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# Transient stripping of subducting slabs controls periodic forearc uplift

## Abstract

Topography in forearc regions reflects tectonic processes along the subduction interface, from seismic cycle-related transients to long-term competition between accretion and erosion. Yet, no consensus exists about the topography drivers, especially as the contribution of deep accretion remains poorly constrained. Here, we use thermo-mechanical simulations to show that transient slab-top stripping events at the base of the forearc crust control uplift-then-subsidence sequences. This 100s-m-high topographic signal with a Myr-long periodicity, mostly inaccessible to geodetic and geomorphological records, reflects the nature and influx rate of material involved in the accretion process. The protracted succession of stripping events eventually results in the pulsing rise of a large, positive coastal topography. Trench-parallel alternation of forearc highs and depressions along active margins worldwide may reflect temporal snapshots of different stages of these surface oscillations, implying that the 3D shape of topography enables tracking deep accretion and associated plate-interface frictional properties in space and time.

## Introduction

Uplift and subsidence of the forearc domain have been long suspected to be controlled by tectonic processes taking place along the subduction interface1,2,3,4. Combined with erosion, these vertical displacements shape the long-term topography defined by a coastal high separated from the volcanic arc by a depression, which characterizes many active subduction zones worldwide despite their variable thermal structure, kinematic parameters and net mass flux5,6 (Fig. 1; see also Supplementary Fig. 1 and Supplementary Note 1 for details on forearc topography along the Circum-Pacific belt). Multiple mechanisms at very different timescales have been invoked to explain this coastal topography that requires permanent (i.e. anelastic) deformation. They include cumulative co-seismic slips on the subduction interface7,8 and/or on forearc faults9 and long-term aseismic processes, such as crustal deformation10,11 and tectonic underplating12,13,14,15,16, both being partly driven by the frictional state of the underlying subduction interface10,11,17,18. However, the critical lack of constraints on the long-term (i.e. Myr-scale) dynamics of these aseismic processes and the scarcity of geological markers of absolute vertical displacements at such long timescales prevent a robust assessment of forearc topography drivers. This is especially true for tectonic underplating (i.e. deep accretion at the base of the forearc crust) that occurred in the past and is probably still active along many present-day subduction zones, as evidenced along the Circum-Pacific belt from geological records13,19,20,21,22 and geophysical imaging1,23,24 (Fig. 1a).

Here, we use two-dimensional, thermo-mechanical numerical experiments to characterize the long-term dynamics of tectonic underplating and associated forearc topographic response with an unprecedented high spatial and temporal resolution. A pulse-like, deep accretionary pattern is herein recognized, marked by Myr-scale vertical surface oscillations that generate a background topographic signal that may have been hitherto overlooked in natural observations.

## Results

### Modelling strategy

We carry out a set of numerical simulations governed by conservation laws and visco-elasto-plastic rheologies solved using a marker-in-cell technique25 to reproduce an ocean-continent subduction system and its topographic evolution in a high-resolution spatial and temporal frame (see Methods and Supplementary Fig. 2 for details on the modelling procedure and the initial set-up). The top of the lithospheres is solved as an internal free surface by using a low-viscosity layer26,27 (i.e. sticky-air method). The effects of erosion or sedimentation are also accounted for the calculation of the topography, depending on whether this surface is located above or below the sea level (i.e. y = 10 km). A 0.3 mm year−1 erosion rate is thus prescribed in all experiments, in agreement with the range of erosion rates obtained from drainage basins in seismically active regions28. Terrigenous sedimentation at a rate of 1 mm year−1 is restricted to offshore regions with steep surface slopes (i.e. >17°) for smoothing the topography of the continental slope. Note that the elevation in our numerical experiments is relative to a fixed sea level, implying that predicted topographic variations and vertical surface velocities are more relevant indicators of topography dynamics than absolute elevations.

