The topographic signature of temperature controlled rheological transitions in an accretionary prism

. The local topographic slope of the accretionary prism is often used together with the critical taper theory to determine the effective friction on subduction megathrust. In this context, extremely small topographic slopes associated with extremely low effective basal friction ( µ ≤ 0 . 05 ) can be interpreted either as seismically locked portions of megathrust, which deforms episodically at dynamic slip rates or as a viscously creeping décollement. Existing mechanical models of the long-term evolution of accretionary prism, sandbox models, and numerical simulations alike, generally do not account for heat conservation 5 nor for temperature dependent rheological transitions. Here, we solve for advection-diffusion of heat with imposed constant heat flow at the base of the model domain. This allows the temperature to increase with burial, and therefore to capture how the brittle-ductile transition and dehydration reactions within the décollement affect the dynamic of the accretionary prism and its topography. We investigate the effect of basal heat flow, shear heating, thermal blanketing by sediments, the thickness of the incoming sediments. We find that while reduction of the friction during dewatering reactions result as expected in a 10 flat segment often in the fore-arc, the brittle-ductile transition result unexpectedly in a local increase of topographic slope by decreasing internal friction. We show that this counter-intuitive backproduct of the numerical simulation can be explained by the onset of internal ductile deformation in between the active thrusts. Our models, therefore, imply significant viscous deformation of sediments above a brittle décollement, at geological rates, and we discuss its consequences in term of interpretation of coupling ratios at subduction megathrust. We also find that, with increasing burial and ductile deformation, the internal

the influence of many parameters such as the geometry (Dahlen et al., 1984;Davis et al., 1983;Koyi and Vendeville, 2003;Mandal et al., 1997;Smit et al., 2003;Ruh et al., 2016), basal friction (Colletta et al., 1991;Lallemand et al., 1994;Mulugeta, 60 1988; Nieuwland et al., 2000;Burbidge and Braun, 2002;Ruh et al., 2012;Cubas et al., 2008), surface processes e.g., (Storti and McClay, 1995;Mary et al., 2013;Willett, 1999;Leturmy et al., 2000;Konstantinovskaya and Malavieille, 2005;Bonnet et al., 2007;Fillon et al., 2013;Mary et al., 2013;Stockmal et al., 2007;Hoth et al., 2006;Simpson, 2006), or the presence of viscous material along the décollement (Gutscher et al., 2001;Costa and Vendeville, 2002;Smit et al., 2003;Couzens-Schultz et al., 2003;Bonini, 2007;Pichot and Nalpas, 2009;Simpson et al., 2010;Ruh et al., 2012;Yamato et al., 2011;Borderie 65 et al., 2018). Despite the large amount of published studies, none of them included the dependence of effective basal friction on temperature due to metamorphic reaction or brittle-ductile transition. year −1 , the top boundary behaves as a free surface above sea level while the weight of the water column is prescribed as stress normal to the deformed boundary below sea level. Temperature is fixed at the surface, the thermal gradient is prescribed across all other boundaries with the value of zero on vertical ones and value of ∇T b at the bottom boundary. The mesh consists of 512 × ny Q2P1 elements which deform to adapt to the deforming top boundary. Parameters are defined in Table 1. Here, we study how the introduction temperature evolution and its feedback on rock rheology generates deviations from CTT.
For that purpose, we use a typical CTT set up ( Figure 1) and we solve for the heat equation on the same domain with a constant heat flow boundary condition at the base, which corresponds to plate age, to allow the temperature to increase with burial. As 70 this contribution focuses on the thermal effect, we also include shear heating and thermal blanketing of sediments. We present different series of 2D thermo-mechanical simulations which assess how the brittle-ductile and the smectite-illite transitions affect the topographic slope of an accretionary prism and its internal deformation. We briefly discuss internal deformation the morphology of the wedge and its potential seismic behavior. We, therefore, retrieve the spatial and temporal variation of the morphologies and deformation patterns and discuss their implications in terms of the fore-arc basin and fore-arc high genesis 75 and nature.
2 Modelling Approach

