Mode conversion at a planar elastic interface

An obliquely incident in-plane P- or SV-wave generally produces reflected and transmitted P- and SV-waves. Continuity of displacement and traction supplies four scalar conditions for their four amplitudes, while frequency and tangential wavenumber are shared.

Phase matching at a planar interface preserves frequency and tangential wavenumber. Thus waves of speeds $c_j$ and angles ${\theta }_j$ from the normal satisfy