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.

[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).

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