Acoustic Wave Interaction with Surfaces of Inhomogeneous Solids.

When a plane wave strikes the plane surface of a homogeneous elastic solid, it is simply reflected and transmitted. If the elastic properties of the solid change along the surface, however, the incident wave can be diffracted as well. Attempts to quantify this interaction lead to nonseparable boundary value problems which, in most cases, must be treated approximately. Here, we calculate the diffraction resulting from a plane wave incident on an inhomogeneous plane elastic surface, by perturbing the problem from a homogeneous surface. We solve the boundary value problem for the first term in the perturbation series and write the solution as a Fourier integral. Uniformly valid asymptotic expansions are developed in order to describe the pressure field in two and three dimensions. Both the short wavelength and far field expansions for the two dimensional field are valid for any size inhomogeneity on the elastic surface. Some specific results of this analysis include: (1) The diffraction coefficients for diffraction from a slightly inhomogeneous elastic plate in two and three dimensions. (2) Uniformly valid explicit formulas for the determination of the scattered field from a slightly but arbitrarily inhomogeneous elastic surface in two dimensions. (3) A uniformly valid asymptotic expansion of the Green's function for the acoustic field in the fluid generated by a point source acting on the plane, fluid-loaded surface of a general homogeneous elastic solid.