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Three-dimensional dynamic models of subducting plate-overriding plate-upper mantle interaction

Authors


Abstract

[1] We present fully dynamic generic three-dimensional laboratory models of progressive subduction with an overriding plate and a weak subduction zone interface. Overriding plate thickness (TOP) is varied systematically (in the range 0–2.5 cm scaling to 0–125 km) to investigate its effect on subduction kinematics and overriding plate deformation. The general pattern of subduction is the same for all models with slab draping on the 670 km discontinuity, comparable slab dip angles, trench retreat, trenchward subducting plate motion, and a concave trench curvature. The narrow slab models only show overriding plate extension. Subduction partitioning (vSP⊥ / (vSP⊥ + vT⊥)) increases with increasing TOP, where trenchward subducting plate motion (vSP⊥) increases at the expense of trench retreat (vT⊥). This results from an increase in trench suction force with increasing TOP, which retards trench retreat. An increase in TOP also corresponds to a decrease in overriding plate extension and curvature because a thicker overriding plate provides more resistance to deform. Overriding plate extension is maximum at a scaled distance of ~200–400 km from the trench, not at the trench, suggesting that basal shear tractions resulting from mantle flow below the overriding plate primarily drive extension rather than deviatoric tensional normal stresses at the subduction zone interface. The force that drives overriding plate extension is 5%–11% of the slab negative buoyancy force. The models show a positive correlation between vT⊥ and overriding plate extension rate, in agreement with observations. The results suggest that slab rollback and associated toroidal mantle flow drive overriding plate extension and backarc basin formation.

1 Introduction

[2] Subduction occurs along convergent plate boundaries involving a downgoing oceanic plate and an overriding plate that is oceanic or continental. During subduction, the overriding plate might experience shortening (e.g., Andes, Japan), extension (e.g., Lau basin, Mariana Trough, Aegean Sea), or remain relatively neutral (e.g. Java, Aleutians), while the subducted slab shows different geometries and kinematics [Jarrard, 1986]. It remains unclear what controls the different styles of backarc and forearc deformation observed on Earth and what drives such deformation. Thus far, numerous conceptual models have been proposed to explain overriding plate deformation at subduction zones, and different physical parameters have been put forward that might control it, including active diapirism in the mantle wedge below the backarc [Karig, 1971], basal shear tractions resulting from subduction-induced poloidal flow in the mantle wedge [e.g., Sleep and Toksöz, 1971; Toksöz and Hsui, 1978], motion of the overriding plate relative to the subduction zone trench [e.g., Jarrard, 1986], slab rollback/roll-forward and trench migration rate [e.g., Elsasser, 1971; Molnar and Atwater, 1978; Lonergan and White, 1997], slab age [Molnar and Atwater, 1978], subducting plate-overriding plate convergence rate [e.g., Somoza, 1998], and shear coupling along the subduction zone interface [e.g., Lamb and Davis, 2003]. The difficulty with the models from Sleep and Toksöz [1971] and Karig [1971] is that they predict backarc extension for all subduction zones, while numerous subduction zones have a neutral overriding plate or are characterized by overriding plate shortening (e.g., Sunda, Aleutians-Alaska, Kuril, Central America, South America, Makran). Furthermore, a recent global investigation of active subduction zones shows that from the remaining parameters mentioned above, all except trench migration rate have a negligible or low correlation with overriding plate deformation rate (|R| ≤ 0.25) [Schellart, 2008a]. Even for trench migration rate, which is most strongly correlated with overriding plate deformation rate, the correlation is only moderate (|R| = 0.63).

[3] To investigate the dynamics of subduction zones, and to investigate the impact of a slab on the sub-lithospheric mantle and/or on the overriding plate, many geodynamic models have been performed in the past using numerical and laboratory techniques. Thus far, many three-dimensional models either include a subducting plate [e.g., Kincaid and Olson, 1987; Schellart, 2004a, 2008b; Stegman et al., 2006, 2010; Funiciello et al., 2008; Goes et al., 2008; Di Giuseppe et al., 2009; Irvine and Schellart, 2012] or only an overriding plate [e.g., Hatzfeld et al., 1997; Gautier et al., 1999; Martinod et al., 2000; Schellart et al., 2002], but not both of them. There are fully dynamic two-dimensional models of progressive subduction with an overriding plate [e.g., Zhong and Gurnis, 1995; Capitanio et al., 2010] or without an overriding plate [e.g., Christensen, 1996] and two-dimensional models with kinematic boundary conditions [e.g., van Hunen et al., 2000; Billen and Hirth, 2007; van Dinther et al., 2010; Rodríguez-González et al., 2012]. Such 2-D models do not capture the three-dimensional nature of subduction zones that has been proposed to be of fundamental importance [e.g., Schellart et al., 2007, 2010]. There are also several 3-D models with both a subducting plate and overriding plate, but the models lack a time component [e.g., Billen et al., 2003; Govers and Wortel, 2005; Jadamec and Billen, 2010] and can therefore not study the progressive evolution of subduction.

[4] Three-dimensional subduction models with an overriding plate that do include a time component mostly use applied kinematic boundary conditions [e.g., Shemenda, 1993; Heuret et al., 2007; Guillaume et al., 2009; Druken et al., 2011; Boutelier et al., 2012]. In models that use a velocity or force boundary condition, the energy within the system is not conserved as energy is continuously being added to the system. To our knowledge, this added energy has not been quantified in laboratory models, and furthermore, it is unclear how much external energy (from the velocity/force boundary condition) is used to deform the overriding plate and how much internal energy (from the slab's potential energy) is used. In a fully dynamic subduction model without externally imposed velocity or force boundary conditions that has internal conservation of energy, all deformation is ultimately driven by the slab's negative buoyancy, and such a model is thus in a better position to quantify how much of this buoyancy force is used to drive overriding plate deformation.

[5] Previous three-dimensional fully dynamic subduction models with only a subducting plate show that slabs preferentially roll back for Earth-like settings [e.g. Kincaid and Olson, 1987; Schellart, 2004a, 2008b; Morra et al., 2006; Stegman et al., 2006; Schellart et al., 2007; Funiciello et al., 2008]. It remains unclear if slab rollback continues to operate with the inclusion of an overriding plate and how rollback velocity, and subduction kinematics in general, might be affected. Furthermore, it remains unclear how an overriding plate modifies the geometry of the slab, such as its dip angle and hinge curvature. A statistical analysis of the physical parameters of active subduction zones [Lallemand et al., 2005] shows that slab dip angle is correlated with the nature of the overriding plate (i.e., oceanic or continental plate). The contact area between subducting plate and overriding plate is generally larger with a continental overriding plate (due to the greater thickness of the continental plate), which would promote a gentle dipping slab through additional trench suction that acts against the negative buoyancy of the slab that promotes a steep slab [Lallemand et al., 2005]. Thickness of the overriding plate is thus thought to influence the slab dip angle.

[6] Here we present the results of fully dynamic three-dimensional models of progressive subduction, including a subducting plate and an overriding plate. These are generic subduction models that are particularly suitable to study and quantify the magnitude of the driving and resistive forces that operate during subduction. In this work, we focus on the force that is used to drive overriding plate extension. We further investigate the influence of an overriding plate and the influence of its thickness on the kinematics of subduction and on the geometry of the subducting slab (in particular, its dip angle and its plan-view curvature). We also investigate the evolution of the overriding plate strain field and strain rates during progressive subduction and how the deformation pattern and strain rates might vary with overriding plate thickness. The new models ultimately provide new insight into the driving mechanism of overriding plate deformation at subduction zones.

