontal and vertical uncertainties below 2 km. The earthquakes are also plotted onto the geological cross section of Fig. c and the compositional image of the final stage (15 Myr) of Model 1 (Fig. b and c). Several studies have asserted that the depths and focal mechanism solutions indicate that high-angle reverse faults in the basement are responsible for major earthquakes in the SE Zagros (e.g., Jackson and Fitch, 1981; Berberian, 1995; Talebian and Jackson, 2004). Others have argued that most of the strongest earthquakes in the ZSFB probably lie in the lower sedimentary cover, but their aftershock activity mostly occurs deeper in the basement (e.g., Nissen et al., 2011, 2014). A more recent work by Karasözen et al. (2019) used a calibrated earthquake relocation to show that the Zagros earthquakes nucleate in both the cover and the basement. According to our numerical results, the activation of basement structures localizes topographic features and affects thrust faults within the overlying sedimentary cover (Figs. f, b, and ). Notable examples of active basement faults in the Fars Arc include the Surmeh Fault and the Mountain Front Fault, which have distinct structural and topographic characteristics (Jackson,1980; Jackson and McKenzie, 1984; Berberian, 1995; Mouthereau et al., 2007b). Critical wedge modeling confirms that basement-involved shortening is the primary factor influencing deformation and topography in the Fars Arc (Figs. f and b; Mouthereau et al., 2006). Balanced cross sections provide additional evidence of the basement's involvement in shortening through major thrusts rooted in a deep décollement level within the lower crust (Molinaro et al., 2005; Mouthereau et al., 2007b; Najafi et al.; 2014; Najafi et al.; 2021).

The majority of earthquakes are concentrated within the sedimentary cover, aligning with the décollement faults (Fig. b and c). This observation supports the theory of the sedimentary cover decoupling from the basement, influenced by the presence of the basal salt layer. The depth trend of earthquakes in the basement exhibits a notable correlation with the High Zagros Fault and the Surmeh Fault, which confirms the existence of pre-existing weak zones within the basement at these locations. Furthermore, the depth distribution of the earthquakes supports the idea of a listric geometry for the basement faults. By examining the deformation within the basement and the earthquake depths, we estimate the transition zone from brittle to ductile behavior at around 30 km. While this depth is influenced by multiple factors, including material parameters, temperature, and strain rate (stress), our approximation is based on typical conditions relevant to the region. This suggests that diabase rheology, combined with the applied geotherm, is appropriate for modeling the basement under these specific conditions. Mouthereau et al. (2006), on the other hand, concluded that diabase might be too weak to reproduce the observed topography in the Fars Arc. However, they apply a crustal thickness of 45 km, which implies increased temperature conditions and thus a weaker diabase detachment.

Our modeling results indicate that reverse faults cutting both flanks of décollement anticlines are likely responsible for the shallower earthquakes (Fig. c). This phenomenon was studied in the Shanul anticline, southeast of our study region, where earthquakes with reverse mechanisms occur on both flanks of the anticline at depths mostly ≤ 4 km (Jamalreyhani et al., 2021). However, basement faults are the source of deeper and larger earthquakes across the Zagros fold belt, generally concentrated in NE-dipping linear trends (e.g., Nissen et al., 2019; Fig. ).

Lacombe and Mouthereau (2002) discussed the relative chronology between mid-crustal décollement thrusting and shallow décollement folding of sedimentary cover in various orogenic belts, such as Taiwan, the Pyrenees, and the Alps. This relationship has been further investigated through analogue and numerical modeling in the Jura, Appalachians, Kopet Dagh, and Zagros fold-and-thrust belts (e.g., Pohn, 2000; Orjuela et al., 2021; Ruh and Vergés, 2018; as presented in this study). A comprehensive analysis of these studies, in alignment with our results, suggests that there is no definitive sequence for thin- and thick-skinned tectonics in all orogenic belts. This sequence appears to be controlled, at least in part, by the rheology and temperature of basement rocks, the thickness of evaporitic layers in the sedimentary cover, the dip and flatness of inherited basement faults, as well as their orientation in relation to the tectonic transport direction.