Method
In order to model the long-term behavior of the accretionary prism, we use pTatin2d (May et al., 2014(May et al., , 2015, a code based on finite element method that employs an arbitrary Lagrangian-Eulerian (ALE) discretization together with the material point 80 method to solve the conservation of momentum (Eq. 1), mass (Eq. 2) and energy (Eq. 3) for an incompressible fluid. It allows solving thermo-mechanical problems. It has been widely used to model lithospheric scale long-term tectonic problems coupled to surface processes (Jourdon et al., 2018;Perron et al., 2021) and benchmarked with sandbox experiments (Buiter et al., 2016).
The code solves for velocity v and pressure P assuming conservation of momentum: 85 in an incompressible fluid assuming of nonlinear effective viscosity η and constant density ρ.ε is the strain rate tensor and g the gravity acceleration. Evolution of temperature T is obtained by solving the time ,t, dependent conservation of heat, (3)

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The coefficients of eq.3 are κ the thermal diffusivity, Cp the heat capacity, and H the heat production. We do not include radiogenic heat production in our simulation and H = 2η ε 2 xx + 2ε 2 xy + ε 2 yy (4) corresponds to the sole shear heating.
The Stokes problem eqs. 1 and 2 is solved using high order stable elements (Q 2 -P 1 ), while the heat equation eq.3 is dis-95 cretized on Q 1 elements. Physical properties of rocks are computed on Lagrangian markers and projected to gauss points using constant value per element. Averaging of marker-defined coefficients within element is geometric for viscosity and algebraic for other properties. At every time step, the surface of the models, h, is smoothed according to the Culling diffusive erosion law, with a diffusion coefficient k. Details on implementation of the surface process model in pTatin2d are to be found in (Jourdon et al., 2018).

Rheological model
We use temperature and pressure-dependent nonlinear rheologies. Effective viscosity is evaluated on material points using first the Arrhenius flow law for dislocation creep, written in term of the second invariant of the strain rate tensorε II . The activation volume is set to V = 8 × 10 −6 m 3 .mol −1 for all the lithologies, the other constants A, n, Q are listed for each lithology in Table 1. If the prediction of the second invariant of stress for a viscous rheology 110 exceeds the Drucker-Prager frictional plastic yield criterion, which depends on ϕ the internal friction angle and C the cohesion, the effective viscosity of the marker is corrected in order to return to the yield envelop with 115 Finally, the friction angle ϕ and cohesion C decrease linearly with accumulation of strain in the plastic regime ε p from an initial friction ϕ 0 to a final friction ϕ ∞ (resp. C 0 and C ∞ for cohesion): over a range of accumulated plastic strain varying from ε min = 0 to ε max = 0.5. This drop of friction and cohesion does not apply to the décollement. Frictional parameters are listed together with viscous parameters, density, and thermal diffusivity 120 in Table 1. As all stokes solvers, pTatin2d also applies cut-off values on effective viscosity in order to maintain a reasonably well-conditioned system of equations. These are set to a minimum value η min = 10 16 Pa.s and a maximum value η max = 10 25 Pa.s. We made sure that the minimum is never reached to ensure that the frictional properties of the décollement reflect its extremely low friction.

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The model domain is 500 km long and its initial thickness is either 4 or 7.5 km (Figure 1). It is constituted of 2 layers, a 500 m thick décollement modeled by shales, while the rest is modeled by sandstones/quartz. The domain is discretized with a mesh of 512×16 and 512×24 Q2 elements, respectively. In the y-direction, two mesh elements are aligned with the initial décollement layer to better capture its interface and friction at small strain. The décollement material is considered as part of the domain, as such, we allow shales to be dragged in the rest of the model domain contrarily to frictional boundary conditions adopted  (Ranalli and Murphy, 1987) and b from (Shea and Kronenberg, 1992). * In models M13 to M15 the friction in the Shale is temperature dependent.
to benchmark the code with sandbox experiments (Buiter et al., 2016). The shortening of the model is driven by a constant horizontal velocity v x = 4cm/yr applied both at the right and bottom boundaries. Above the décollement level, the left side of the domain is rigid. Within the 2 mesh elements of the left boundary which belongs to the décollement, a vertical velocity gradient is applied to ensure the continuity with the bottom boundary. The surface of the domain is modeled with a free surface above sea level (located 3 km above the top of the mechanical model, Figure 1), below sea level additional normal stress: is applied on the deformed surface to mimic the weight of water, yet shear stress is zero like above sea level.
The thermal boundary conditions assign the temperature T 0 = 0 o C at the surface, a constant thermal gradient ∇T b = ∂T ∂y y=y b at the base and no horizontal gradient/(insulating boundary) on the vertical walls of the domain. As we assume no radiogenic heat production, the initial temperature in the domain is fixed to: consistently with the boundary conditions.