A set of numerical simulations are herein presented with different imposed plate convergence rates (Vconv comprised between 2 and 10 cm year−1, in agreement with natural estimations; Fig. 1) or a variable amount of subducting sediments to assess the role of plate kinematics and mass flux at the trench on accretion dynamics and associated forearc topographic response (Supplementary Table 1). Other subduction-related parameters, rheological properties, and boundary conditions are kept equal in all experiments. Note also that the accuracy of the results presented hereafter has been validated by a numerical-resolution test (see Supplementary Fig. 3 and Supplementary Note 2 for details).

### Steady-state underplating and periodic topography evolution

In our reference model (Vconv = 5 cm year−1; model sed5.0; Fig. 2; see also Supplementary Movie 1), oceanic subduction is first associated with the underplating of successive basaltic tectonic slices (Fig. 2a), which recalls mafic terrane accretion during the early stages of subduction as identified in present and former Circum-Pacific subduction zones such as Cascadia29 (i.e. Crescent terrane), Patagonia30 (i.e. Lazaro unit) and New Caledonia31 (i.e. Poya terrane). Then, both frontal and basal accretions are predicted during the entire model duration (i.e. ~80 Myr). Contribution of both pelagic and terrigenous sediments leads to the formation of a ~50-km-wide frontal wedge as commonly reported along active accretive margins involving >1-m-thick trench-filling sediments5. At higher depth, successive underplating events between ~15 and ~30 km depth result in the growth of a dome-shaped structure, the so-called duplex, composed of sedimentary and basaltic slices (Fig. 2). In the deeper part of the forearc crust, basaltic material is preferentially and regularly underplated for ~65 Myr. Afterwards, only pelagic sediments are added to the base of the forearc domain, forming a homogenous sedimentary sequence (Fig. 2c). This change in accretionary dynamics may result from long-term, fluid-related weakening of the subduction channel, preventing major stress accumulation and hampering the stripping of thick basaltic slices after 68 Myr of convergence18. Eventually, the persistence of tectonic underplating events combined with surface erosion prescribed in the experiment result in the exhumation of a ~60-km-wide duplex up to the surface, evidencing an overall vertical mass flow throughout the forearc domain (Fig. 2). Coevally, long-term basal erosion is predicted along a ~20-km-long subduction segment in between the frontal wedge and the duplex, leading to partial consumption of previously accreted material (Fig. 2d).

The forearc margin is characterized by an ~8000-m-deep trench and a ~50-km-wide and >1000-m-high topography composed of two highs located near the coastline, directly above the basal-accretion sites (Fig. 2d). Landward, elevation decreases substantially to form a wide depression that reaches >1000 m depth before getting into the arc domain. Modelled long-term topography results from a periodic evolution in a region extending from the coastline to ~100 km landward (Fig. 3a). Each topographic pulse consists in a surface uplift event ranging from ~400 to ~700 m, followed by a subsidence episode of equivalent amplitude and rates ranging from ~0.5 to ~1.5 mm year−1 (Fig. 3b, c). Coevally, the horizontal location of the coastline varies by ~5 km, leading to an overall constant distance between the coastline and the topographic highs (i.e. ~10 km from 0- to 1000-m high; Fig. 3a). Balance between uplift and subsidence shapes the long-term evolution of the margin topography, first characterized by an overall rise of the coastal high for ~56 Myr, reaching ~1800 m high (Fig. 3b). Afterwards, basal erosion of the forward part of the duplex modifies the equilibrium state of the accretionary wedge (Fig. 2d), resulting in a decrease of this topography down to ~1000 m high, before it stabilizes after ~68 Myr. The frequency of the topographic signal is robust between ~20 Myr (i.e. after initial topographic equilibration) and ~68 Myr, with a periodicity of ~2.8 Myr according to a Fourier transform calculation on the vertical surface velocity (Fig. 3c). After ~68 Myr, the amplitude of the topographic pulses drops to ~100 m with uplift and subsidence rates of <0.5 mm year−1 and a shorter periodicity (i.e. ~1.6 Myr).

