Elastic waves in a transitional solid with arbitrarily small rigidity

Abstract

The system of ODE that governs elastic-wave propagation in plane stratified media becomes singular as the elastic rigidity approaches zero. Two approximate methods are presented to address the problem. First, for P-SV waves, one can impose the condition that the displacement is curl-free in the transitional solid. This condition suppresses shear waves. Second, one can represent a thin transitional solid as a massive elastic interface (MEI). The MEI boundary conditions do not become singular as the MEI rigidity approaches zero.