A note on the effect of the free surface on the elastic deformation due to a long dip-slip fault

Abstract

To calculate the elastic deformation due to a thrust fault in the lithosphere-asthenosphere composite, Nur and Mavko (1974) used the exact solution of Mura (1968) for an edge dislocation parallel to the boundary of two elastic half-spaces in welded contact. They approximated the effect of the free surface by considering Mura's solution for two equal and opposite edge dislocations with the free surface midway between them. By considering a simpler problem of a long dip-slip fault in a uniform half-space, we show that the approximate method used by Nur and Mavko does not yield satisfactory results. For small dip angles and beyond a certain epicentral distance, while the exact solution predicts subsidence, the approximate solution predicts uplift. Moreover, the approximate solution yields non-zero values for the surface tractions at the free surface.