3-D simulation of tectonic evolution of the Mariana arc–back-arc system with a coupled model of plate subduction and back-arc spreading

We developed a mechanical model for the nonlinear, coupled system of plate subduction and back-arc spreading on the basis of mathematical formulation for internal deformation due to a moment tensor in an elastic–viscoelastic layered half-space under gravity. In our modeling the plate subduction and the back-arc spreading are rationally represented by the increase of tangential displacement discontinuity at the plate interface and normal displacement discontinuity at the spreading center, respectively. Through 3-D numerical simulation with this model we obtained a possible scenario for the tectonic evolution of back-arc basins as follows. At the first stage, steady plate subduction gradually forms tensile stress fields in the back-arc region. When the accumulated tensile stress reaches a critical level, back-arc spreading starts at a structurally weak portion of the overriding plate. The back-arc spreading pushes out the frontal part of the overriding plate toward the plate boundary and leads to the increase of slip rates at the plate interface. The local increase of slip rates at the plate interface produces additional tensile stress in the back-arc region. The incremental tensile stress is canceled out by further back-arc spreading. Such a feedback mechanism is necessary to maintain steady back-arc spreading. The long duration of slip-rate excess due to back-arc spreading leads to the gradual protrusion of the plate boundary toward the descending plate (trench retreat). As the plate boundary moves away from the back-arc spreading center, the accumulation rate of tensile stress at the spreading center gradually decreases, and the slip-rate excess at the plate interface due to back-arc spreading also decreases. Then, the original back-arc spreading center becomes less effective in releasing the tectonic tensile stress, and new active back-arc spreading will start somewhere closer to the plate boundary. Such a qualitative scenario accords with the evolution history of back-arc basins in the Mariana region. We obtained the slip-rate excess of 7 mm/year at the plate interface and the 20 km trench retreat for the last 4.5 Myr. These simulation results are significantly smaller than observations in the Mariana region. The discrepancy between simulation results and observations can be ascribed to the effect of the negative buoyancy acting on cold descending slab, which advances spontaneous plate subduction and directly increases the slip-rate excess and the trench retreat in our model.