On the existence of surface-wave solutions for anisotropic elastic half-spaces with free surface

A proof is developed that for a given direction of propagation on the free surface of a half-infinite anisotropic crystal, a surface-wave solution with a certain phase velocity vR<vL, where vL is the limiting velocity, will always exist, except in the special case when the bulk wave defining the limiting velocity satisfies the condition of a free surface. The proof is in terms of the surface impedance, which relates the amplitude at the surface of a surface wave with the external forces needed at the surface. The properties of the impedance as a function of phase velocity determines whether a surface wave not requiring external forces at the surface exists for a certain phase velocity. The proof is valid also in the case of degeneracies in the eigenvalue problem entering the analysis.