Topography of the Overriding Plate During Progressive Subduction: A Dynamic Model to Explain Forearc Subsidence

Abstract

Overriding plate topography provides constraints on subduction zone geodynamics. We investigate its evolution using fully dynamic laboratory models of subduction with techniques of stereoscopic photogrammetry and particle image velocimetry. Model results show that the topography is characterized by an area of forearc dynamic subsidence, with a magnitude scaling to 1.44–3.97 km in nature, and a local topographic high between the forearc subsided region and the trench. These topographic features rapidly develop during the slab free-sinking phase and gradually decrease during the steady state slab rollback phase. We propose that they result from the variation of the vertical component of the trench suction force along the subduction zone interface, which gradually increases with depth and results from the gradual slab steepening during the initial transient slab sinking phase. The downward mantle flow in the nose of the mantle wedge plays a minor role in driving forearc subsidence.

Key Points

• Three-dimensional dynamic analogue subduction models are used to study time-evolving topography of overriding plate
• Forearc topographic subsidence rapidly develops during slab free-sinking phase and decreases during steady state slab rollback phase
• Trench suction at subduction interface is predominantly responsible for the transient forearc subsidence

1 Introduction

The origin, evolution, and spatial variability of topography at subduction zones have been studied with geodynamic models for more than two decades (Bonnardot, Hassani, & Tric, 2008; Buiter et al., 2001; Guillaume et al., 2010; Gvirtzman & Nur, 2001; Hampel & Pfiffner, 2006; Hassani et al., 1997; Husson et al., 2012; Martinod et al., 2013, 2015; Schellart & Spakman, 2015; Yang et al., 2016; Zhong & Gurnis, 1992, 1994). Topography shapes the free top surface of the lithosphere and contains important information about the dynamics of the tectonic plates and the sublithospheric mantle. For example, dynamic topography is caused by the vertical movement of the lithosphere in response to its viscous coupling with the underlying sublithospheric mantle. It is different from isostatically supported topography generated by isostatic equilibrium (e.g., crustal thickness variations) and has instead been ascribed to the vertical component of mantle flow below the plates (Boschi et al., 2010; Braun, 2010; Coblentz & Karlstrom, 2011; Flament et al., 2013; Gurnis et al., 1998; Hager et al., 1985; Lithgow-Bertelloni & Silver, 1998; Pysklywec & Mitrovica, 1998; Saleeby & Foster, 2004). Another important form of topography results from the tectonic forces in the plates and at the plate boundaries, such as subduction zones. Investigating topography around subduction zones can provide quantitative and conceptual insights into the interaction between the plates, the slabs, mantle flow, and the associated stresses. As the present-day topography is only transient, geodynamic modeling can be an effective tool to study the evolution of topography back in time and to gain insights into the driving mechanisms of topography formation and evolution.

A number of geodynamic modeling studies have previously been conducted to investigate the evolution of subduction-associated topography during progressive subduction (Cattin et al., 1997; Hampel & Pfiffner, 2006; Hassani et al., 1997; Husson et al., 2012; Zhong & Gurnis, 1994), during slab detachment (Bonnardot, Hassani, & Tric, 2008; Buiter et al., 2001; Gvirtzman & Nur, 2001; Pysklywec & Mitrovica, 1998), or during progressive slab sinking after slab detachment (Braun, 2010; Flament et al., 2013; Gurnis et al., 1998; Hager et al., 1985; Schellart & Spakman, 2015; Yang et al., 2016). In earlier analogue subduction models investigating topography, an overriding plate was either excluded (Husson et al., 2012) or included, but in that case there was either a large physical gap between the two plates (Guillaume et al., 2013, 2010) or convergence in the models was kinematically imposed with a piston to sustain subduction (Luth et al., 2010; Martinod et al., 2013; Sokoutis & Willingshofer, 2011). Such models provide new insights that can help understand the geodynamics of topography associated with subduction. However, the lack of an overriding plate or the large physical gap between the plates prevented the existence of a subduction zone interface with proper dimensions and rheological scaling. Therefore, to study the effect of forces acting at the subduction zone interface on topography, we used a modeling approach that is based on recently developed buoyancy-driven analogue models of subduction incorporating an overriding plate and a realistic interplate coupling (Chen et al., 2015, 2016; Duarte et al., 2013, 2015; Meyer & Schellart, 2013). This modeling approach allows one to investigate the evolution of topography in the forearc region of subduction zones in a fully dynamic framework.

