Back-arc strain in subduction zones: Statistical observations versus numerical modeling

1] Recent statistical analysis by Lallemand et al. (2008) of subduction zone parameters revealed that the back-arc deformation mode depends on the combination between the subducting (nu(sub)) and upper (nu(up)) plate velocities. No significant strain is recorded in the arc area if plate kinematics verifies nu(up) = 0.5 vsub - 2.3 (cm/a) in the HS3 reference frame. Arc spreading ( shortening) occurs if nu(up) is greater ( lower) than the preceding relationship. We test this statistical law with numerical models of subduction, by applying constant plate velocities far away from the subduction zone. The subducting lithosphere is free to deform at all depths. We quantify the force applied on the two converging plates to sustain constant surface velocities. The simulated rheology combined viscous (non-Newtonian) and brittle behaviors, and depends on water content. The influence of subduction rate vs is first studied for a fixed upper plate. After 950 km of convergence ( steady state slab pull), the transition from extensional to compressive stresses in the upper plate occurs for vs similar to 1.4 cm/a. The effect of upper plate velocity is then tested at constant subduction rate. Upper plate retreat ( advance) with respect to the trench increases extension ( compression) in the arc lithosphere and increases ( decreases) the subducting plate dip. Our modeling confirms the statistical kinematic relationship between vsub and nu(up) that describes the transition from extensional to compressive stresses in the arc lithosphere, even if the modeled law is shifted toward higher rates of upper plate retreat, using our set of physical parameters ( e. g., 100 km thick subducting oceanic plate) and short- term simulations. Our results make valid the choice of the HS3 reference frame for assessing plate velocity influence on arc tectonic regime. The subduction model suggests that friction along the interplate contact and the mantle Stokes reaction could be the two main forces competing against slab pull for upper mantle subductions. Besides, our simulations show that the arc deformation mode is strongly time dependent.