2 Model Setup

[7] The experimental models represent a 3-D subduction zone in a fully dynamic system, including both a subducting plate and an overriding plate. We use the thin viscous sheet approach to model the lithosphere, as has been adopted previously [e.g., Bird and Piper, 1980; Vilotte et al., 1982; England and McKenzie, 1982; England and Houseman, 1988], which assumes that over geological time (millions to tens of millions of years), the lithosphere's rheological response to stresses is dominantly viscous. A high-viscosity silicone oil-iron powder mix and a low-viscosity glucose syrup are used to model the lithosphere and the sub-lithospheric upper mantle, respectively (Figure 1). The dynamic (shear) viscosity of the syrup (ηUM) is of the order ~120 Pa⋅s, while that of the subducting plate (ηSP) and that of the overriding plate (ηOP) are of the order 2.4 × 104 Pa⋅s (Table 1). The silicone putty-iron powder mix is a visco-elastic material that only behaves in a viscous manner at experimental strain rates [Weijermars, 1986]. Rheological tests with an Anton Paar Physica MCR 301 rheometer confirm that the experimental timescale is at least three orders of magnitude longer than the Maxwell relaxation time (~1 s). The glucose syrup is a Newtonian fluid [Schellart, 2011a]. To model the dynamics at a convergent margin, free movement of both plates is allowed, and we assume that subduction is primarily driven by the slab's negative buoyancy. It is assumed that the plates are surrounded by weak plate boundaries (spreading centers and transform faults) that have a low viscosity as in the upper mantle. We model the subduction process of a single slab into a confined upper mantle reservoir (Figure 1), and thus subduction occurs in isolation and is not affected by any other nearby subduction zones or other processes such as regional or global mantle flow, which originally results from radiogenic or latent heat, or externally forced plate motion. With our setup we can thus investigate the cause-effect relation between a sinking slab (cause) and deformation in the overriding plate and flow in the mantle (effect) without the complications of other possible far-field influences such as neighboring slabs, regional or global mantle flow, or regional plate forces, which could be important in nature.

Figure 1.

Schematic diagram of the experimental setup for modeling of upper mantle free subduction of a narrow subducting plate below a narrow overriding plate. For each experiment the thickness of the overriding plate is varied (between 0 cm, i.e., no overriding plate, and 2.5 cm). The lateral boundaries and the bottom boundary are zero velocity boundaries, and the top boundary is a free surface. Note that 1 cm in the model scales to 50 km in nature.

Table 1. Experimental Parametersa
ExperimentTOP (cm)Temperature (°C)Δρ (kg/m3)ηSP (Pa·s)ηUM (Pa·s)ηSP/ηUM
  1. a

    Physical parameters for the experiments described in the text. TOP is the thickness of the overriding plate (at the start of the experiment), Δρ is density contrast between the subducting plate and upper mantle, and ηSP and ηUM are the dynamic shear viscosity of the subducting plate and upper mantle, respectively. For all experiments, the subducting plate thickness TSP = 1.6 cm, and the width for both the overriding plate and subducting plate is 15.0 cm, while density contrast between the overriding plate and upper mantle is zero. Errors: Δρ ± 2 kg/m3, ηSP ± 2%, ηUM ± 3%, ηSP/ηUM ± 5%.

6020.35102.324,120120.5200.2
110.520.55102.524,033113.5211.7
51.020.45102.524,076112.7213.6
91.519.9102.224,318127.4190.9
72.019.9102.224,318127.4213.6
102.520.3102.324,141110.9217.6

[8] The principal challenge of the experiments is to model progressive subduction with the inclusion of an overriding plate. This requires efficient decoupling between the two plates to ensure the progressive subduction of the downgoing plate under the overriding plate without the two plates getting stuck together and thereby stalling subduction. To reduce the coupling between the two plates, the subduction zone plate boundary interface (the subduction channel) is lubricated with a thin low-viscosity, linear viscous layer (Australian Rainforest honey mixed with 5% of water, ηSC = 6 Pa⋅s). The subduction channel is on average 2–3 mm thick (scaling to 10–15 km). We note, however, that for the initial subduction stage (slab length up to ~10 cm), the subduction channel is somewhat thicker (maximum of 6–8 mm at the start and decreasing to 2–3 mm at 10 cm of subduction). This is because of practical limitations of the model setup when the subduction instability is first produced and the two plates are placed in their position. At the start of an experiment, the initial channel thickness cannot be reduced to less than 6–8 mm because of the risk of the two plates locally touching each other, which would result locally in full coupling of the two plates and locking of the subduction zone. During progressive subduction the low-viscosity channel becomes thinner as it is progressively eroded, and therefore, a thin horizontal band of the honey-water mix (1–2 mm thick and <10 mm wide (trench-normal extent) scaling to 5–10 km and <50 km in nature) is added at the trench on top of the subducting plate every 2–3 min. Such a scenario mimics a weak (low-viscosity) prism of sedimentary material on top of the subducting plate that is progressively subducted as the downgoing plate sinks into the mantle.

[9] The experiments are carried out in a large tank (100 cm long, 60 cm wide, and filled up to 13.3 cm) at constant temperature (20°C ± 0.7°C). By keeping the temperature as constant as possible during individual experiments and between consecutive experiments, we avoid large density and viscosity differences between slab and ambient upper mantle for different experiments. The laboratory experiments are isothermal, and so time-dependent variations in density and viscosity that are implied for subduction zones in nature due to progressive warming of the slab and cooling of the plates have not been incorporated in the experiments. Such effects are likely of subordinate importance at the timescale of the experiments (~20 million years).

[10] The dimensions of the subducting plate are kept constant (47 cm long, 15 cm wide (trench-parallel extent), and 1.6 cm thick). A relative small width (scaling to 750 km) and high thickness (scaling to 80 km) are used to promote significant slab rollback and to reduce trench curvature. The overriding plate is 30 cm long and 15 cm wide, while its thickness is varied between 0 and 2.5 cm to investigate the effect of overriding plate thickness on the system. The parameters of the experiments discussed in the paper are shown in Table 1. Experiments are conducted at very low Reynolds number (of the order 1–2 × 10−5 using vSP⊥ and of the order 2–3 × 10−4 using vT⊥) to ensure that inertial forces are negligible and that the mantle is in the laminar symmetrical flow regime (i.e., no eddy formation downstream of the slab).

[11] For each experiment, the length dimensions assure at least 11.5 cm between box sidewalls and the trailing edge of each plate, while the width dimensions leave 22.5 cm on each side of the plates; the edges are thus reasonably far from the sidewalls of the tank to minimize boundary effects on our system. The plates overlie a glucose syrup reservoir, and the combined thickness of the plates and the syrup is 13.3 cm, scaling to 665 km, and thus represents the upper mantle. The bottom of the tank represents an infinite viscosity step at the upper-lower mantle discontinuity. This simplification is acceptable for relatively weak and narrow slabs as here (W scales to 750 km), which are expected to subduct mostly through slab rollback with draping and flattening on the discontinuity [Stegman et al., 2006; Schellart et al., 2010].

[12] We use a density contrast between the subducting plate and the upper mantle of Δρ ≈ 100 kg/m3 (upper mantle glucose density ≈ 1420 kg/m3 and subducting plate silicone mix density ≈ 1520 kg/m3), which is somewhat higher than for subducted mature oceanic lithosphere with Δρ ≈ 80 kg/m3 [Cloos, 1993]. We use this somewhat higher density contrast in the models as a first-order approximation to negate surface tension effects between the glucose and the silicone, which are operative at the free top surface [Jacoby, 1976; Schellart, 2008b]. The forces related to such surface tension are subordinate to the main driving force in the experiments (i.e., the negative buoyancy force of the slab), but they are not negligible. The overriding plate has a neutral buoyancy relative to the upper mantle to prevent it from sinking and to prevent gravitational spreading. As such, all deformation of the overriding plate is a consequence of imposed normal and shear tractions at its lateral boundaries and its base.