In this work, we have conducted fully dynamic analogue models of time-evolving subduction in three-dimensional space (no externally imposed velocity or force boundary condition). In order to capture and record the progressive subduction process, we have used a stereoscopic particle image velocimetry (sPIV) system that can simultaneously track surface topography, surface deformation, and flow in the sublithospheric mantle. In our models, topographic subsidence was observed in the forearc lithosphere and the mantle flow velocity field in the mantle wedge was mapped to determine if any causal link could be established. Based on an analysis of forces acting on the forearc lithosphere and a comparison of our model results with previous geodynamic modeling studies, we provide new insights into the mechanism that drives subsidence in the forearc region of the overriding lithosphere at subduction zones.

2 Methods

The experiments were carried out in a transparent square tank (Figure 1). The tank was filled with low-viscosity glucose syrup to a depth of 13.3 cm to simulate the viscous sublithospheric upper mantle, such that the rigid tank bottom represents the 670 km discontinuity. Two mixtures of high-viscosity silicone putty and iron powder in different proportions were used to represent the subducting oceanic lithosphere and an overriding lithosphere and were placed on the surface of the glucose syrup. The overriding plate was neutrally buoyant with respect to the upper mantle, whereas a density difference of 100 kg/m³ between the subducting plate and the sublithospheric upper mantle was used to simulate the negative buoyancy of the slab (Cloos, 1993). The viscosity ratio between the subducting plate and the upper mantle was 188–203, which falls in the suggested range of ~100–500 as proposed in earlier subduction modeling work (Funiciello et al., 2008; Ribe, 2010; Schellart, 2008). To achieve a weak coupling at the subduction zone interface, the top surface of the subducting plate was lubricated with a mixture of petrolatum and paraffin oil (Duarte et al., 2013), which has a relatively low effective viscosity of ~0.8–1.5 Pa s and low yield stress. It results in a reasonable viscosity ratio (191–383) between the sublithospheric upper mantle (286–306 Pa s) and the weak lubricant material. The weak lubricant has proven realistic in simulating the subduction zone interface from a comparison between dynamical subduction experiments and natural observations (Duarte et al., 2015).

Figure 1

Three-dimensional configuration of experimental subduction setup. This setup of subduction includes a free high-viscosity subducting plate, a free/fixed high-viscosity overriding plate, a low-viscosity sublithospheric upper mantle, and a weak interplate mechanical coupling. The experiments have been conducted in a transparent plexiglass tank of 100 cm long by 100 cm wide, which has been filled with a 13.3 cm deep layer of glucose syrup simulating the viscous sublithospheric upper mantle, such that the rigid tank bottom represents the 670 km discontinuity. The thickness of the subducting plate and overriding plate are 2.0 cm, representing 100 km thick oceanic lithosphere, and 1.5 cm, representing 75 km thick lithosphere, respectively. The PIV system consists of a laser and three PIV high-resolution cameras. Two PIV cameras were located above the tank to map the progressive evolution of topography of the overriding plate, and one PIV camera was located on the side to map the progressive mantle flow simultaneously. Two normal cameras (one above and another on the side) were used to record the subduction kinematics. The red line across the center of the overriding plate indicates the position of the overriding plate topography profiles in Figure 3.