### Role of plate kinematics and mass flux on forearc topography

Additional experiments are carried out to test the critical role of plate convergence and subducting sediments on tectonic underplating and topographic evolution (Supplementary Figs. 47; Supplementary Movies 24). By increasing the convergence rate (Vconv = 6.5, 8 and 10 cm year−1; models sed6.5, sed8.0 and sed10.0, respectively), the overall evolution of the forearc margin is akin to the reference model, except that very few basaltic slices are accreted into the duplex, which is, instead, dominated by pelagic and terrigenous sedimentary material (Supplementary Fig. 4). Topographic evolution is also equivalent in these two models, but with a higher coastal topography (i.e. reaching ~2000-m high) and a shorter periodicity for each uplift/subsidence pulse (Fig. 4 and Supplementary Fig. 6). Alternatively, by decreasing the convergence rate (Vconv = 3.5 and 2 cm year−1; models sed3.5 and sed2.0, respectively), tectonic underplating is achieved by a mostly horizontal mass flow at the base of the forearc domain, leading to the horizontal growth of a wide accretionary wedge (Supplementary Fig. 5). Associated topography is markedly lower than in the previous experiments with a maximum elevation of ~1000 m below the sea level and no apparent periodicity is predicted (Supplementary Fig. 6). Finally, by removing the sediments entering the trench, the subduction regime becomes mostly erosive, resulting in an overall subsidence of the forearc domain and a low topography with no apparent periodicity (Supplementary Fig. 7). For details on the modelling results of all the additional experiments, the reader is referred to Supplementary Notes 3 and 4.

## Discussion

Our models of a lithospheric-scale subduction zone predict that a significant topography is built through a series of tectonic underplating events at the base of the forearc crust despite constant prescribed parameters over time (e.g. sediment thickness, convergence rate; Figs. 2 and 3; see also Supplementary Figs. 4 and 6). Furthermore, the good agreement between natural and modelled topographic profiles (Figs. 1b and 2d) provides an independent confirmation that ongoing underplating activity is a plausible mechanism to account for the present-day coastal high, which is in line with geological and geophysical evidences for deep accretion along active margins1,14,24, as well as with earlier wedge-scaled analogue and numerical studies32,33,34,35,36. The coastal topography generally localizes directly above a 30–40-km-depth plate interface, trenchward from the intersection of the continental Moho (Supplementary Fig. 1; see also Supplementary Note 1 for details), which corresponds to a preferential site for tectonic underplating1,18 (Fig. 2). Landward, the inner-forearc depression predicted in our experiments may be related to surface slope adjustments to maintain a critical taper37,38 or to elastic loading by plate underthrusting39. The modelled depression depth is, however, overestimated with respect to Circum-Pacific forearc depressions (Fig. 1b), probably because our simulations do not account for crustal deformation and magmatic processes in the arc region.

More importantly, our results highlight a pulsing rise of the coastal topography and a direct temporal correlation between transient stripping events along the plate-interface and uplift pulses (whether the tectonic slices are preserved in the duplex or basally eroded; Fig. 3b, c). After each accretion event, a period of internal re-equilibration of the forearc wedge is marked by a subsidence period as predicted by the Coulomb wedge theory37. No variations in the dynamics of underplating and associated forearc topography evolution are predicted after the thick, early accreted basaltic lid has been exhumed and partly eroded (Fig. 1), suggesting that these early basaltic underplating events do not critically affect the subsequent mechanical evolution of the forearc margin (Fig. 2b). Furthermore, our experiments suggest that the Myr-scale evolution of forearc topography may be a relevant indicator of the nature and influx rate of deeply accreted material (Figs. 2 and 3c; see the correlation between underplating dynamics and the topographic signal after ~68 Myr in our reference model). Such an oscillating forearc rise is achieved in all the simulations displaying a vertical mass flow associated with tectonic underplating (Supplementary Figs. 4 and 6). Our set of experiments also reveals an anti-correlation between the periodicity of vertical surface oscillations above the underplating sites and the plate convergence rate as already suspected in time-unscaled sandbox analogue models35,40 (Fig. 4). Because this periodicity reflects the time needed to reach differential stresses high enough to trigger tectonic slicing, a faster-subduction regime would promote a more rapid succession of tectonic underplating events. Indeed, fast kinematics allows for a faster stress build-up along the plate-interface and weak-sediment underplating (prevailing in fast subduction models) requires less stress build-up than sediment-and-basalt underplating (see Supplementary Note 3 for details). Finally, a comparison with analogue models highlights a correlation between the periodicity of stripping events and the depth of the accretion site (i.e. 10–100-kyr- and 2–3-Myr-long periods for frontal accretion and ~15–30 km-deep underplating events, respectively), which likely reflects the increase of rock-failure threshold with depth (Fig. 4).

