Displacements and stresses in two welded half-spaces caused by two-dimensional sources

Abstract

Closed-form analytic expressions for the displacements and stresses at any point of either of two homogeneous, isotropic, perfectly elastic half-spaces in welded contact caused by various two-dimensional sources are obtained. The method consists of first finding the integral expressions for two half-spaces in welded contact from the corresponding expressions for an unbounded medium by applying suitable boundary conditions at the interface and then evaluating the integrals analytically. The case of a long dip-slip dislocation source is considered in detail. Graphs showing the variation of the displacements with the distance from the fault and with the distance from the interface (depth) for a vertical dip-slip fault are presented. It is found that, although at a large distance from the fault, the variation with depth is smooth, at short distances the variation with depth is complex, with sharp maxima and minima.