Both the trailing edges and the lateral edges of the subducting plate were free, representing mid-oceanic ridges and strike-slip faults that offer negligible resistance to plate motion. The lateral edges of the overriding plate were free, while the trailing edge was either free or fixed, representing a small and relatively mobile plate or a large, relatively immobile plate, respectively. Subduction initiation was generated by manually pushing down an ~3–5 cm long slab segment at the tip of the subducting plate. Thereafter, the subduction process was self-controlled due to the negative buoyancy of the subducted slab, which is the only driving force in our experiments. Our experiments were scaled to nature assuming that the sinking velocity of the slab can be approximated by the Stokes velocity (please refer to Duarte et al., 2013 and Jacoby, 1973 for the scaling procedure and factors used in this type of experiments). In the models, 1 cm corresponds to 50 km in nature, 1 s corresponds to 8300 years in nature, and 0.01 mm/s is equivalent to 0.6 cm/yr in nature.

In our experiments we scale for density contrasts in relation to the density of the sublithospheric upper mantle. For such scaling procedure, a topographic correction factor should be introduced to scale the topography developed in the models to nature (Schellart & Strak, 2016). Consequently, we can calculate the scaled topography in nature (h^p) using

(1)

where l^p/l^m is the length scale ratio, h^m is the topography formed in the analogue experiments, and C_Topo is the topographic correction factor

(2)

where is the density of the sublithospheric upper mantle in models and is the density of the sublithospheric upper mantle in nature. In our experiments the density of glucose syrup representing the sublithospheric upper mantle is 1,428 kg/m³ and in nature we choose the average density of the sublithospheric upper mantle, which is 3,220 kg/m³, giving C_Topo = 0.44. Considering that the length scale ratio l^p/l^m = 5.0 × 10⁶ and C_Topo = 0.44 in our models, 1 mm of topography in the experiments should represent 2.22 km of topography in nature.

To monitor simultaneously the overriding plate topography and the upper mantle flow occurring in the mantle wedge during progressive subduction, a stereoscopic particle image velocimetry (sPIV) technique was used (Figure 1). The sPIV technique can monitor the subduction-induced mantle flow in the mantle wedge during progressive subduction by using a laser sheet that illuminates fluorescent particles that are homogeneously distributed throughout the mantle fluid. Please refer to Strak and Schellart (2014) for detailed technical information about this type of recording. Furthermore, with a stereoscopic photogrammetry technique we can compare top view photographs to calculate the overriding plate topography. Two high-resolution PIV cameras were installed above the model with an angle of ~30° between them and very light white powder was seeded on the top surface of the overriding plate to allow mapping the overriding plate topography. Another high-resolution PIV camera was located on the side to map the cross-sectional velocity field of the subduction-induced mantle flow occurring in the mantle wedge of the subduction zone along the central plane. To allow computing the cross-sectional mantle flow velocity field we used an interval time, defined as one loop (L). Two normal cameras, one on top and another on the side, were also used to track the kinematics of the subducting and overriding plates using white passive tracers.

3 Results

3.1 Topography of Overriding Plate

During the early free sinking phase of subduction (defined as the early subduction phase during which the negatively buoyant slab is sinking through the sublithospheric upper mantle before the slab tip starts interacting with the upper-lower mantle discontinuity), the topography of the overriding plate was characterized by an elongated area of subsidence striking parallel to the trench and separated from the trench by a distance of 1–5 cm (Figures 2a and 2b and 2e and 2f). The magnitude of the maximum depression increased with progressive subduction, reaching 1.35–1.79 mm (scaling to 3.00–3.97 km) in the center of the subduction zone (see Figures 3a and 3b, 3e and 3f, and 4b and 4c). Closer to the trench, the topography was still negative but characterized by a trench-parallel ridge with a local relative high. After a phase of interaction between the slab tip and the rigid bottom discontinuity, subduction reached a steady state rollback phase during which the slab geometry, the trench kinematics, and plate kinematics remained relatively constant (Figures 3c and 3d, 3g and 3h, and 4b and 4c). During this phase the magnitude of the depression progressively decreased to 0.65–0.80 mm (scaling to 1.44–1.78 km) (Figures 2c and 2d, 2g and 2h, and 4b and 4c). During the entire subduction process, the rest of the overriding plate, including the backarc region, had a relative flat topography. The horizontal position of the maximum depression in the forearc region was always located within 5 mm (scaling to 25 km) of the deepest point of contact between the subducting and overriding plates at the subduction zone interface (Figure 3). Furthermore, the local ridge in between the depression and the trench became progressively less pronounced during the steady state rollback phase and almost disappeared in the final stages of subduction (Figures 3c and 3d and 3g and 3h).

