Scattering of SH Waves by a Rough Half-Space of Arbitrary Slope

Abstract

The method of matched asymptotic expansions is used to look into the problem of the scattering of plane SH waves by topographic irregularities of a restricted range in an otherwise plane half-space when the characteristic length dimension of the irregularity is much smaller than the wavelength of the incident wave. In contrast to previous work the slope of the irregularity remains arbitrary. Expressions for the near and far scattered fields are obtained. Comparison between this theory and the regular perturbation technique (which also assumes that the irregularity has a small slope) show that both agree when the slope is small but differ in the general case. Results are given for irregularities in the shape of triangles, trapezia and semicircles.