Post-processing
Models are named by a number within a bullet on the left of the panels. This number refers to Table 2 which contains all the specific parameters used for this realization of the model. For each simulation, we show the finite strain and the current state The current state figure displays whether the material is yielding plastically (blue) or deforms viscously (red). It is overlaid by green shades of the second invariant of strain rate to outline structures that are currently active by comparison to finite strain. A cut-off range from 5 ×10 −16 s −1 to 2 ×10 −14 s −1 is used for the post-processing. The actual values span a larger range. We also represent three isotherms (180, 300, and 450 o C) which have been chosen to correspond to the onset of viscous deformation in low strain islands, brittle-ductile transition for quartz at average strain-rate and completely ductile behavior. In 155 the simulation with dehydration reactions, the 120 o C isotherm is added to locate the onset of the dehydration reaction. Finally, we represent the local slope with a color code at the top of the slice. Our aim is to provide the community with a first assessment of the topographic expression of the change in thermorheological regime with burial in an accretionary prism. We, therefore, have chosen a simple reference model which produces 160 well defined thrust and back thrust, with a moderate amount of sedimentation. The effects of softening, basal friction, and basal slope on accretion have already been thoroughly studied e.g., (Graveleau et al., 2012;Buiter et al., 2016;Ruh et al., 2012Ruh et al., , 2014.

Experimental plan
Hence, we here concentrate on parameters that are known to affect the geotherm: basal heat flow (represented by basal thermal gradient ∇T b ), initial burial (H s ), coefficient of diffusion of the topography (erosion and sedimentation) (k), and shear 165 heating (SH) following the plan listed in Table 2. In all the experiments, thermal blanketing (Jeffreys, 1931;Wangen, 1994) is very roughly simulated by using a lower thermal diffusivity for sediments produced by the surface process model (see Table   1). As we do not simulate the compaction of sediments with burial, thermal insulation is probably over-estimated but it allows testing potential effects of sedimentation on the thermal state of the accretionary wedges.  wedge doubles (close to sea level at x c.a. 300 km), the back-thrusts are more active in the purely brittle wedge than in the thermally controlled wedge for these brittle parameters. This results in the deactivation of one ramp over two, which leads to the formation of the distinct twinned-slice patterns observed between x = 430km and x = 300km in M0. In M1, the twinning of slice by back thrust occurs only once the temperature at the base of the model reaches 300 o C.

Main Results
Looking at the internal part of the two accretionary prisms, the differences become of course more striking. In the case 180 without thermal coupling (M0), deformation continues by pairing together more and more slices within sequences of thrust and back-thrust which root deeper and deeper as the accretionary prism thickens. The prolonged activity of these out-ofsequence thrusts and back trust is best measured by the small out-of-sequence basins that form at their top, discordant on the older sediments. Very little exhumation occurs close to the back-stop. In the case of thermal coupling, as soon as the 450 o C isotherm is reached, deformation becomes highly partitioned vertically. A thick layer at the base accommodates the simple 185 shear and branches on main frontal thrusts which root at the brittle-ductile transition. The ductile material is exhumed along a normal fault that roots on the backstop. In between, the deformation in the brittle part is either very distributed or almost nonexistent as the strain rate remains below our visualization threshold.
In the end, zooming out of these details and looking at the topographic slope, we can see that while the brittle accretionary wedge displays a rather constant 4 o slope, as predicted by the CTT taking into account the softening parameter (Ruh et al.,190 2014), the mature brittle-ductile wedge forms three distinct segments with a rather low but non zero topographic slope close to the backstop, a CTT predicted slope close to the toe of the wedge and in between a zone with a distinctively larger topographic slope which corresponds to the brittle-ductile transition.
3.2 From the emergence of the transition slope to steady state wedge Figure 3 shows the structural evolution of the reference simulation M1 through time. The wedge grows horizontally by in-195 sequence thrusting and vertically by reactivation of thrusts within the wedge. Most of the horizontal shortening is accommodated by the active frontal thrust. As the wedge evolves, the surface slope also changes and we detail here its evolution in time.
After 1 Myr, accumulated plastic strain shows that the deformation is strongly localized along the frontal part and on the décollement. Shear bands initially occurred in conjugate sets; with ongoing shortening, landward dipping shear zones are 200 preferred and back-thrusts are almost abandoned. The wedge is trying to reach a critical state by creating a topographic slope.
Due to internal frictional softening, the brittle wedge present a slopeᾱ, which corresponds to the slope predicted by CTT for  constant. This increase in slope causes an increase in sedimentation rate at the front where piggyback basins tend to be more starved than in the initial phase favoring the activity of thrusts, and a lengthening of the slices as predicted by other studies like As the shortening goes on, the temperature continues increasing at the back of the wedge due to burial. Between 5 and 10 Myr, the strain rate shows that the thickness of the décollement increases to reach 2 km. A normal fault forms near the backstop and starts accommodating the exhumation of high metamorphic grade rocks, which deforms in a ductile manner. At the front of this wide ductile horizontal shear zone, which terminates right at the 300 o C isotherm, roots a system of low angle thrusts At 20 Myr, the overall architecture of the accretionary prism has not changed, the whole wedge is just shifted towards the right as the ductile part of the wedge has grown wider. One could state that the brittle-ductile wedge has reached some sort of steady state between 10 and 15 Myr. Rocks that are incorporated in the wedge start by rotating along with brittle thrust and maybe deforming in a pure brittle manner within the slice. In a second semi-brittle phase, internal viscous-ductile deformation 225 affects the whole tectonic slices separated by brittle thrusts. This phase corresponds to crossing the zone with a higher than normal topographic slope. Finally, depending on whether they were incorporated in the ramp or not, they go through passive rotation by distributed pure shear thickening associated with low temperature or intense ductile simple shear before being exhumed for large temperature.
In conclusion, the large slope segment which corresponds to the brittle-ductile transition is acquired as soon as some vis-230 cous internal deformation occurs in between faults. The brittle-ductile wedge reaches a steady state when ductile deformation becomes predominant on the décollement that is for temperature greater than 450 o C.