Figure 2

Topographic evolution of a free/fixed overriding plate during progressive subduction at (a, b and e, f) two different stages of the slab free-sinking phase, during which the slab is sinking freely in the upper mantle, and (c, d and g, h) two different stages of the steady state slab rollback phase, during which the slab is rolling back in a stable fashion. “L” is an abbreviation of “Loop.” The numbers after L indicate different loop numbers. The interval time of each loop is constant, 48 s for free overriding plate models and 20 s for fixed overriding plate models. Note that we define the reference point for elevation (z = 0 mm) at a point close to the far-field edge of the overriding plate. In the color bar, red, orange, and yellow (positive) indicate positive topography (uplift), while blue (negative) indicates negative topography (depression). The red dashed lines indicate the positions of the topographic profiles shown in Figure 3.

Figure 3

Evolution of free/fixed overriding plate topography profile (top panels) and corresponding mantle flow velocity field (bottom panels) across the center of the overriding plate at four different stages. In the color bar red (positive) indicates upward flow in the sublithospheric mantle, whereas blue indicates downward flow. For the position of the topography profiles please refer to Figures 1 and 2. L is an abbreviation of Loop. The numbers after L indicate different loop numbers. The interval time of each loop is constant, 48 s for free overriding plate models and 20 s for fixed overriding plate models. The red dashed line and red zone indicate the approximate position of maximum subsidence in the forearc region of the overriding plate, while the blue zone indicates the approximate position of the trench.

Figure 4

(a) Schematic diagram of interaction of plates and subduction-induced poloidal flow in the mantle wedge. Red arrows indicate the direction of subduction-induced mantle flow in the mantle wedge. d₁ is the topography at a point close to the far-field edge of the overriding plate, while d₂ is the maximum depression in the forearc region of the overriding plate. Note that we define the reference point for elevation (z = 0 mm) at a point close to the far-field edge of the overriding plate. (b,c) Evolution of kinematics of subduction and maximum depression (d = d₂ − d₁) in the forearc region of the overriding plate for free overriding plate (Figure 4b) and fixed overriding plate (Figure 4c). Subducting plate and trench velocities are the velocities of subducting plate (trenchward is positive) and trench (retreat is positive) moving with progressive subduction, respectively, while the subduction velocity is the rate at which the subducting plate submerges into the sublithospheric upper mantle. Its magnitude can be calculated from the sum of the subducting plate velocity and trench velocity. The overriding plate deformation velocity is the variation in total length of the overriding plate in the trench-normal direction divided by a time interval (trench-normal extension is positive). Red arrow, blue arrow, and green arrow indicate the maxima of trench-normal subduction velocity, trench-normal subducting plate velocity, and subsidence during progressive subduction. L is an abbreviation of Loop. The numbers after L indicate different loop numbers. The interval time of each loop is constant, 48 s for free overriding plate models and 20 s for fixed overriding plate models. The variation of the trench suction force along the subduction zone interface for (d) the slab free-sinking phase (when the slab dip angle progressively increases) and (e) the steady state slab rollback phase (when the slab dip angle remains approximately constant). The two schematic drawings were inspired from Hassani et al. (1997).

