Reflection of an SV-wave from a rigid plane

An incident SV-wave generally reflects as both an SV-wave and a P-wave. A rigid boundary determines their amplitudes by requiring both displacement components to vanish, while phase matching preserves frequency and tangential wavenumber.

For incident SV angle $\theta$, tangential phase matching gives $\sin \varphi =(c_P/c_S)\sin \theta$ for the reflected P-wave. It is evanescent when $\sin \theta >c_S/c_P$.

When the converted P-wave is evanescent, its amplitude decays away from the boundary and the reflected SV amplitude has modulus one. The P field stores reactive energy near the boundary but carries zero mean normal power.

At a perfectly rigid plane, every component of the displacement field vanishes.