Sensitivity Analysis
Depending on the chosen thermal parameters, the three segments described above are more or less developed in our simulations. A major player in the development of the ductile flat part of the wedge associated with high grade metamorphic rock 235 exhumation and formation of a forearc basin is the occurrence of shear heating.
Shear heating might be largely reduced by several factors and noteworthy enough the presence of water which reduces the ductile strength of the material or by thermal pressurization during earthquakes (Sibson, 1973;Lachenbruch and Sass, 1980;Smith, 1984, 1987;Segall and Rice, 2006). Gao and Wang (2014) actually showed that megathrusts that produce great earthquakes tend to dissipate less heat than megathrusts that slip mainly by creep. Hence, our shear heating models give 240 a maximum bound for the heat that could be produced in the system. In order to study the other bound, we ran some model with shear heating off which would correspond to a system where most slip is accommodated by earthquakes.
Results are clear, all models with shear heating (Figure 4) develop a large flat area because the shear at depth helps the temperature to rise above the 450 o C isotherm, which correlates with the formation of the topographic plateau where high grade metamorphic rocks are exhumed. Models with no shear heating hardly develop a plateau and a normal fault to exhume 245 high grade material at the back ( Figure 5).
Actually, only models with large erosion coefficients, i.e. M4 and M6, do produce exhumation and a small plateau when shear heating is deactivated. The peak metamorphic temperature of rocks exhumed at the back-stop in presence of shear heating or in models with large erosion rate is compatible with thermochronometry studies in stationary accretionary prism like Taiwan (Suppe et al., 1981;Willett and Brandon, 2002) which indicate the samples exhumed to the surface by rock uplift to compensate 250 for the mass lost by erosion (Fuller et al., 2006) have experienced temperatures in excess of 300-365 o C but below 440 o C e.g., (Lo and Onstott, 1995;Fuller et al., 2006). Models with larger sedimentation rate (models M3, M4, M6, M8, M10, M12) produce, as expected from former studies (Storti and McClay, 1995;Simpson et al., 2010), a smaller number of thrusts and a larger spacing between them. Erosion and sedimentation also participate at reducing the slope at every step, thus favoring out-of-sequence activity ( Figure 5 M2 and 255 M4). In our models, sediments also affect the thermal regime because they are attributed a lower thermal diffusivity; thick sediment sequences act therefore as a blanket isolating the heat flux coming from below. As a result, temperature raises faster at depth when large sedimentary basin forms. This explains why, in absence of shear heating ( Figure 5), only models with large sedimentation rate develop a ductile flat at the back ( Figure 5 M4 and M6).
Thermal blanketing also affects the geotherm at a smaller scale as shown by the distinctive wiggles in the isotherms. For In absence of heat production and large vertical advective terms, the temperature is more or less proportional to depth and thermal gradient in the models, experiments with thick sequences (M5 and M6 in Figure 5 and M7 and M8 in Figure 4) or larger imposed basal gradient (M9, 10, 11, 12 in Figure 6) reach the onset of brittle-ductile transition earlier. As a result, the 265 completely brittle part of the accretionary prism, located at the toe of the wedge, is less developed in models with a larger pile of incoming sediments and in models with a larger thermal gradient. The local slope in these models is always larger than the CTT predicted one and back-thrust appear earlier in the history of deformation.