3.2 Subduction-Induced Mantle Flow in the Mantle Wedge

In the center of the subduction zone, the slab sinking and rolling back in the sublithospheric upper mantle forced the mantle wedge material to flow in a poloidal fashion (Figure 3). This poloidal cell had a downwelling component in the mantle wedge just above the top surface of the slab, as a result of viscous drag by the sinking slab. The downwelling velocity reached ~7 mm/min (scaling to 7 cm/yr) during the free sinking phase and ~3 mm/min (scaling to 3 cm/yr) during the steady state phase (Figure 3), which correlates well with the velocities attained by the subducting plate during these phases (Figures 4b and 4c). We also observed upward mantle flow in the far backarc mantle wedge. This upwelling was stronger during the free sinking phase with a maximum velocity of up to ~2 mm/min (scaling to 2 cm/yr), and it was located at ~75–175 mm (scaling to 375–875 km) from the trench (Figure 3a). The velocity magnitude thereafter decreased during the steady state phase, and the upwelling migrated farther away from the trench as the poloidal cell became elongated horizontally as a response to the slab draping over the 670 km discontinuity (Figures 3c and 3d and 3g and 3h). We note that the vertical velocities of the mantle wedge poloidal flow were higher during the free sinking phase and lower during the steady state phase, generally, in good correlation with the subducting plate velocity (Figures 4b and 4c).

4 Discussion

4.1 Origin of the Topographic Subsidence in the Forearc Region

An important observation concerns the horizontal position of the maximum depression, which corresponds with that of the deepest contact point between the subducting and overriding plates at the subduction zone interface (Figure 3). This observation will help us to differentiate between the different possible driving forces responsible for the forearc subsidence. We propose that there are three potential candidates to explain the subsidence formation. Our subduction models are buoyancy driven as in nature and have a realistic subduction interface. Therefore, the three forces acting on the forearc region and likely leading to the forearc topographic subsidence in the models should be comparable in natural subduction settings. These three forces are the shear force at the subduction zone interface, the trench suction force (normal to the subduction zone interface), and the viscous drag force induced by the vertical movement of the mantle flow in the mantle wedge region (Figure 4a).

In several previous works using two-dimensional numerical subduction models, the influence of the subduction zone interface shear force on the forearc topography has been investigated, through varying the coefficient of friction at the subduction zone interface (Buiter et al., 2001; Cattin et al., 1997; Hampel & Pfiffner, 2006; Hassani et al., 1997; Zhong & Gurnis, 1994). Some modeling studies show that increasing the coefficient of friction leads to an increase in forearc depression (Buiter et al., 2001; Hampel & Pfiffner, 2006; Zhong & Gurnis, 1994), whereas others show an opposite relationship (Cattin et al., 1997; Hassani et al., 1997). In our models, an internal subsidence area, located at 1–5 cm away from the trench, has been observed particularly during the slab free-sinking phase. However, this transient subsidence cannot be explained by the shear force at the subduction zone interface.

We have quantified the stress that drives dynamic subsidence in our models. To get the maximum vertical stress for subsidence, the forearc subsidence map has been used, for which the maximum depth of the depression has been quantified, which is ~1.5 mm (Figure 3). The density contrast between the sublithospheric upper mantle (1,428 kg/m³) and air (1.225 kg/m³) is 1,426.775 kg/m³, while the gravitational acceleration is 9.8 m/s². From the product of the maximum depression depth, density contrast, and gravitational acceleration, we calculate the maximum vertical stress for forearc dynamic subsidence in our models, which is of the order 20.97 Pa. We can also estimate the shear stress at the subduction zone interface. The effective flow stress of the lubrication material filled in the subduction channel of our models is 1.0–1.5 Pa at a shear strain rate of 0.1 s⁻¹ (Duarte et al., 2014). We assume that the thickness of the subduction channel in our models is ~1 mm (Duarte et al., 2013). The average subduction velocity in our models is ~0.06–0.13 mm/s (Figure 4), giving an average shear rate in the subduction channel of 0.06–0.13 s⁻¹, and the subduction dip angle is approximately 30–45°. From this we can calculate that the magnitude of the vertical component of the shear stress at the subduction zone interface is 0.54–1.25 Pa, which is much less than the estimated vertical stress for forearc dynamic subsidence (20.97 Pa). This comparison indicates that the shear force at the subduction zone interface plays only a minor role in driving the internal transient forearc subsidence. Nevertheless, the shear force at the subduction zone interface applies a bending moment to the overriding plate, which would induce a more gradual increase in depression in the overriding plate toward the trench, as observed in the experiments (Figures 3d and 3h).

