A kinematic model for deformation of the lithosphere at subduction zones

Abstract

A subduction model that interprets the whole pattern of topography and gravity anomalies across the island arc‐trench system has been constructed on the basis of dislocation theory. We model the lithosphere‐asthenosphere system by a gravitating, stratified half‐space, which consists of an elastic surface layer, an intervening layer with Maxwell viscoelasticily, and an elastic substratum. The steady subduction of the oceanic plate beneath the continental plate is represented by uniform slip at a constant rate over the plate interface which divides the elastic‐viscoelastic half‐space into two blocks. Using the limiting value theorem of the Laplace transform, we can show that the steady slip on the interface deeper than the lithosphere‐asthenosphere boundary does not contribute to surface deformation in the steady state. Accordingly, the pattern of surface deformation associated with the steady state subduction depends only on the thickness of the lithosphere and the geometry of the plate interface shallower than the lithosphere‐asthenosphere boundary. Numerical results show that the pattern of vertical motion at subduction zones is characterized by steep uplift on the continental side, sharp subsidence at the plate boundary, and gentle uplift on the oceanic side. This pattern bears a striking resemblance to the general pattern of topography across island arc‐trench systems. The whole pattern of topography and gravity anomalies across the southern Kurile arc is well matched by the subduction model with a lithosphere thickness of 50 km and a dip angle of 30° at depths.