Effect of Dehydration reactions
We now report some models which intend to tackle the effect of fluid over pressure due to dehydration of shale materials which 270 potentially corresponds to smectite-illite transition. In clay-rich accretionary complexes, this transition appears at ∼2.5 -5 km depth corresponding approximately to 100-150 o C (Pytte and Reynolds, 1988;Hyndman et al., 1995;Oleskevich et al., 1999). Smectite and illite clays are frictionally weak but illite is slightly stronger (Morrow et al., 1982;Saffer and Marone, 2003). We, therefore, consider that our clay rich décollement is initially smectite rich with an internal friction angle of 5 o . Once dehydration reaction is terminated the same décollement is considered illite rich and affected a friction angle of 10 o . We do not 275 have a kinetic reaction included in the code but we assume that the reaction is occurring at fast rate in the 120-140 o C window. This is slightly smaller than the 100-150 o C reported in the literature and it is aimed at roughly accounting for a slow kinetic at lower temperatures and the lack of reactant (smectite) left at higher temperatures. During this phase of fast reaction, fluids  are released in the clay rich décollement of low permeability permitting to build strong local fluid over pressure (Bekins et al., 1994;Lanson et al., 2009). The code does not explicitly include fluids, but these overpressures are reflected by an effective 280 friction angle of 0.1 o within the reaction temperature window. The evolution of friction with temperature in the décollement layer is reported in Figure 7.

Slopes and modes of deformation
The thermomechanical model provides an opportunity to investigate the specific variations of topographic slope of an accretionary prism, supported by the CTT analysis (Davis et al., 1983). Our results show that very simple models of accretionary prism lead to the formation of four different structural zones which corresponds to three different type phases of deformation 310 related to transitions in the rheology.
The frontal brittle part of the wedge is characterized by an imbricated zone and active in-sequence thrusts faults ahead. The décollement and the above sequence behave plastically (Figure 9a). The topographic slope created in this section is controlled by the basal and average internal frictions and is consistent with the CTT predictions (Figure 9b and c, blue star).
The presence of a smectite-illite transition (dehydration reaction) leads to a segment characterized by a flat topographic 315 slope and little internal deformation, in between the frontal brittle wedge and the brittle-ductile transition (Figure 9a). This flat segment appears during the early stage of the accretionary prism formation. As the wedge shortens and grows, the temperature increases at the back due to burial and the wedge becomes thicker and warmer, reducing this frontal flat segment.
The brittle-viscous transition zone is characterized by out-of-sequence thrusts and backthrusts with high internal deformation ( Figure 9a). This part forms a steeper topography slope than the brittle part. A careful examination of the behavior of this 320 segment reveals that the décollement remains brittle, but the above sequence has entered the viscous phase (Figure 9a). By plotting the surface slope on the critical taper diagram, we notice that this part is consistent with a critical taper of a lower internal friction angle (Figure 9b, red star).
The viscous part presents an approximate flat zone without effective internal deformation. Décollement and above sequence deform viscously. The topographic slope is again consistent with the critical taper theory, considering that a viscous décolle-325 ment is equivalent to a brittle décollement of extremely low friction. Therefore, the increase of the topographic slope between the brittle and viscous segments results from an equivalent decrease of internal friction rather than an increase of basal friction.