The second force possibly causing the forearc topographic subsidence is trench suction, which is normal to the subduction zone interface. This force has been proposed by Shemenda (1993) using analogue models of subduction, in which it was described as hydrostatic suction that prevents the plates from being separated, and it was suggested to provide a driver for backarc extension. In our models, trench suction also plays a role in maintaining the two plates in contact. Furthermore, the magnitude of this force would correlate with the level of resistance to translation of the overriding plate. Specifically, the magnitude of this force would be related to the velocity of the slab in the direction perpendicular to the subduction zone interface during progressive slab rollback (Figures 4d and 4e). Moving a longer distance implies larger trench suction. During the slab free-sinking phase, we observe a progressive increase of the slab dip angle with progressive subduction (Figures 3a and 3b and 3e and 3f). An increase in the slab dip angle results in a gradual increase of the vertical component of the trench suction toward the lower part of the interface (Figure 4d), thereby causing a relatively deep topographic depression in the forearc region, with the maximum depth corresponding to the lowest contact point of the interface (Figure 3). In contrast, during the steady state slab rollback phase the vertical component of the trench suction is nearly the same along the subduction zone interface because of the steady state slab rollback velocity along the interface and the relatively constant slab dip angle (Figure 4e). This results in minor variations in the vertical component of the trench suction along the interface, thereby generating a topographic subsidence in the forearc region that is spatially more constant with respect to the slab free-sinking phase. Therefore, during the steady state phase the trench suction force, like the shear force at the subduction zone interface, will mostly bend the overriding plate downward at the trench, thereby promoting a forearc topographic subsidence that gradually increases toward the trench.

We have confirmed that the suction force at the subduction zone interface is predominantly responsible for the transient forearc subsidence. This indicates that the vertical force for the dynamic subsidence and vertical component of trench suction at the subduction zone interface have approximately equal magnitudes. We can roughly estimate the trench suction force from quantifying the force that drives dynamic subsidence. In our models, the width (perpendicular to trench) of the depression is ~0.05 m (Figure 2), and the length of the depression is ~0.15 m. The average depth of the maximum depression is ~0.001 m. So the total volume of the depression is ~3.75 × 10⁻⁶ m³. By multiplying the volume of the depression by the density contrast of 1426.775 kg/m³ and the gravitational acceleration, we get an average vertical force that drives the depression in our models of 0.052 N, which is also the approximate magnitude of the suction force. Furthermore, in our models the width and thickness of the overriding plate are 0.15 m and 0.015 m, respectively, and we assume that the slab dip angle is approximately 30–45°. This gives a subduction zone interface surface area of 3.18–4.50 × 10⁻³ m². The total shear force results from multiplying the shear stress (1.0–1.5 Pa, given above) by the surface area of the subduction zone interface. The vertical component of the total shear force at the interface is then 0.0016–0.0048 N, which is about an order of magnitude less than the trench suction force.

We can also estimate the negative buoyancy force of the subducting slab and then compare it with the suction force. The density contrast between the slab and lithospheric upper mantle in our models is 100 kg/m³. The width and thickness of the slab are 0.15 m and 0.02 m, respectively. We will assume that there is a 10 cm long subducting slab. This gives a total negative buoyancy force of the subducting slab of 0.29 N, compared with the estimated vertical suction force (0.052 N). Considering that the driving force in our models only comes from the negatively buoyant subducting slab, our model results indicate that some 17.8% of the negative buoyancy of the slab is used to drive the forearc dynamic subsidence during the transient slab free-sinking phase.