A pulsing underplating dynamics is suspected in the long-term geological record by gradually decreasing ages from the top to the base of exhumed paleo-duplexes. This age pattern results from transient accretion events separated in time by a few million years, such as documented in the case of the Franciscan complex41 or Chilean Patagonia22 and in agreement with our modelling results (Fig. 2). Accordingly, Myr-scale vertical oscillations of forearc topography should be expected along subduction segments where active tectonic underplating takes place (Fig. 3). Sedimentary and tectonic record from forearc basins shows successive subsidence and uplift periods lasting several millions of years, which were interpreted in terms of change in plate motion42 (e.g. Cascadia) or varying sediment flux at the trench43,44,45 (e.g. Chile). It is worth noting that the fluctuation of sediment supply (e.g. related to glacial/interglacial periods) and the subduction of topographic highs (e.g. seamounts, ridges46,47,48,49) also affect forearc deformation and make the surface evolution difficult to decipher as it interferes with the aforementioned periodic topographic signal obtained despite constant kinematic and boundary conditions (Fig. 3).

Episodic uplift and subsidence are widely reported along active forearc margins at short timescales, either from Global Positioning System (GPS) measurements, historical records, coral growth or geomorphological markers, reflecting the visco-elastic response of the upper plate to the successive stages of the seismic cycle at timescales of ~101–102 years50,51,52 or else to potential earthquake supercycles over longer timescales of ~102–103 years53,54. Marine terraces are also insightful markers for tracking coastal uplifts at intermediate timescales (i.e. 104–106 years) with interpreted ~104-year-scale temporal variations proposed to relate to earthquake temporal clustering on upper-plate crustal faults9 or cumulative megathrust earthquakes8. This transient signal is questioned by some authors that ascribe it to the uncertainty on age measurements of the terraces and to their fragmentary record controlled by the ~40- to ~100-kyr-long sea level oscillations55. This debate remains open and is beyond our main focus. It is however noticeable that all these uplift-then-subsidence signals overlap in space and time. This implies that the vertical displacements occurring at the forearc surface actually encompass contributions from different processes, chiefly including tectonic underplating (Fig. 5). An important consequence is that topographic variations observed at year to kyr scale may display opposite vertical displacement vectors than the Myr-scale signal (compare grey, red and orange curves on Fig. 5). Forearc subsidence, recorded by GPS or geomorphological markers, thus does not preclude active deep accretion and associated uplift over a Myr-scale period, and vice versa. As a consequence, we posit that the underplating-related background signal is likely inaccessible to short-term geodetic and geomorphological records.

