Abstract
Abstract Using energy conservation and causality considerations, the completeness of scattering states is established for plane waves impinging on an irregular interface. Provided certain limiting operations commute with differentiation, it is shown that surface waves need not be explicity included in the Weyl representation of the Green's function in the presence of a rough interface. Rather, surface waves are implicity included through the poles of the scattering amplitudes. This result was used implicitly in a recently developed scheme to treat scattering in a duct using half-space scattering amplitudes (Berman, J. Acoust. Soc. Am. 92 (1992), 309–314).
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