The last force to be discussed as being a potential cause for the formation of overriding plate topography is the force generated by vertical movement of mantle flow in the mantle wedge. Previous natural observations and modeling studies have demonstrated that the vertical mantle flow can cause a long-wavelength, low-amplitude topography, which is referred to as dynamic topography (Gurnis et al., 1998; Hager et al., 1985; Lithgow-Bertelloni & Silver, 1998; Pysklywec & Mitrovica, 1998). In our models, an area of maximum downward mantle velocity has always been observed in the mantle wedge very close to the downgoing slab within 10 cm, scaling to 500 km, from the trench (Figure 3). Previous analogue and numerical subduction models have shown that the corner flow induced by slab rollback in the mantle wedge can generate a pressure gradient with higher suction in the nose of the mantle wedge and progressively lower away from it (Hall et al., 2000; Kneller & van Keken, 2007, 2008; MacDougall et al., 2014). Such suction produced by the vertical component of the subduction-induced mantle flow should also exist in our models and would thus influence the forearc topography by a drag down effect. However, this drag force should play a minor role in the formation of the forearc subsidence. This is because in our experiments the maxima of the forearc subsidence were observed above the deepest contact point between the subducting and overriding plates at the subduction zone interface (Figures 3b and 3f) rather than within 5–10 cm from the trench where the downward mantle wedge velocity is maximum.

4.2 Comparison With Previous Studies

4.2.1 Analogue Modeling

Several analogue models of subduction have been previously conducted to investigate the topography around subduction zones, in which the overriding plate was either excluded (Husson et al., 2012) or included, but the two involved plates were separated by a thin layer of glucose syrup, with a distance up to 20 mm (scaling to ~120 km for their models) at the surface between the two plates (Guillaume et al., 2013, 2010). In the work of Husson et al. (2012), the model setup consisted of a free or fixed subducting plate but without an overriding plate. Because of the lack of an overriding plate, the surface of the glucose syrup would represent the Earth's surface and the topography of this surface was scanned. Their model results showed that the forearc region is depressed to a depth of up to 0.20 mm. This subsidence corresponds to a dynamic topography induced by vertical motion of the subduction-induced mantle flow. Considering the similar model setup adopted in their models and our models, except for the lack of an overriding plate in their models, and that the maximum subsidence depth in their models (0.2 mm) is far shallower than that in our models (0.65–1.79 mm), these results support our analysis that the force generated by the downward motion of mantle flow in the mantle wedge makes a secondary contribution to the observed forearc topographic subsidence. In the work of Guillaume et al. (2013), a topographic profile parallel to and at ~15 mm away from the trench showed that there is an area of subsidence existing in the middle of the overriding plate. This is comparable with our model result showing a subsidence observed at an average distance of 30 mm away from the trench. Some minor difference between the two studies is probably because in their models there is a window in the middle of the slab but not in our models. Furthermore, in our models the subducting plate is free while in their models the far-field edge of the subducting plate is fixed.