As discussed above, tracking this potential Myr-scale topographic signal along active subduction zones is challenging. An alternative approach is to consider trench-parallel topographic variations along active forearc margins as equivalent to snapshots of different temporal stages of the surface oscillations predicted in our experiments (Fig. 3), in a similar way to compare different stages of short-term crustal deformation from several subduction zones to get a comprehensive picture of the seismic cycle52. The outer-forearc morphology typically consists of an along-strike succession of basins and topographic highs, some of them emerging as coastal promontories, such as the Mejillones, Tongoy and Arauco peninsulas (Chilean margin) and the Kii, Muroto and Ashizuri peninsulas (SW-Japan margin) (Supplementary Fig. 1). Considering our new results evidencing a forearc uplift and associated trenchward migration of the coastline for each underplating event (Fig. 3a), we propose that these local topographic highs are transiently formed by deep accretion of laterally constrained tectonic slices over few-Myr-long periods (Fig. 6). This is notably consistent with the recent emersion of the peninsulas as antiformal structures15,56,57, interpreted here as the surface expression of deep duplexing, along with active normal faulting (Fig. 2e). On these peninsulas, either normal, thrust or strike-slip faulting has been observed, suggesting that additional tectonic processes may disrupt the upper-crust deformation pattern, including translation or rotation of forearc crustal blocks15,56,58. In contrast, offshore forearc basins and embayments in between these topographic highs may correspond to regions undergoing relaxation subsidence after a former stage of tectonic underplating.

Local forearc topographic highs are spatially correlated with high gravity anomalies and correspond to mostly aseismic subduction segments where megathrust earthquake ruptures tend to stop3,4,51,59. This reveals variations in the frictional properties of the plate interface, which have to remain stable over Myr timescales to reconcile the seismogenic behaviour with geological and topographic observations3,10,57 and to control the detachment of large tectonic slices18,60. On the basis of these correlations, we conclude that laterally constrained tectonic underplating events allow for reconciling the frictional pattern on the interface and the rise of these local topographic highs. Succession of Myr-long underplating events all along active margins may then result in the periodic formation of local topographic highs with the possible emergence and submersion of peninsulas and the rise of a high-elevation coastal belt supported by a duplex structure at depth over tens of Myr (Figs. 1b and 6).

Our findings thus highlight the first-order importance of transient tectonic underplating for shaping forearc topography in subduction zones worldwide through a characteristic Myr-scale periodic signal, which cannot be adequately tracked with short-term geodetic and geomorphological records. Instead, trench-parallel and trench-perpendicular forearc topographic profiles appear as more insightful long-term markers for assessing spatial and temporal variations of underlying accretion processes along the subduction interface.

## Methods

### Conservation equations

The two-dimensional numerical experiments are carried out with the I2ELVIS code, which solved the continuity, momentum and heat conservation equations, based on a finite difference scheme and a marker-in-cell technique25. The continuity equation describes the conservation of mass, assuming a visco-elasto-plastic compressible fluid. It is solved on a fully staggered Eulerian grid and has the form:

$$\frac{{{\mathrm{D}}\ln \rho _{{\mathrm{eff}}}}}{{\mathrm{D}t}} + \frac{{\partial v_x}}{{\partial x}} + \frac{{\partial v_y}}{{\partial y}} = 0,$$
(1)

where ρeff is the effective density of rock calculated in Eq. (7), t the time, vx and vy the viscous velocity components in x (i.e. horizontal) and y (i.e. vertical) directions. The momentum of the compressible fluid is then solved using the Stokes equations:

$$- \frac{{\partial P}}{{\partial x}} + \frac{{\partial \sigma _{xx}}}{{\partial x}} + \frac{{\partial \sigma _{xy}}}{{\partial y}} = - \rho _{{\mathrm{eff}}},$$
(2)
$$- \frac{{\partial P}}{{\partial y}} + \frac{{\partial \sigma _{yx}}}{{\partial x}} + \frac{{\partial \sigma _{yy}}}{{\partial y}} = - \rho _{{\mathrm{eff}}}\;g,$$
(3)

where P is the pressure, σxx, σyy, σxy and σyx the components of the deviatoric stress tensor and g the gravitational acceleration (= 9.81 m s−2). The heat conservation equation is formulated in a Lagrangian form to avoid numerical diffusion of temperature:

$$\rho _{{\mathrm{eff}}}C_{\mathrm{p}}\frac{{{\mathrm{D}}T}}{{{\mathrm{D}}t}} = - \frac{{\partial q_x}}{{\partial {\mathrm{x}}}} - \frac{{\partial q_y}}{{\partial {\mathrm{y}}}} + H_{\mathrm{r}} + H_{\mathrm{a}} + H_{\mathrm{s}},$$
(4)

where Cp is the isobaric heat capacity, T the temperature, Hr the radiogenic heat production, Ha the adiabatic heat production, Hs the shear heating (see ref. 25 for details on calculation of Ha and Hs) and qx and qy the heat flux components solved as:

$$q_x = - k\frac{{\partial T}}{{\partial {\mathrm{x}}}},$$
(5)
$$q_y = - k\frac{{\partial T}}{{\partial {\mathrm{y}}}},$$
(6)

where k is the thermal conductivity depending on temperature, pressure and rock type (Supplementary Table 2).

### Rock density and rheology

The effective density ρeff for each rock phase prescribed in the experiments is solved as follows:

$$\rho _{{\mathrm{eff}}} = \rho _{{\mathrm{rock}}}\left( {1 - X_{{\mathrm{fluid}}}} \right) + \rho _{{\mathrm{fluid}}}\;X_{{\mathrm{fluid}}},$$
(7)

where Xfluid is the mass fraction of fluid (i.e. the bound mineral water content), ρfluid the reference fluid density (=1000 kg m−3) and ρrock the rock density calculated as:

$$\rho _{{\mathrm{rock}}} = \rho _0\left( {1 - \alpha \left( {T - 298} \right)} \right)\left( {1 + \beta \left( {P - 0.1} \right)} \right),$$
(8)

where ρ0 is the standard density of rock, α the thermal expansion and β the compressibility. Non-Newtonian visco-elasto-plastic rheologies are employed in these experiments, implying that the deviatoric strain rate $${\dot{\mathbf{\varepsilon }}}_{ij}$$ includes the three respective components:

$${\dot{\mathbf{\varepsilon }}}_{ij} = {\dot{\mathbf{\varepsilon }}}_{ij_{{\mathrm{viscous}}}} + {\dot{\mathbf{\varepsilon }}}_{ij_{{\mathrm{elastic}}}} + {\dot{\mathbf{\varepsilon }}}_{ij_{{\mathrm{plastic}}}},$$
(9)

with

$${\dot{\mathbf{\varepsilon }}}_{ij_{{\mathrm{viscous}}}} = \frac{1}{{2\eta _{{\mathrm{eff}}}}}\sigma _{ij},$$
(10)
$${\dot{\mathbf{\varepsilon }}}_{ij_{{\mathrm{elastic}}}} = \frac{1}{\mu }\frac{{{\mathrm{D}}\sigma _{ij}}}{{{\mathrm{D}}t}},$$
(11)
$${\dot{\mathbf{\varepsilon }}}_{ij_{{\mathrm{plastic}}}} = 0\quad{\mathrm{for}}\;\sigma _{{\mathrm{II}}} \, <\, \sigma _{{\mathrm{yield}}},$$
(12)
$${\dot{\mathbf{\varepsilon }}}_{ij_{{\mathrm{plastic}}}} = {\chi}\frac{{\sigma _{ij}}}{{2\sigma _{{\mathrm{II}}}}}\quad{\mathrm{for}}\;\sigma _{{\mathrm{II}}} = \sigma _{{\mathrm{yield}}},$$
(13)

where ηeff is the effective creep viscosity calculated from experimentally constrained dislocation creep flow laws61 (see Supplementary Table 2 for details), σij the deviatoric stress components, µ the shear modulus, $$\frac{{{\mathrm{D}}\sigma _{ij}}}{{{\mathrm{D}}t}}$$ the objective co-rotational time derivative of the deviatoric stress components and χ the plastic multiplier when satisfying the Drucker–Prager plastic yielding condition:

$$\sigma _{{\mathrm{II}}} = \sigma _{{\mathrm{yield}}},$$
(14)

where σII is the second invariant of the deviatoric stress tensor and σyield the plastic strength solved as:

$$\sigma _{{\mathrm{yield}}} = C + P\sin \left( {\varphi _{{\mathrm{dry}}}} \right)\;(1 - \lambda _{{\mathrm{fluid}}}),$$
(15)

where C is the cohesion, φdry the internal friction angle for dry rocks and λfluid the pore fluid pressure factor. The latter is calculated according to the presence (or not) of fluid markers, which is solved by considering fluid hydration, dehydration and transport processes in the experiments. For details on the fluid implementation, the reader is referred to refs. 18,62.

### Internal free surface and surface processes

In the numerical experiments, the surface topography is calculated as an internal free surface by using a low-viscosity layer to minimize shear stresses along this major rheological boundary27. According to ref. 26, the applied sticky-air method is valid as long as the top of the lithospheres acts as a traction-free surface on isostatic timescales, which is defined as:

$$C_{{\mathrm{isost}}} \ll 1\infty ,$$
(16)

with

$$C_{{\mathrm{isost}}} = \frac{3}{{16{\uppi}^3}}\left( {\frac{L}{{h_{{\mathrm{st}}}}}} \right)^3\frac{{\eta _{{\mathrm{st}}}}}{{\eta _{{\mathrm{relax}}}}},$$
(17)

where L is the characteristic length scale of the model, hst and ηst the thickness and viscosity of the sticky-air layer and ηrelax the viscosity controlling the relaxation. In our experiments, investigated forearc topography is mostly controlled by lithospheric deformation because of the presence of the underlying slab. Thus, ηrelax is here given by ηlithosphere. In addition, by considering subduction dynamics and associated mantle corner flow, L is usually considered as corresponding to the height of the model box. Accordingly, Cisost = 4.84 × 10−5 (for hst = 10 km, ηst = 1 × 1018 Pa s and ηlithosphere = 1 × 1024 Pa s), which implies negligible stresses exerted on the surface topography. The low-viscosity layer is defined as air or water, depending on its location from the prescribed sea level (y = 10 km). Changes in the surface topography are controlled by the mechanical transport and surface processes through the conversion of rock markers to air/water (i.e. erosion) and vice versa (i.e. sedimentation). These vertical variations are then calculated by applying the following equation at the surface:63

$$\frac{{\partial y_{{\mathrm{surf}}}}}{{\partial t}} = v_y - v_x\frac{{\partial y_{{\mathrm{surf}}}}}{{\partial x}}\, - v_{{\mathrm{sedim}}} + v_{{\mathrm{erosion}}},$$
(18)

where ysurf is the y coordinate of the surface, vx and vy the horizontal and vertical velocity components of the Stokes velocity field at the surface and verosion and vsedim the global erosion and sedimentation rates, respectively, defined as

verosion = 0.3 mm year−1 and vsedim = 0 mm year−1 for y < 10 km,

verosion = vsedim = 0 mm year−1 for y > 10 km.

Note, however, that an increased erosion and sedimentation rate (=1 mm year−1) is applied to regions with steep surface slopes (i.e. >17°) for smoothing the topographic surface. This is particularly relevant for the offshore forearc domain where the increased sedimentation rate counterbalances the absence of global sedimentation rate prescribed in our experiments. Newly formed sedimentary rocks are labelled as terrigenous sediments and display the same properties than the pelagic sediments (Supplementary Table 2).