[13] A viscosity ratio of ηSP/ηUM = ~200 is reached at 20°C, which is close to estimates of the viscosity ratio in nature [e.g., Schellart, 2008b; Funiciello et al., 2008; Loiselet et al., 2009; Stegman et al., 2010; Ribe, 2010]. The small difference in the temperature at which each experiment is run causes minor differences in the density and the viscosity of the glucose syrup, as well as the density and the viscosity of the silicone putty, but much less than for the glucose (Table 1).

[14] A length-scale ratio of xe/xn = 2.0 × 10−7 (1 cm in the experiment represents 50 km in nature), as well as a time-scale ratio of te/tn = 3.8 × 10−12 have been chosen, where the e indices stand for the experimental values and the n indices stand for the values in nature. One can then calculate the viscosity for the upper mantle that we model in our experiments using:

display math(1)

[15] With Δρe = 100 kg/m3, Δρn = 80 kg/m3, and ge/gn = 1, the glucose syrup viscosity represents an upper mantle viscosity of ~1.36 × 1020 Pa⋅s, which is in the range of viscosity estimates (1019–1021 Pa⋅s) for the sub-lithospheric upper mantle [Ranalli, 1995]. We note that, because we model a type of Stokes flow in our subduction experiments, we have to scale the velocities, viscosities, and forces using the density contrast rather than density. Furthermore, dynamic similarity between experiments and nature requires the same ratios of the various forces essential for the process under investigation. In our experiments of subduction, and in nature, the main driving forces are buoyancy forces, and the main resistive forces are viscous drag forces. Thus, because our fluid dynamic experiments are conducted at very low Reynolds number (Re = 10−5–10−4), dynamic similarity does not require the exact scaling of densities of different materials in our experiments, but only the scaling of the density contrast, because inertial forces and kinetic energy are negligible, as for subduction zones in nature.

[16] In the initial configuration, the leading edge of the subducting plate is forced down to a depth of about 4 cm within the glucose syrup to initiate subduction. It is thus clear that we do not study the process of subduction initiation. Two cameras record the progressive evolution of the experiments from the top and from the side. We incorporate neutral-buoyancy particles on the side and on the top of the plates as markers to measure the displacement and calculate the deformation of the plates.

3 Results

3.1 Dynamics of the Subducting Plate, Trench, and Overriding Plate

[17] Inclusion of an overriding plate and a low-viscosity subduction channel does not significantly modify the general behavior of the subducting plate (Figures 2 and 3). The experiments without an overriding plate (TOP = 0), with an intermediate thickness overriding plate (TOP = 1.0 cm), and thick overriding plate (TOP = 2.5 cm) all show the same evolution of the subducting slab and similar subduction kinematics (Figure 2). For all the experiments, the initial sinking phase is characterized by steepening of the slab and an increase in trench retreat velocity and trenchward subducting plate velocity until the tip of the slab first touches the bottom of the tank (Figure 2). During the interaction phase between the slab tip and the bottom of the tank, both the trench velocity and the subducting plate velocity decrease, after which the trench velocity and the subducting plate velocity increase again and become approximately steady (Figure 3). During this steady-state phase, the slab rolls back and is draped on top of the bottom of the tank. The subducting plate velocity is directly associated with the slab down-dip sinking velocity and is more affected by the interaction between the slab tip and the bottom of the tank, i.e., it decreases more than the trench velocity and the overriding plate velocity when the tip reaches the bottom of the tank. This is because its displacement vector is oriented sub-perpendicular to the plane of the bottom of the tank. As the slab subducts, it drags the low-viscosity decoupling material (honey) with it into the underlying mantle, and it remains at the top surface of the slab.

Figure 2.

Side-view photographs showing the evolution of subduction for three different experiments with a different overriding plate thickness (TOP). (a1–a5) Experiment 6 (TOP = 0, i.e., no overriding plate). (b1–b5) Experiment 5 (TOP = 1.0 cm scaling to 50 km). (c1–c5) Experiment 10 (TOP = 2.5 cm scaling to 125 km). Note the comparable subduction evolution with comparable slab geometries in all three models. Note that the apparent large thickness of the subduction channel in Figures 2c1, 2c2, and 2c3 is largely because of the high reflectivity of the surface of the overriding plate bordering the subduction channel. Also note that the apparent large slab thickness in Figure 2a is due to the plan-view slab curvature, which is most significant in the experiment shown in Figure 2a because of the absence of an overriding plate.

Figure 3.

Diagrams showing the trench-normal trench velocity (vT⊥, blue diamonds), trench-normal subducting plate velocity (vSP⊥, red circles), and overriding plate velocity (vOP⊥, green squares) for six experiments with different overriding plate thicknesses (TOP). vOP⊥ and vSP⊥ are measured at the trailing edge of the overriding plate and of the subducting plate, respectively, while vT⊥ is measured at the leading edge of the overriding plate. Note that deformation in the subducting plate is negligible during the experiment (|ε| < 2%), such that vSP⊥ at the trailing edge is representative of vSP⊥ at the trench. (a) Experiment 6 (TOP = 0). (b) Experiment 11 (TOP = 0.5 cm). (c) Experiment 5 (TOP = 1.0 cm). (d) Experiment 9 (TOP = 1.5 cm). (e) Experiment 7 (TOP = 2.0 cm). (f) Experiment 10 (TOP = 2.5). The vertical grey line indicates the time when the tip of the slab first touches the bottom of the tank. Maximum error in velocity values is ±0.02 mm/s.

[18] The trench velocity appears to slightly decrease with increasing overriding plate thickness (Table 2 and Figure 3). At the same time, the models also show a weak trend of an increase in subducting plate velocity with increasing overriding plate thickness. However, the trends for the trench-normal trench velocity (vT⊥, retreat is positive) and trench-normal subducting plate velocity (vSP⊥, trenchward motion is positive) are relatively subtle. The velocities in Figure 3 are all affected by small-moderate variations in the viscosity of the glucose syrup due to small (unwanted) variations in temperature for the different experiments. The viscosity of glucose syrup is strongly dependent on temperature, and variations in temperature of only 1°C can change the viscosity by ~15% [Schellart, 2011a]. An increase in glucose viscosity affects all the velocities by offering more resistance to plate motion and sinking.

Table 2. Some Experimental Resultsa
ExperimentTOP (cm)vSP⊥ (mm/s)Scaled vSP⊥ (cm/yr)vT⊥ (mm/s)Scaled vT⊥ (cm/yr)vOP⊥ (mm/s)Scaled vOP⊥ (cm/yr)Total extension (%)
  1. a

    Average velocities during the steady-state phase of each experiment and total trench-normal horizontal extensional strain of the overriding plate at the end of an experiment (measured along the centerline of the plate and averaged for the entire length of the plate). Note that model velocities, as well as scaled velocities, are given. TOP is the thickness of the overriding plate, vSP⊥ is trench-normal subducting plate velocity (trenchward is positive), vT⊥ is trench-normal trench velocity (retreat is positive), and vOP⊥ is trench-normal overriding plate velocity (trenchward is positive).