4.2.2 Numerical Modeling

A number of numerical models have previously investigated the parameters that potentially affect the overriding plate topography. These parameters include the coefficient of friction at the subduction zone interface (Bonnardot, Hassani, Tric, Ruellan, et al., 2008; Buiter et al., 2001; Cattin et al., 1997; Hampel & Pfiffner, 2006; Hassani et al., 1997; Zhong & Gurnis, 1992, 1994), the variation of the slab dip angle (Brink, 2005; Hassani et al., 1997), the density contrast between the lithosphere and the asthenosphere (i.e., the age of the lithosphere) (Bonnardot, Hassani, Tric, Ruellan, et al., 2008; Buiter et al., 2001; Hampel & Pfiffner, 2006; Hassani et al., 1997; Zhong & Gurnis, 1992, 1994), the asthenosphere viscosity (Bonnardot, Hassani, & Tric, 2008; He, 2012), the rheology of the subducting plate (Bonnardot, Hassani, & Tric, 2008; Zhong & Gurnis, 1992, 1994), the trenchward velocity of the overriding plate (Buiter et al., 2001; Hampel & Pfiffner, 2006), and the thickness of the overriding plate (He, 2012). Probably, the first numerical subduction modeling studies in a dynamically self-consistent manner to investigate the topography at subduction zones were published more than two decades ago (Zhong & Gurnis, 1992, 1994). In these subduction models, a fault represents the interface between the subducting plate and the overriding plate and a viscous slab subducts into a viscous medium. This setup is similar to that of our models, except that they used a two-dimensional spatial setup (and our models are three-dimensional) and a prescribed interface geometry (which is self-determined in our models). In the work from Zhong and Gurnis (1992, 1994), the backarc region developed a topographic subsidence with a depth of up to ~1.5 km, typically ~150 km away from the trench, when the plates have a Newtonian rheology. They proposed that it was caused by the mantle flow in the backarc extension region. In addition, in their models a subsidence with a ~3 km depth was observed at the trench. This is comparable with and consistent with our model results showing a subsidence depth of 1.0–1.72 mm at the trench, scaling to 2.22–3.82 km in nature. Their model results implied that two main parameters, namely, the age of the lithosphere and the shear stress at the subduction zone interface, have a significant influence on the overriding plate topography. The impact of these two parameters on the overriding plate topography has been tested later (Bonnardot, Hassani, Tric, Ruellan, et al., 2008; Buiter et al., 2001; Cattin et al., 1997; Hampel & Pfiffner, 2006; Hassani et al., 1997). In these models, the age of the lithosphere, represented by the density contrast between the lithosphere and the asthenosphere, and the coefficient of friction along the subduction zone interface have been varied. The observed topographic subsidence in the forearc region was comparable with that in our models. For example, in the work of Hassani et al. (1997), when the density contrast is 100 kg/m³, which is the same as that in our models, an area of topographic subsidence was observed in the forearc region. In their models, the total convergence amount since subduction initiation was only 400 km, indicating that the slab had not yet reached the 670 km discontinuity. Therefore, their models can only be compared with the slab free-sinking phase in our models. They ascribed the forearc topographic subsidence of the overriding plate to the hydrostatic suction (referred to as trench suction in our models) at the subduction zone interface. This explanation for the formation of topographic subsidence in the forearc region is in agreement with our present analysis. Furthermore, in the work of Buiter et al. (2001), a velocity of 4 cm/yr was imposed on a subducting plate with a thickness of 25 km. The model results showed a subsidence with a depth of up to 4 km in the forearc region, which the authors ascribed to slab rollback. This is in general agreement with the findings presented in this study. In addition, Buiter et al. (2001) found that an increase in the density contrast between the lithosphere and the asthenosphere deepens the forearc subsidence to a maximum of 6 km. Such subsidence depths are comparable to the subsidence depths observed in the experiment described in this work (1.44–3.97 km).

5 Conclusions

In our models, two types of negative topography were observed in the forearc lithosphere: (1) a gradual increase in subsidence toward the trench and (2) superimposed on this first topographic signal a local depression striking parallel to the trench, which was most pronounced during the free sinking phase but gradually decreased during the steady state subduction phase. Through analyzing three forces acting on the forearc lithosphere and comparing our model results with previous investigations of overriding plate topography using geodynamic models, we conclude that the shear force and trench suction force control the first type (gradual, long wavelength) of forearc topographic subsidence, through bending the overriding plate at the trench. Furthermore, the downdip increase of the vertical component of the trench suction force along the subduction zone interface, caused by the progressive slab steepening during the free sinking phase, is the main driver in the formation of the forearc topographic depression. Finally, the vertical component of the subduction-induced mantle flow in the mantle wedge plays a minor role in driving the topographic subsidence observed in the forearc region of the overriding plate.

Acknowledgments

This project was supported by Discovery grants DP110103387 and DP120102983 from the Australian Research Council (ARC) awarded to W. P. S. Z. C. was supported by APA and IPRS scholarships from the Australian Government and by a JSPS Postdoctoral Fellowship. W. P. S. was supported by a Future Fellowship (FT110100560) from the ARC and a Vici fellowship from the Dutch Science Foundation (NWO). J. C. D. was supported by a DECRA fellowship from the ARC. J. C. D. also acknowledges FCT through project UID/GEO/50019/2013—Instituto Dom Luiz. We would like to thank two anonymous reviewers for their constructive comments that improved the manuscript, and we would like to thank the Editor Jeroen Ritsema for handling this manuscript. All data and methods necessary to understand, evaluate, replicate, and build upon the reported research are presented in the manuscript.