AN APPROXIMATE ELASTIC TWO-DIMENSIONAL GREEN'S FUNCTION FOR A CONSTANT-GRADIENT MEDIUM

Abstract

Approximate analytical formulae for elastic 2-D Green's functions for a constant-gradient propagation velocity medium are presented. These solutions correspond to unit line forces per unit length: the antiplane SH line source and the in-plane P-SV line sources, respectively. They are based on the asymptotic ray theory and account for both near-source effects and low frequencies. The analytical expressions obtained are tested by means of the pseudospectral method with a velocity-stress staggered grid. The agreement of the approximate analytical displacement and stress fields with their numerical counterparts is generally very good. A measure of relative error is proposed.