A simple analytical approximation to the temperature structure in subduction zones

A simple model is employed to find scaling relations between key features of the temperature structure of subduction zones and subduction zone parameters. Flow in the wedge of mantle between the slab and the overriding plate is approximated by the corner flow of a Newtonian viscous fluid. The flow maintains an advective boundary layer on top of the slab that controls the temperature at the interface between the slab and the wedge. This temperature, the maximum temperature in the wedge above the slab, and the thickness of the advective boundary layer, all depend on a single dimensionless distance, Vrdelta(2)/kappa, where V is the speed of plate convergence, r is distance from the corner of the wedge, delta is the dip of the slab and kappa is thermal diffusivity. The observation that volcanic fronts at island arcs lie above places where the slab reaches a depth that correlates negatively with convergence rate and slab dip suggests that the thermal structure of subduction zones may be described by the simple scaling developed here, and that the locations of the arcs are controlled by a strongly temperature-dependent process taking place in the wedge.