600.0543.20.1237.4   
110.50.0905.40.1448.60.0744.436.5
51.00.0885.30.1167.00.0774.624
91.50.0905.40.1388.30.0794.714.3
72.00.0774.60.1016.10.0633.822.8
102.50.1056.30.1156.90.0935.69.8

[19] To circumvent the effect that small variations in temperature have on the experimental results, non-dimensional subduction partitioning ratios (vSP⊥/vS⊥, with vS⊥ = vSP⊥ + vT⊥) have been calculated and compared for the steady-state subduction phase (Figure 4). There is a clear trend where vSP⊥/vS⊥ increases with increasing overriding plate thickness, and a linear best-fit line shows a relatively high correlation (correlation coefficient R = 0.89, coefficient of determination R2 = 0.79). Calculated confidence intervals for the linear best-fit correlation shown in Figure 4b using Fisher's z indicate that the positive correlation is statistically significant at 98% confidence level. Furthermore, a Spearman rank correlation analysis of the data using Fisher's z indicates that the positive correlation is statistically significant at 95% confidence level. Thus, with increasing overriding plate thickness, vSP⊥ increases at the expense of vT⊥.

Figure 4.

Diagrams illustrating the subduction partitioning (vSP⊥/vS⊥, where vS⊥ = vSP⊥ + vT⊥) for six experiments with different overriding plate thicknesses (TOP = 0–2.5 cm). (a) Subduction partitioning with progressive (normalized) time during the steady-state subduction phase (the period of slab draping on top of the 670 km discontinuity, which is after first contact of the slab tip with the discontinuity). Note that we use normalized time to allow for accurate comparison between experiments, where t is time, tSTEADY is the start time of the steady state period, and tEND is the time at the end of subduction. (b) Average vSP⊥/vS⊥ for the steady-state period plotted against overriding plate thickness, illustrating that TOP and vSP⊥/vS⊥ are positively correlated. Error bars are given for data points in Figure 4b. Note that R2 is the coefficient of determination for the linear best-fit line (continuous grey line). For the linear best-fit correlation shown in Figure 4b, confidence intervals have been calculated for R using Fisher's z indicating that the positive correlation is statistically significant at 98% confidence level. A Spearman rank correlation analysis of the data using Fisher's z indicates that the positive correlation is statistically significant at 95% confidence level.

3.2 Slab Geometry: Shape, Dip, and Curvature

[20] Both systems with and without an overriding plate reveal a similar evolution of the slab geometry during the subduction process, with a relatively steep upper mantle slab that flattens at the 670 km discontinuity on the overriding plate side (Figure 2). During the initial free-sinking stage, the slab dip angle increases progressively until the slab tip reaches the bottom of the tank (Figure 2). After this, the slab dip remains approximately constant (Figure 5) just as the velocities of the plates and the trench remain approximately constant (Figure 3). The range of slab dip angles observed in the experiments is 65°–80°, while for individual experiments temporal variation in slab dip angle is 5°–10° during the steady-state phase (Figure 5a). The laboratory models do not show any dependence of slab dip angle on overriding plate thickness and are relatively comparable for the steady-state phase (Figure 5b). Even before the steady-state phase the slab dip angles are rather comparable. For example, in the subduction stage just before the slab tip touches the bottom, slab dip angles for the lowermost 7 cm (corresponding to 350 km) of slab are ~76°, ~76°, and ~74° for the experiments with TOP = 0, 1.0, and 2.5 cm, respectively (Figures 2a3, 2b3, and 2c3).

Figure 5.

Diagrams illustrating the slab dip angle for six experiments with different overriding plate thicknesses (TOP = 0–2.5 cm). (a) Slab dip angle with progressive (normalized) time during the steady-state subduction phase (the period of slab draping on top of the 670 km discontinuity, which is after the first contact of the slab tip with the discontinuity). Note that we use normalized time to allow for accurate comparison between experiments, where t is time, tSTEADY is the start time of the steady state period, and tEND is the time at the end of subduction. (b) Average slab dip angle for the steady-state period plotted against TOP. Error bars are given for data points in Figure 5b. Note that slab dip angle is measured in the depth range 3.8–7.8 cm (scaling to 190–390 km). Also note the lack of correlation between TOP and slab dip angle.

[21] The trench and the slab rapidly form a plan-view curvature that is concave towards the mantle wedge (convex toward the subducting plate) (Figure 6). This curvature increases with progressive time, and the models show a general trend in which such curvature decreases with increasing overriding plate thickness (Figure 6d). For the models with an overriding plate, the curvature is also observed in the frontal part of the plate and is accommodated by a progressive increase in overriding plate extension from the edges of the plate towards the center (Figures 6b and 6c).

Figure 6.

Variation in trench curvature as a function of overriding plate thickness. (a–c) Top view photographs of three experiments after 27 cm of subduction (scaling to 1350 km), with (Figure 6a) experiment 6 (TOP = 0), (Figure 6b) experiment 5 (TOP = 1.0 cm), and (Figure 6c) experiment 10 (TOP = 2.5 cm). (d) Trench curvature at three different stages of subduction (14, 27, and 37 cm of subduction for blue diamonds, green triangles, and red crosses, respectively) for six subduction experiments with different overriding plate thicknesses (TOP = 0–2.5 cm). Note that trench curvature is expressed as 1/r2, where r is the radius of curvature, which is measured for the innermost 10 cm of the plate. Error bars are given for data points in Figure 6d. Continuous lines in Figure 6d are exponential best-fit lines, with coefficients of determination R2 = 0.84 (blue diamonds), R2 = 0.69 (green triangles), and R2 = 0.67 (red crosses).

3.3 Overriding Plate Deformation

[22] The trench velocity is always higher than the overriding plate velocity at its trailing edge, and the overriding plate accommodates this difference by stretching in the direction of trench retreat. By measuring the displacement of the passive markers along the centerline of the overriding plate, the incremental strain of each segment between markers can be calculated during each time interval by dividing the finite difference in length after a time interval by the initial length, following:

display math(2)

where L1 and L2 are the initial length and the length after a time interval, respectively.

[23] In all experiments, overriding plate deformation is characterized and dominated by extension (Figures 7 and 8). Overriding plate shortening has not been observed, except potentially for very minor shortening near the edge of the overriding plate in experiment 5 with TOP = 0.5 cm (Figure 8b). Considering that the maximum error in strain in Figure 8 is ±4%, this apparent shortening might not be real. The horizontal strain rate of the overriding plate follows the dynamics of the subduction system. The (local) maximum in extension rate during the early free-sinking stage for each individual experiments corresponds with the (local) maximum in trench retreat velocity (cf. Figure 7a with vT⊥ in Figure 3). Furthermore, the (local) minimum extension rate for the experiments during the slab tip-bottom boundary interaction phase corresponds with the (local) minimum in vT⊥. Also, the trends in the curves for extension rate and vT⊥ during the steady-state rollback phase are very similar for individual experiments. Figure 7b shows positive linear correlations between vT⊥ and trench-normal strain rate for all experiments with an overriding plate, where an increase in extensional strain rate corresponds with an increase trench retreat velocity. Those experiments with a thin overriding plate (0.5 and 1.0 cm) particularly show strong correlations (R2 = 0.89 and 0.78). The correlations confirm that the overriding plate accommodates trench retreat partly by stretching.

Figure 7.

Trench-normal horizontal strain rate of the overriding plate for five experiments with different overriding plate thicknesses (TOP = 0.5–2.5 cm scaling to 25–125 km). (a) Development of strain rate with progressive time. (b) Strain rate as a function of trench-normal trench velocity plotted for individual time steps. Continuous lines are linear best-fit lines, and R2 is the coefficient of determination. Strain rate is measured along the centerline of the overriding plate and is averaged for the entire overriding plate length. Maximum error in strain rate values is ±2.5 × 10−5 s−1. Note that data points in Figure 7b are statistically not independent. Also note that positive strain represents extension.

