An approximate elastic two-dimensional Green's function for a constant-gradient medium

Approximate analytical formulae for elastic 2-D Green's functions for a con stant-gradient propagation velocity medium are presented. These solutions c orrespond 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 as ymptotic ray theory and account for both near-source effects and low freque ncies. The analytical expressions obtained are tested by means of the pseud ospectral method with a velocity-stress staggered grid. The agreement of th e approximate analytical displacement and stress fields with their numerica l counterparts is generally very good. A measure of relative error is propo sed.