Reflection and Scattering by a Slightly Undulatinginterface

However, in reality most interfaces are not planar on both micro and macro scales. The purpose of this study is to investigate the interaction between elastic waves and a slightIy non-planar interface. The method of asymptotic analysis is used to derive elose form solutions for the problem of reflection and scattering of a time-harmonic SH-wave at a slightly, but otherwise arbitrarily, non-plan ar interface. The case of in-plane waves will be considered elsewhere. Both periodie and non-periodic interface profiles are considered. For simplicity, our discussion in this paper will be restricted to the interface between an elastic half-space and a rigid substrate.