Figure 8.

(a and b) Total trench-normal horizontal strain of the overriding plate at the end of the experiment as a function of distance from the trench with (Figure 8a) total trench-normal strain measured along the centerline for five experiments with different overriding plate thicknesses (TOP = 0.5–2.5 cm scaling to 25–125 km) and (Figure 8b) total overriding plate strain for experiment 5 (TOP = 1.0 cm) measured along seven lines that run parallel to the length of the plate, where line 1 and 7 are located closest to the edges of the plate, line 4 is the centerline, and lines 2, 3, 5, and 6 are located in intermediate positions. Note that positive strain represents extension. Maximum error in strain is ±4%.

[24] The total horizontal overriding plate strain along the length of the overriding plate shows that deformation is not homogeneously distributed (Figure 8). The maximum total extension along the centerline is located at ~4.0–8.0 cm from the trench, corresponding to ~200–400 km in nature (Figure 8a). This distance is independent of the thickness of the overriding plate. Extension is maximum in the center of the subduction zone and decreases toward both sides of the subduction zone (Figures 8b, 6b, and 6c). Thus, there is a trench-parallel variation in trench-normal extension from the center to the sides. Such a trench-parallel variation in overriding plate extension accommodates the progressive curvature of the trench. Furthermore, the trench-normal distance between trench and maximum extension increases from the center of the subduction zone toward the edges. In the center, this distance is 7.5 cm (scaling to 375 km), while near the edges, it is up to 12.5 cm (scaling to 625 km) (Figure 8b).

[25] The total horizontal trench-normal overriding plate extension at the end of the experiments is in the range 4.6–7.3 cm (scaling to 230–365 km) for TOP = 0.5–2.5 cm. There is a general trend where total extension decreases with increasing TOP, while overriding plate velocity increases (Figure 8a and Table 2). One can deduce that with increasing strength (due to increasing thickness in the current experiments) of the overriding plate, backward slab migration is increasingly accommodated by overriding plate motion rather than overriding plate deformation. This general trend can be deduced from the trench velocity curves (blue lines) and the overriding plate trailing edge velocity curves (green lines) in Figure 3. The vertical separation between the two curves indicates the total rate of (trench-normal) extension. In Figure 3b (TOP = 0.5 cm), the curves are widely separated and vOP⊥ ≈ 0.5–0.6 vT⊥, and thus a large amount of trench retreat (~40%–50%) is accommodated by extension. In Figure 3f (TOP = 2.5 cm), the curves are much closer together and vOP⊥ ≈ 0.8–0.9 vT⊥, indicating that a relatively small part (~10%–20%) of the trench retreat is accommodated by extension.

[26] We can quantify the average horizontal trench-normal tectonic force (a deviatoric tensional force) in the overriding plate that drives extension (FEXT) using:

display math(3)

where math formula is the trench-normal extensional strain rate averaged over the length and width of the overriding plate, ηEXT is the extensional viscosity of the overriding plate material, and A is the trench-parallel cross-sectional surface area of the overriding plate (A = TOPWOP, where WOP is the width of the overriding plate). For Newtonian fluids, the (dynamic) extensional viscosity and the (dynamic) shear viscosity (η) are related as such [Trouton, 1906; Petrie, 2006]:

display math(4)

[27] Calculations have been done for the initial transient sinking stage (before the tip hits the bottom) at the time when the strain rate is maximum (see Figure 7a). At this time, FBu can be calculated most accurately because the slab tip is not interacting yet with the bottom boundary. The results show that for the five experiments with TOP = 0.5–2.5 cm, FEXT is of the order 0.012–0.025 N at these times (Figure 9a). We can compare these values with the only driving force in the experiments, the slab negative buoyancy force FBu:

display math(5)

where VSLAB is the slab volume, Δρ is the density contrast between the slab and ambient mantle, and g is the gravitational acceleration (9.8 m/s2). With Δρ = 102.2–102.5 kg/m3 (Table 1), slab lengths of 8.7–9.6 cm at these times, slab width of 15.0 cm, and a slab thickness of 1.6 cm, FBu is of the order 0.21–0.23 N. Figure 9b shows that FEXT/FBu ratios are in the range 0.05–0.11, indicating that FEXT constitutes 5%–11% of the negative buoyancy force of the slab. The data in Figure 9 show moderate positive correlations (R = 0.68 for FEXT and R = 0.73 for FEXT/FBu), suggesting that FEXT and FEXT/FBu increase with increasing TOP. It should be noted though that confidence intervals calculated using Fisher's z indicate that these correlations are statistically not significant at 95% confidence level.

Figure 9.

Trench-normal horizontal force that drives overriding plate extension (FEXT) for five experiments with different overriding plate thicknesses (TOP = 0.5–2.5 cm scaling to 25–125 km) (see equation (3)). (a) FEXT as measured during the peak strain rate in the initial free-sinking phase (before the slab tip touches the bottom). (b) FEXT/FBu for the same time as in Figure 9a, where FBu is the slab negative buoyancy force (see equation (5)). Note that data points for experiments are represented by black diamonds, while continuous lines represent linear best-fit lines. Further note the moderate positive correlations in both diagrams. These correlations are, however, statistically not significant at 95% confidence level using Fisher's z.

4 Discussion

4.1 Discussion of Model Results

[28] The experiments of free subduction of a narrow slab with a weak subduction zone interface show that the inclusion of an overriding plate does not significantly affect the slab dip angle, the slab geometry (always a slab flattening geometry at the bottom below the overriding plate), the style of subduction (retreating subduction zone), and the velocities of the plates and trench. The trench retreat velocity is always higher than the subducting plate velocity and the overriding plate velocity. We observe comparable results for models with and without an overriding plate for our particular setup, with a narrow and relatively weak slab (ηSP/ηUM ≈ 200) and with relatively short plates that are laterally unconstrained. One can expect though that with certain model setups the effect of an overriding plate on the subduction zone evolution will be more pronounced. For example, using a much larger overriding plate, or fixing it to the side wall, will constrain its lateral motion and affect the trench migration velocity, and thus the subduction kinematics, the slab geometry, and its dip angle.

[29] In our experiments, with our particular setup, inclusion of an overriding plate does have an impact on the partitioning of subduction, where an increase in overriding plate thickness corresponds with a moderate increase in subducting plate velocity at the expense of the trench velocity (Figure 4). The observed trend supports the hypothesis that the presence of an overriding plate, and its increase in thickness, increases the suction at the trench (due to an increase in down-dip length of the subduction zone interface), thereby retarding slab rollback and trench retreat while promoting subduction through trenchward subducting plate motion. Note that with trench suction we mean the deviatoric tensional normal stress at the subduction interface, which is induced by the retreating subduction zone hinge. The viscosity of the subduction channel will probably also play a role in the partitioning of subduction between vT⊥ and vSP⊥, but this remains to be tested.

[30] Furthermore, although the overall geometry is not significantly affected by the presence of an overriding plate, the trench curvature is reduced (Figure 6). Considering that the trench is directly coupled to the leading edge of the overriding plate, resistance to the curvature of the trench and hinge is indeed expected to increase with an increase in overriding plate thickness due to its increase in strength. As such, trench curvature decreases with increasing overriding plate thickness. We note though that the inclusion of side plates (with a viscosity higher than that of the sub-lithospheric mantle) and transform plate boundaries would have reduced the curvature of the trench due to horizontal suction forces normal to the transform fault planes.

