Elastic waves in a transitional solid with arbitrarily small rigidity

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.