Comparision with exhumed accretionary prism
Based on the models, we can interpret that the rocks exhumed at the back of the models have been through 3 main phases of deformation through time. The first phase D1 is purely brittle and corresponds to the onset of accretion at the toe of the 330 accretionary prism. The passive transport through the dehydration flat segment does not cause important deformation. D1 is therefore overprinted by a phase D2, which corresponds to the start development of a low grade metamorphic foliation as a result of penetrative horizontal shortening. This change in material behavior at depth, from brittle to viscous, due to an increase of temperature at depth, favors the activation of brittle backthrusts and causes the steepening of the slope. In an accretionary prism with large basal heat flow, or thick incoming sedimentary, the sequence D2 appears closer to the toe of the prism and 335 might replace D1. Warmer models then develop a phase in which deformation is partitioned between ductile simple shear at depth (D3) and distributed shortening at the surface (more penetrative version of D2). Once the horizontal ductile shear zone corresponding to D3 has formed, it branches on a shallow dipping splay fault accompanied by a very vertical back-thrust. The Figure 9. a. Proposed model for the mature brittle ductile wedge which forms three distinct segments; pure brittle wedge with a rather constant slope predicted by the CTT at the front (blue star), low but non zero topographic slope close to the backstop corresponds to viscous deformation (black star) and, larger topographic slope in between these segments as a result of the brittle ductile transition (red star and yellow rectangle). b. Topographic slope versus internal friction for ϕ basal =5 o . c. Basal friction versus topographic slope for ϕint 10, 17 and 25 o . three phases of deformation recorded by the rocks exhumed at the back of the models along a normal fault correspond to the different phases recorded in exhumed accretionary prism like the Shimanto Belt (Raimbourg et al., 2014), although this paper 340 would classify our D1 and D2 as more or less localised deformation related to frontal accretion and in our case the high grade ductile foliation D3 would show a more marked asymmetry.

Forearcs basins
Every phase of deformation is accompanied by different types of sedimentary basins. Indeed, while phase D1 is accompanied by piggy-back basins which length depends on the sedimentation rate (e.g., Figure 4), D2 is accompanied with the formation 345 of trench slope basins discordant on the early piggy-back basins, and the onset of D3 pinpoints the start of activity of the splay fault and its back-thrust. These structures isolate the ductile part of the prism, where forearc sediments can accumulate within small basins in discordance on the sediments accreted during D1 and D2, from the brittle part of the prism. The splay fault and its conjugate high angle back-thrust serve as a current backstop for the brittle part before being incorporated into the ductile forearc part of the prism as accretion continues.

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Backthrusting between the imbricated segment and forearc basins have been described along various accretionary margins of high sedimentation rate (Silver and Reed, 1988). Along the Sumatra subduction zone, well-known for its high sedimentation rate and high thermal gradient (Chlieh et al., 2008), the slope break predicted by our model is visible on seismic images of northern (Chauhan et al., 2009) and southwestern (Singh et al., 2010) Sumatra, and a clear backthrust has been imaged down to 7 s (15 km) (Chauhan et al., 2009). Backthrusts have also been imaged along the Antilles subduction zone, in particular along 355 the Barbados region, again known for its high sedimentation rate psilver1988backthrusting, laigle2013along. A backthrust is also well documented in New Zealand (Barnes and Nicol, 2004) but has been interpreted as resulting from a change in basal friction. Noda (2016) reviews a number of other compressive accretional margins which all seem to develop an active backthrust at the edge of the forearc basin like in our models.
However, most of these seismic studies place the splay fault and its back-thrust at the limit of the continental crust which 360 posits, in a way, a stable position through time, at least relative to the upper plate. In our simulations, the location of the splay fault is given a more dynamic nature as it corresponds more or less to the 450 o C isotherm (Figure 10a). This isotherm at 15 km depth corresponds to greenschist facies metamorphic conditions. Using typical sediments composition, perplex software yields typical continental crust seismic attributes with 5.5 > Vp > 5 km/s and Vs 2.5 km/s. With volcanoclastic sediments, larger velocities are expected for similar metamorphic conditions. As a result, seismic refraction investigation of active margin would 365 definitely identify this part of the models as a continental crust or former arc crust. Using the location of the splay fault in warm, compressional accretionary contexts like Southern Sumatra (Figure 10b) and Lesser Antilles (Figure 10c), we propose that what is typically interpreted as attenuated continental or arc crust could also well mark the location of the brittle-ductile transition.
According to our models, along with accretionary prisms of little seismic activity, the forearc basin should correlate with the fully viscous domain at least along high sedimentation rate and high thermal gradient compressive accretionary margins.