[31] Inclusion of an overriding plate does not have any discernable effect on the slab dip angle (Figure 5). This is in accordance with the idea that the dip angle of the slab in the current experiments (with a constant subducting plate thickness) results from two competing effects. On the one hand, an increase in overriding plate thickness promotes an increase in trench suction due to a longer subduction channel. An increase in trench suction promotes a large lifting force on the slab and thereby a decrease in slab dip angle [e.g., Dvorkin et al., 1993]. On the other hand, an increase in trench suction due to increasing overriding plate thickness promotes a decrease in the trench velocity. Previous work shows that the slab dip angle is influenced by trench migration [e.g., Tao and O'Connell, 1992; Griffiths et al., 1995; Schellart, 2004a; Lallemand et al., 2005]. Kinematic subduction models [Griffiths et al., 1995] and dynamic subduction models [Schellart, 2004a] both show a decreasing slab dip angle with increasing trench retreat velocity. A reduction in trench retreat velocity due to an increase in overriding plate thickness thus promotes an increase in slab dip angle. The influence of both a decrease in the trench retreat velocity and an increase in trench suction appears to negate any effect that inclusion of an overriding plate, and its thickness, might have on the slab dip angle. The thickness and the viscosity of the subduction channel, as well as the slab width, are also likely to have an influence on the slab dip angle, but these parameters have not been tested in our experiments.

4.2 Overriding Plate Deformation

[32] The experiments only show overriding plate extension. This is because we use a narrow, negatively buoyant, and relatively weak subducting plate, and we use a very weak subduction zone interface (ηSC/ηUM = 0.05). With such conditions, subduction is dominated by slab rollback and trench retreat, and the overriding plate only shows extension. There are other subduction zone parameters that affect trench migration and the coupling along the interface, which could cause overriding plate deformation to be episodic, e.g., alternating between extension and quiescence, or the deformation style to change from extension to shortening [e.g., Clark et al., 2008]. For example, using a stronger subduction interface rheology, including a zone of positive buoyancy on the subducting plate (e.g., representing an aseismic ridge), or bigger plates could cause a change in overriding plate deformation, possibly including shortening. This remains to be tested in future work.

[33] There is a significant correlation between overriding plate deformation rate and trench velocity, where an increase in vT⊥ corresponds with an increase in extension rate (Figure 7b and cf. Figure 7a and vT⊥ in Figure 3). In addition, deformation in the overriding plate is always extensional and the trench is always retreating, implying a causal relation between trench retreat and overriding plate extension, as suggested many times before [e.g., Elsasser, 1971; Malinverno and Ryan, 1986; Lonergan and White, 1997; Faccenna et al., 2001; Schellart et al., 2002; Rosenbaum et al., 2002; Rosenbaum and Lister, 2004; Martin, 2007; Schellart, 2008a]. The increase in overriding plate thickness decreases deformation of the overriding plate (Figure 8 and Table 2), highlighting the importance of the overriding plate strength in the deformation process.

[34] The overriding plate is neutrally buoyant, so the only tectonic forces acting on the overriding plate are shear tractions and normal tractions at the base of the plate and along the lateral edges. The tractions that could possibly drive overriding plate deformation are the shear tractions at the base of the overriding plate and the shear and normal tractions at the subduction zone interface. During subduction, shear tractions at the subduction interface can only induce compression in the overriding plate, the magnitude of which depends on the subduction channel viscosity and the shear rate (which depends on the subduction rate and channel thickness). The shear tractions in our experiments are generally low, ~3.0–9.0 × 10−4 N for an overriding plate that is 0.5 cm thick and ~1.5–4.5 × 10−3 N for a 2.5 cm thick overriding plate during the steady-state subduction period. These values are only ~0.1%–1.6% of the slab negative buoyancy force. Such low shear stresses at the subduction interface can explain why the leading edge does not show any shortening. This leaves us with only two forces: the shear tractions at the base of the overriding plate and the normal tractions at the subduction channel.

[35] In case the normal tractions at the subduction channel would be the main driver of overriding plate extension, then the maximum extension should be found right at the trench. Indeed, thin-viscous-sheet models indicate that the velocity u(x) in the viscous sheet decreases exponentially with distance x from a moving boundary with width (W) that is retreating or advancing at velocity U0 according to the following equation [England and Houseman, 1988]:

display math(6)

[36] Here, n is the stress exponent (n = 1 for a Newtonian viscosity, as is the case for our experiments). Because velocities decrease exponentially with x, strain rates will also decrease exponentially with x. Considering that in our models the trench-normal extensional strain rate is not highest at the trench, but at a significant distance from the trench, 4–8 cm (scaling to 200–400 km) (Figure 8a), and remembering that our overriding plate is neutrally buoyant and laterally homogeneous, this indicates that extension does not result primarily from forces at the trench but from forces below the overriding plate. Nevertheless, in our models, there is still a tensile deviatoric normal stress at the subduction interface (which we refer to as trench suction) because the leading edge of the overriding plate shows a moderate extensional strain (Figure 8a).

4.3 Comparison with Previous Models

[37] The models presented here show a general agreement with previous fully dynamic models of progressive free subduction in 3-D space (without an overriding plate) that use a relatively weak and narrow slab as here (ηSP/ηUM ≈ 200, W ≈ 750 km), where the trench and slab generally retreat, and the slab is draped on the 670 km discontinuity [e.g., Schellart, 2004a, 2008b; Stegman et al., 2006, 2010]. Previous models also show development of trench and slab curvature that is concave towards the mantle wedge during trench retreat [Schellart, 2004a; Morra et al., 2006; Loiselet et al., 2009], which results from slab rollback-induced toroidal-type return flow around the lateral slab edges.

[38] In our models, trenches always move faster than the overriding plates, and overriding plate extension is coincident with trench retreat. This is in disagreement with previous 3-D experimental models of Heuret et al. [2007], which show higher overriding plate velocities than trench velocities and correlations where an increase in trench retreat velocity corresponds with an increase in overriding plate shortening rate. This difference results primarily from the fact that both the subducting and overriding plate velocities are imposed in the models from Heuret et al. [2007]. Moreover, the viscosity ratio between the subducting plate and the surrounding mantle had been fixed at 12,000, which is nearly two orders of magnitude higher than our viscosity ratio. It thus appears likely that in the models from Heuret et al. [2007], trench retreat and overriding plate shortening are forced by the kinematically applied boundary condition that drives the overriding plate trenchward. In the current experiments, trench retreat, mantle flow, and overriding plate deformation are driven by the negative buoyancy of the slab. We argue that our model setup is more suitable to investigate and quantify the driving forces and resistive forces of overriding plate deformation during progressive subduction and trench migration.

[39] The driving and resistive forces of subduction have been investigated previously using geodynamic models [e.g., Shemenda, 1993, 1994; Schellart, 2004b; Arcay et al., 2008] or using observational constraints and theoretical calculations [e.g., Lallemand et al., 2008]. In these previous works, only Shemenda [1993, 1994] quantified the stresses that cause extension in the overriding plate using quasi 2-D laboratory models of subduction. He investigated the trench-normal deviatoric tensile horizontal stress (σH) in the overriding plate and concluded that it is 10%–20% of the yield limit of his visco-plastic lithospheric plates (σY). In his models, σH resulted entirely from the deviatoric tensile normal stresses at the subduction zone interface (i.e., trench suction, which he referred to as hydrostatic suction). Basal shear tractions were negligible in his models because of the usage of an extremely low-viscosity asthenosphere (made of water). We can roughly estimate FEXT/FBu in Shemenda [1993] for his experiment 5. At the time of break-up in the backarc in Figure 6d in Shemenda [1993], σH = 0.1–0.2σY, so with σY = 30 Pa, and TOP = 0.023 m, then FEXT = σHTOPWOP = 0.069–0.138WOP N. Furthermore, with a slab length of ~0.13 m, TSP = 0.023 m, Δρ = 30 kg/m3, and g = 9.8 m/s2, then FBu = 0.88WSP N (here WSP is the width of the subducting plate). With WOP = WSP, then FEXT/FBu ≈ 0.08–0.16. This estimate for the experiment in Shemenda [1993] is thus comparable to our experimental results with FEXT/FBu = 0.05–0.11, which is remarkable, considering that in Shemenda [1993], FEXT results entirely from stresses at the trench, while in the current work, FEXT results mostly from shear tractions at the base of the overriding plate.