### Numerical set-up

The computational domain measures 1500 × 200 km in the x and y direction, respectively (Supplementary Fig. 2a) and is discretized using an Eulerian grid of 1467 × 271 nodes with variable grid spacing. This allows a grid resolution of 0.5 × 0.5 km in the vicinity of the plate boundary (i.e. the area subjected to the largest deformation) and of 2.0 × 1.5 km elsewhere. Additionally, ~8 millions of randomly distributed Lagrangian markers are initially prescribed for advecting material properties and computing water release, transport and consumption. This number may vary during the experiment, notably depending on dehydration/hydration processes. The initial set-up for an ocean-continent subduction zone is designed with a 30-km-thick overriding continental crust composed of 15 km of felsic upper crust and 15 km of mafic lower crust and a 7.5-km-thick subducting oceanic crust made up of 0.5 km of pelagic sediments, 2 km of hydrated basaltic crust and 5 km of gabbroic crust (Supplementary Fig. 2b). A temperature threshold of 1200 °C is used to distinguish the underlying lithospheric mantle from the asthenosphere. To initiate subduction, the oceanic crust is initially underthrusted below the continental margin and a 10-km-thick weak zone is prescribed at the interface between the two plates. The convergence between the two domains is defined by prescribing a fixed convergence condition region belonging to the subducting oceanic lithosphere (e.g. 5 cm year−1 for the reference model sed5.0; Supplementary Fig. 2a). The velocity boundary conditions are free slip for the left, right and upper boundaries, while the lower boundary is open to ensure mass conservation in the computational domain. As described above, an internal free surface is prescribed at the top of the oceanic and continental lithospheres, allowing to model the topography, which is initially prescribed at the plate boundary as a continuous slope from y = 12 km (i.e. 2000 m below the sea level) at the trench to y = 8 km (i.e. 2000 m above the sea level) at the continental margin (Supplementary Fig. 2b). Note that y coordinates are here indicated from the top of computational domain (i.e. y = 0 km), while in the main text, model topography and depth are expressed from the sea level (i.e. y = 10 km).

The thermal structure of the oceanic lithosphere is calculated by applying a half-space cooling age model from 10 kyr (x = 0; i.e. simulating a mid-oceanic ridge on the left boundary of the computational domain) to 53 Myr (x = 854 km; i.e. corresponding to initial location of the subduction zone). To limit the size of the computational domain, the cooling of the oceanic lithosphere is prescribed as 10 times faster for 0 ≤ x ≤ 200 km. This high cooling zone is located at ~600 km away from the subduction zone, which allows to avoid any thermal or mechanical effect on modelled forearc dynamics. A geothermal gradient of ~15° km−1 down to 90 km is defined for the continental lithosphere. Below, the asthenospheric geothermal gradient is 0.5° km−1.

## Data availability

Output files from numerical experiments presented in this study and associated MATLAB codes are accessible as a Source Data file [https://doi.org/10.5281/zenodo.3697463].

## Code availability

The numerical code presented in this study is available from the corresponding author or from the main code developer (taras.gerya@erdw.ethz.ch) upon reasonable request.

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## Acknowledgements

This study was funded with an IDEX-USPC research chair grant 16C538 and was partly supported by IdEx Université de Paris ANR-18-IDEX-0001. Numerical simulations were performed on ETH cluster Euler. Special thanks are due to Michael Bostock for the fruitful discussions. This is IPGP contribution #4125.

## Author information

Authors

### Contributions

S.A. conceived the original idea, T.G. designed the 2D thermo-mechanical code, A.M. elaborated the numerical study together with S.A. and T.G. and A.M. performed all the numerical experiments and interpreted the results, A.M., S.A., T.G., R.L., M.S. and R.G. discussed the results and interpretations and participated in writing the paper.

### Corresponding author

Correspondence to Armel Menant.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Communications thanks Fabio Crameri and the other, anonymous, reviewer for their contribution to the peer review of this work. Peer reviewer reports are available.

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Menant, A., Angiboust, S., Gerya, T. et al. Transient stripping of subducting slabs controls periodic forearc uplift. Nat Commun 11, 1823 (2020). https://doi.org/10.1038/s41467-020-15580-7

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