Up and down-dip end of the seismogenic zone
We here confirm that the smectite-illite transition produces a flat segment that can explain, for young or cold accretionary complexes, the observed correlation between deep-sea terraces or fore-arc basins with large subduction earthquakes (Song and Simons, 2003;Wells et al., 2003). In such specific contexts, the flat segment would thus underline the up-dip limit of the seismogenic zone. Along seismically active accretionary prisms, an increase of topographic slope and decrease in apparent 375 geodetic coupling are interpreted as the down-dip limit of the seismogenic zone (Cubas et al., 2013). In the first case, the rise in topographic slope indicates an increase of effective basal friction which corresponds to the down-dip end of dominant seismic slip (Cubas et al., 2013;Pajang et al., 2021). In the second case, geodetic deformation at velocities that differs from subducting plate velocities is generally interpreted as a lack of coupling on the plate interface based on elastic models (Perfettini et al., 2010;Chlieh et al., 2008). Here we show that the brittle-ductile transition corresponds to the onset of internal distributed 380 viscous deformation in between brittle structures in the accretionary prism above a brittle décollement. This causes a decreased geodetic coupling and an increased apparent basal friction but does not imply any modification in the interface frictional properties or deformation mode. This questions both the search for field analogs of the down-dip end of the seismogenic zone and the interpretation of seismic coupling in terms of locked/creeping décollement.

Limitations and perspectives
Our simple models permit us to understand first order mechanisms in forearc formation, but improvements are still needed to better understand how the brittle-ductile transition affects the formation of splay faults providing an alternative model to the formation of forearc basins as well as an alternative origin for the forearc crust. We find that, the drop in friction between the ductile and brittle part of the accretionary prism and smectite to illite dehydration reaction is not sufficient to explain the normal faults observed along some accretionary margins like Chile or Makran Cubas et al. (2013); Pajang et al. (2021). This 390 result leads us to conclude that the normal faults arise from phenomena we neglected in our simplified approach. This includes: the effect of heterogeneities in the subducting plate, the effect of elastic deformation during the seismic cycle and/or the over simplification of the bottom boundary conditions which does not allow an increase in taper angle with burial like in Beaumont et al. (1992); Ruh (2020). 395 We plan on testing these other hypotheses in the future and posit that improving the bottom mechanical boundary conditions will also permit performing more accurate simulations of the sedimentation in the forearc basins by keeping them below sea level.

Conclusions
Despite the simplicity and limitations of our simulations, their results are sufficient to propose a new model for the interpretation 400 of changes in topographic slope at compressive accretionary margins, at least, warm margins with large sedimentary supply.
Using only the topographic gradient, our model distinguished four segments, which corresponds to 3 modes of deformations observed in exhumed accretionary complexes: brittle décollement and internal deformation at the toe where the topographic slope respects the CTT; a flat area with little internal deformation in young accretionary prisms, if a dehydration reaction is considered;

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brittle décollement and viscous internal deformation of fault-bounded blocks, where the topographic slope is in excess compared to the CTT and these large slopes should not be interpreted as the downdip limit of the seismogenic zone; viscous décollement and backthrust bounded blocks in the most internal part where the topographic slope is close to zero.
The most important finding is that the onset of internal viscous deformation in fault-bounded blocks increases the topographic 410 slope of the accretionary complex independently of the basal friction.
Comparing the simulations results with natural cases, we show that this anomalous topography related to the brittle-ductile transition is analogue to the forearc high in a compressional accretionary prism. It is indeed the location of an active backthrust and splay fault system rooting on the viscous channel that forms in the internal part where the basal temperature reaches sections that are often interpreted as an attenuated continental crust or former arc crust. Our model provides, we believe, a valid alternative interpretation which has the advantage to explain why the forearc crust is always thinner than the continental crust on seismic sections but also why the warm subduction segments are representative of our mature stage simulation, such as South Sumatra or the Lesser Antilles are considered aseismic.
Code availability. The version of ptatin2d and the input files used in this contribution are archived following FAIR principle at https: //doi.org/10.5281/zenodo.4911354. Input files are located in published_inputs/Pajang2021_SE Video supplement. all simulations are available as movies archived at https://doi.org/10.5281/zenodo.5599365 Author contributions. SP Designed the simulation, run the simulation prepared the figure and wrote the paper, LLP implemented the heat flow bc, LLP and NC, participated to the interpretation of the simulation, application to natural cases and writing the paper .

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Competing interests. Authors declare no competing interest Acknowledgements. Authors thanks Tiphaine Larvet for computing seismic velocity with perplex.