[40] In a recent work, Capitanio et al. [2010] compute 2-D regional numerical models of free subduction that include an overriding plate and study the deformation of the overriding plate. For a smaller Δρ (30, 60, and 90 kg/m3), a higher viscosity ratio (300–3000), and similar plate thicknesses to our plate thicknesses, they obtain compressive stresses near the trench (<300 km) and a large tensional peak stress within 300–400 km from the trench. This value is comparable with our peak value of extensional strain at a distance of 200–400 km from the trench. A detailed comparison between our laboratory models and the numerical models from Capitanio et al. [2010] is not warranted because the numerical models have been performed in 2-D, therefore lacking toroidal mantle flow components, and have periodic boundary conditions on the side walls, which make the mantle flow patterns in these numerical models incompatible with respect to the flow patterns in the laboratory experiments. This difference is significant because we argue that overriding plate extension results mostly from mantle flow patterns and trench-normal mantle velocity gradients just below the base of the overriding plate.

[41] Clark et al. [2008] obtain in their 3-D numerical models of free subduction with an overriding plate mostly smaller trench velocities (~1 cm/yr) than here (6–9 cm/yr). Their experiments were carried out with similar parameters (Δρ = 80 kg/m3, ηSP/ηUM = 200) but with an overriding plate that was always fixed to the lateral side wall of the box, thus preventing the overriding plate from freely migrating, thereby significantly retarding the trench velocity.

4.4 Limitations of the Models

[42] The subduction models contain several simplifications that have to be remembered when the results are applied to subduction zones on Earth or are compared to other subduction models. In the experiments, the rigid bottom of the tank represents an impenetrable 670 km discontinuity. This simplification means that any interaction between the slab and the discontinuity is amplified and more immediate than one would expect in nature (e.g., faster deceleration of sinking velocity) and also that subduction is limited to the upper mantle. Previous 3-D subduction models with a narrow slab that include a high-viscosity lower mantle reservoir show deceleration near the discontinuity, and those that are dominated by trench retreat show slab draping on top of the discontinuity [e.g., Kincaid and Olson, 1987; Griffiths et al., 1995; Stegman et al., 2006; Schellart et al., 2007], similar to what is observed here (Figure 2).

[43] In the experiments, the absence of side plates and the direct contact of the sides of the plates with the low-viscosity glucose syrup imply a system with very low resistance along the transform plate boundaries. Higher resistance would retard plate motion, and thus plate velocities in the models might represent an upper bound. Higher resistance would also likely retard trench migration, as Hale et al. [2010] recently showed that an increase of such resistance reduces the local trench retreat velocity but increases the trench curvature. Nevertheless, investigations of transform plate boundaries do suggest that shear resistance along transform faults can be very low [e.g., Lockner et al., 2011].

[44] We use a very low viscosity material for the subduction zone interface (ηSC/ηSP ≈ 1/4000). Investigations of the frictional properties of mineral assemblages at the subduction zone interface, global mantle convection models, and local subduction zone investigations do imply that the subduction zone interface is generally very weak [Moresi and Solomatov, 1998; Wang et al., 1995; Moore and Lockner, 2007]. New experiments will be required to test the influence of the relative strength (e.g., viscosity) of the subduction zone interface on the subduction dynamics.

[45] We model the subduction process of a single slab into a confined upper mantle reservoir, and thus subduction occurs in isolation. In nature, however, subduction does not occur in isolation but in a global mantle reservoir, and individual subduction zones might be affected by nearby subduction zones or other processes such as regional or global mantle flow, flow due to mantle plumes, or externally forced plate motion. In our model setup, we have excluded all these potential outside influences. The advantage of our setup is that we can accurately quantify the only driving force in the system (FBu) and quantify the resistive forces in the system in relation to the only driving force. If we would use an experimental setup that involves, for example, applied kinematic boundary conditions to the plate or a regional mantle flow, then we would introduce another driving force into the system, and thus another source of energy, which in general would be difficult to quantify (and to our knowledge has not been quantified in analogue models of subduction). A complication is then that it is not clear if such externally imposed forces properly scale with respect to the magnitude of the negative buoyancy force of the slab and to the viscous resistive forces. We argue that at subduction zones in nature the main driving force of the local subduction, local mantle flow in the vicinity of the slab, and local deformation of the overriding plate is the negative buoyancy force of the local slab itself. As such, we think that our models represent a reasonable approximation of subduction zones in nature and that the only driving force (FBu) is properly scaled with respect to the local resistive forces.

[46] The low-viscosity subduction channel material is progressively removed by the subducting plate (due to shear tractions). It moves with the downgoing slab, thereby reducing the coupling between the top of the slab and the ambient mantle. It will thus reduce the corner flow in the mantle wedge. At subduction zones in nature, the top of the slab is generally cool and therefore tends to cool the adjacent mantle material in the wedge, thus increasing its viscosity rather than decreasing it. Such a mechanism has been replicated in numerical subduction models [e.g., Arcay et al., 2008]. However, other processes are also operative at subduction zones, which tend to decrease the effective viscosity of material in the vicinity of the top of the slab. Hydrous minerals in the crust and uppermost lithosphere are progressively subducted, and water is released during dehydration reactions. Recent numerical models show that water is progressively released down to depths of 300 km, flowing along an up-dip direction parallel to the slab top surface [Faccenda et al., 2012]. Furthermore, a shear fabric develops at the top of the slab during progressive subduction, in particular at the subduction zone interface, lowering the effective viscosity in the direction of the shear fabric. Another mechanism that lowers the effective viscosity of the mantle material adjacent to the top of the slab is the strain rate weakening mechanism during strain localization. Numerical models suggest that such a mechanism can lower the effective viscosity by one to two orders of magnitude [Jadamec and Billen, 2010]. These three processes would cause the top of the subducting plate to be relatively weak and thus have a low effective viscosity. Although the combined effect of strengthening due to cooling and weakening due to dehydration, shear fabric development, and increasing strain rates and strain localization on the effective viscosity at the top of the slab is not straightforward, it is generally believed that material at the top of the slab has a viscosity that is one to two orders of magnitude lower [Billen, 2008]. Our models capture some simplified effect of the phenomenon of weakening at the top surface of the subducted slab through the progressive subduction of the subduction channel material.

[47] The usage of a homogeneous Newtonian viscosity overriding plate rheology promotes widespread distributed deformation. Usage of a nonlinear viscous rheology, or a layered rheology with a brittle top layer and a viscous bottom layer, would better model strain localization, which is observed for backarc basins on Earth. Such a more complicated rheology, however, would not allow us to accurately quantify FEXT as presented in Figure 9.

