Subducting slabs provide the main driving force for plate motion and flow in the Earth's mantle, and geodynamic, seismic and geochemical studies offer insight into slab dynamics and subduction-induced flow. Most previous geodynamic studies treat subduction zones as either infinite in trench-parallel extent (that is, two-dimensional) or finite in width but fixed in space. Subduction zones and their associated slabs are, however, limited in lateral extent (250-7,400 km) and their three-dimensional geometry evolves over time. Here we show that slab width controls two first-order features of plate tectonics-the curvature of subduction zones and their tendency to retreat backwards with time. Using three-dimensional numerical simulations of free subduction, we show that trench migration rate is inversely related to slab width and depends on proximity to a lateral slab edge. These results are consistent with retreat velocities observed globally, with maximum velocities (6-16 cm yr(-1)) only observed close to slab edges (<1,200 km), whereas far from edges (>2,000 km) retreat velocities are always slow (<2.0 cm yr(-1)). Models with narrow slabs (< or =1,500 km) retreat fast and develop a curved geometry, concave towards the mantle wedge side. Models with slabs intermediate in width ( approximately 2,000-3,000 km) are sublinear and retreat more slowly. Models with wide slabs (> or =4,000 km) are nearly stationary in the centre and develop a convex geometry, whereas trench retreat increases towards concave-shaped edges. Additionally, we identify periods (5-10 Myr) of slow trench advance at the centre of wide slabs. Such wide-slab behaviour may explain mountain building in the central Andes, as being a consequence of its tectonic setting, far from slab edges.

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[1] Subduction of tectonic plates limited in lateral extent and with a free-trailing tail, i.e., ''free subduction,'' is modeled in a three-dimensional (3-D) geometry. The models use a nonlinear viscoplastic rheology for the subducting plate and exhibit a wide range of behaviors depending on such plate characteristics as strength, width, and thickness. We investigate the time evolution of this progressive rollback subduction, measure the accompanying return flow in the upper mantle, and quantify the plate kinematics. Due to the 3-D geometry, flow is allowed to accompany slab rollback around the lateral edges of the slab (the toroidal component), as opposed to 2-D geometry, where material is forced to flow underneath the slab tip (the poloidal component). A simple force balance is provided which relates the speed of backward trench migration to the resistive forces of generating flow and weakening the plate. Our results indicate most of the gravitational energy of the system (i.e., the negative buoyancy of the subducting slab) is converted into a toroidal flow ($69%), a much smaller amount goes into weakening the plate ($18%), and the remaining amount goes into driving flow parallel to displacement of the slab ($13%). For the trench widths (W) we investigate ( 1500 km), a maximum trench retreat rate occurs for trenches 600 km wide, which is attributed to the interaction between a plate of finite width and the induced flow (which has a lengthscale in the horizontal direction). These numerical results quantitatively agree with comparable 3-D laboratory experiments using analogue models with a purely viscous plate material (Schellart, 2004a(Schellart, , 2004b, including correlations between increasing retreat rate with increasing plate thickness, trench width for maximum retreat rate (500 km), and estimated amount of slab buoyancy used to drive rollback-induced flow ($70%). Several implications for plate tectonics on Earth result from these models such as rollback subduction providing a physical mechanism for ephemeral slab graveyards situated above the more viscous lower mantle (and endothermic phase transition) prior to a flushing event into the lower mantle (mantle avalanche).

[1] Results of fluid dynamical experiments are presented to model the kinematics of lithospheric subduction in the upper mantle. The experiments model a dense highviscosity plate (subducting lithosphere) overlying a less dense low-viscosity layer (upper mantle). The overriding lithosphere is not incorporated. Several important features of slab behavior were investigated including the temporal variability of hinge line migration, the kinematic behavior of the slab and the subduction-induced upper mantle flow. Both fixed and free trailing edge boundary conditions of the subducting plate were investigated. Results show that hinge line retreat is a natural consequence of subduction of a negatively buoyant slab. The migration rate increases until the slab approaches the upper-lower mantle discontinuity, resulting in a decrease in migration rate followed by a renewed increase and finally approaching a steady state. Slab retreat results in mantle flow, with material initially located underneath the slab flowing around the lateral slab edges toward the mantle wedge. Experimental results indicate that all rollback-induced flow occurs around the lateral slab edges, forcing the hinge line to attain a convex shape toward the direction of retreat. No signs for poloidal flow underneath the slab tip have been detected. Only a small component of toroidal-type flow was observed underneath slanting slab tips. For a fixed trailing edge, the slab does not sink vertically downward, but sinks at an angle in a regressive manner. For a free trailing edge, slab sinking is oriented more vertically while the surface part of the subducting plate is pulled into the subduction zone.

[1] Three-dimensional fluid dynamic laboratory simulations are presented that investigate the subduction process in two mantle models, an upper mantle model and a deep mantle model, and for various subducting plate/mantle viscosity ratios (h SP /h M = 59-1375). The models investigate the mantle flow field, geometrical evolution of the slab, sinking kinematics, and relative contributions of subducting plate motion and trench migration to the total rate of subduction. All models show that the subducting plate is always moving trenchward resulting from slab pull. Furthermore, all deep mantle models show trench retreat, as do upper mantle models in the initial stage of subduction before slab tip-transition zone interaction. Upper mantle models with a low h SP /h M (66, 217) continue to show trench retreat after interaction. Upper mantle models with a high h SP /h M (378, 709) show a period of trench advance after interaction followed by trench retreat. Upper mantle models with a very high h SP /h M (1375) show continued trench advance after interaction. The difference in trench migration behavior and associated slab geometries is attributed to both h SP /h M and the mantle depth to plate thickness ratio T M /T SP , which both affect the slab bending radius to mantle thickness ratio r B /T M . Four subduction regimes can be defined: Regime I with r B /T M $0.3, trench retreat, slab draping, and a concave trench; Regime II with $0.3 < r B /T M < $0.5, episodic trench migration, slab folding, and a concave trench; Regime III with r B /T M % 0.5, trench advance, slab rollover geometries, and minor trench curvature; and Regime IV with r B /T M ! $0.8, trench retreat, slab draping, and a rectilinear trench. In all models, slab-parallel downdip motion induces poloidal mantle flow structures. In addition, trench retreat and rollback motion of the slab induce quasi-toroidal return flow around the lateral slab edges toward the mantle wedge. Rollback-induced poloidal flow around the slab tip is not observed in any of the experiments. Finally, comparison between the slab geometries observed in the upper mantle models and slab geometries observed in nature imply that the effective viscosity ratio between slab and ambient upper mantle in nature is less than 10 3 and of the order 1-7 Â 10 2 , with a best estimate of 1-3 Â 10 2 .

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