Influence of trench width on subduction hinge retreat rates in 3-D models of slab rollback

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 (similar to 69%), a much smaller amount goes into weakening the plate (similar to 18%), and the remaining amount goes into driving flow parallel to displacement of the slab (similar to 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, 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 (similar to 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).