4.5 Implications for Subduction Zones in Nature

[48] The subduction models are in general agreement with observations from several relatively narrow subduction zones on Earth, in particular the Scotia subduction zone in the southern Atlantic with a comparable slab width (~800 km) and also the Calabria and Hellenic subduction zones in the Mediterranean. These subduction zones are characterized by concave slab and trench geometries toward the overriding plate, which itself is characterized by backarc extension or spreading [Larter et al., 2003; Thomas et al., 2003; Malinverno and Ryan, 1986; Lonergan and White, 1997; Faccenna et al., 2001; Rosenbaum and Lister, 2004; Angelier et al., 1982; Gautier et al., 1999] and by relatively rapid trench retreat and relatively slow trenchward subducting plate motion [Schellart et al., 2010]. This is also observed in the models. We do note that the slabs in the natural examples are attached to much larger trailing plates (i.e., South America for Scotia and Africa for Calabria and Hellenic) than is the case for the laboratory models, which will further enhance a low vSP⊥ for these subduction zones. In our experiments, we chose to have a free subducting plate because we wanted to test the influence of the overriding plate on the kinematics of the subducting plate and on subduction partitioning. Fixing the subducting plate to the side wall of the box, which might be more representative of a scenario with a very large trailing plate, would have constrained the lateral motion of the subducting plate.

[49] The models also agree with a global compilation of active subduction zones [Schellart, 2008c], showing that trench retreat generally corresponds with overriding plate extension (backarc extension or spreading) and that an increase in trench retreat velocity corresponds with an increase in trench-normal overriding plate extension rate. We note that in their global compilation, using a Pacific hotspot reference frame, Heuret et al. [2007] reach an opposite conclusion, arguing that trench retreat generally corresponds to overriding plate shortening. We prefer the results of Schellart [2008c], who uses an Indo-Atlantic hotspot reference frame, because such reference frames are in better agreement with a number of geophysical constraints such as global mantle anisotropy as derived from shear wave splitting [e.g., Kreemer, 2009] and mantle slab geometries [e.g., Schellart, 2011b]. We do not prefer the Pacific hotspot reference frame from Gripp and Gordon [2002] that is used by Heuret et al. [2007] because we think it shows a net global rotation of the lithosphere with respect to the underlying mantle that is too high (0.44°/Ma counterclockwise rotation around a pole at 56°S, 70°E). Constraints based on mantle anisotropy give a much lower global net rotation of the lithosphere (0.2065°/Ma counterclockwise rotation around a pole at 57.6°S, 63.2°E) [Kreemer, 2009].

[50] The positive correlation between trench retreat velocity and trench-normal overriding plate extension rate as presented in Schellart [2008c] and in the experiments here (Figure 7b) implies that for subduction settings in nature that are comparable with the experiments (i.e., narrow slab or subduction segments close to slab edges), overriding plate extension generally results from slab rollback processes and subduction zone hinge migration away from the overriding plate. The correlation further suggests that overriding plate deformation generally is not driven by motion of the overriding plate with respect to a relatively stationary trench. If this were the case, then trench retreat should correspond with trenchward overriding plate motion and overriding plate shortening, while trench advance should correspond with overriding plate motion away from the trench and overriding plate extension [Schellart, 2008c]. This is not observed in our experiments nor for most subduction zones in nature with active backarc deformation. A notable exception includes the Mariana Trough backarc in the western Pacific, which is adjacent to an advancing subduction zone trench [Carlson and Mortera-Gutiérrez, 1990]. Other exceptions include central segments of wide subduction zones such as in the Central Andes, where westward motion of the South American plate toward the relatively immobile subduction zone hinge causes slow trench retreat (pushback) and overriding plate shortening [Schellart et al., 2007].

[51] The models show rather distributed deformation along the entire length of the overriding plate (up to 1700 km from the trench). Such widespread distributed deformation is to a large extent related to the linear-viscous rheology of the overriding plate. Nevertheless, the models show that trench-normal tensional deviatoric normal stresses in the overriding plate can extend some 1700 km from the trench. This indicates that the subducted slab and the mantle flow patterns that result from subduction have a far-field effect and can drive backarc extension at a considerable distance from the trench. The actual extent of backarc deformation, however, will depend not only on the subduction dynamics and related mantle flow patterns but also on the rheological layering, strength, and buoyancy of the overriding plate [e.g., Gautier et al., 1999; Schellart et al., 2002], as well as lateral variation of these factors.

[52] It is worth noting that the location of maximum extension in the models is at ~200–400 km from the trench, which would thus form the preferential site for the formation of a backarc basin. Strain localization during backarc extension on Earth generally also occurs at some distance from the trench. However, in natural subduction settings, the location of formation of a backarc basin will also depend on the lateral variation in lithospheric strength and buoyancy. Thus, from an overriding plate point of view, one would expect extension to preferentially localize in relatively weak zones with a high potential energy such as a magmatic arc [Karig, 1970; Molnar and Atwater, 1978; Dewey, 1980; Schellart et al., 2002]. Nevertheless, in several continental backarc regions on Earth that have recently started to localize backarc extension, such maximum extension occurs at a comparable distance from the trench as in the models. Examples include southwest Ryukyu (200–380 km), South Shetland (160–200 km), and northwest Mexico (230–350 km).

5 Conclusions

[53] The dynamic 3-D experiments of progressive free subduction with an overriding plate provide new insight into the kinematics of convergent margins and overriding plate deformation. Inclusion of a mobile overriding plate and a weak subduction channel in the system does not modify the general pattern of subduction kinematics, slab geometry, and subduction dynamics. The models with and without an overriding plate always show trench retreat, slab draping on the 670 km discontinuity, comparable slab dip angles, trenchward motion of the subducting plate, progressive curvature of the trench, and a slab that is concave towards the mantle wedge (Figures 2 and 6). Our narrow slab models with an overriding plate only show overriding plate extension. With increasing overriding plate thickness, however, the models do demonstrate an increase in subduction partitioning (i.e., an increase in vSP⊥/vS⊥), indicating that the subduction component due to trenchward subducting plate motion increases at the expense of subduction through trench retreat (Figure 4). An increase in TOP thus results in an increase in trench suction forces, which retard trench retreat and thereby promote subduction through trenchward subducting plate motion. Furthermore, an increase in TOP corresponds with a decrease in trench curvature and overriding plate extension because a thicker overriding plate provides more resistance to curve and extend. Therefore, with increasing TOP, trench retreat is progressively accommodated by trenchward overriding plate motion.

[54] The experiments show that overriding plate deformation is controlled by trench migration and by overriding plate thickness (and thus strength). The models show a positive correlation between trench retreat rate and overriding plate extension rate (Figure 7b), which is in agreement with a global compilation for active subduction zones [Schellart, 2008c]. Overriding plate extension is maximum, not at the trench, but at a distance of ~200–400 km from the trench (Figure 8a), indicating that basal shear tractions resulting from mantle flow below the overriding plate primarily drive extension and that deviatoric tensional normal stresses at the subduction zone interface are of subordinate importance. The trench-normal tectonic force FEXT that extends the overriding plate has been quantified for the free-sinking stage of the slab (before the slab tip touches the 670 km discontinuity) and is of the order 0.012–0.025 N, which constitutes 5%–11% of the only driving force in the experiments (Figure 9), the negative buoyancy force of the slab (FBu = 0.21–0.23 N). Ultimately, the experimental results suggest that toroidal mantle flow patterns, induced by slab rollback and trench retreat, drive the overriding plate basal shear tractions, thereby providing the main driving force for overriding plate extension and backarc basin formation.

Acknowledgments

[55] We are grateful to Serge Lallemand and an anonymous reviewer for their detailed and constructive comments, which have resulted in a much improved paper. The research presented in this paper has been supported by Discovery grants DP110103387 and DP120102983 and Future Fellowship FT110100560 from the Australian Research Council awarded to WPS.