Abstract
This paper discusses three related problems. (1) A semi-infinite elastic medium in which the unperturbed homogeneous bulk material does not extend right up to the surface either because of surface perturbations or else because of a thin overlayer of a different material. If the thickness of this surface region is much smaller than the wavelengths of interest, then the problem can be cast as a modification of the boundary conditions. (2) An analytical discussion of the long wave limit of surface perturbed lattice models and the connection with the above theory of surface perturbed surface waves. (3) A mathematical formalism here developed to solve the perturbed surface wave problem, given the perturbed boundary conditions.
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