Scattering of Rayleigh waves by surface defects

Abstract

The scattering of Rayleigh waves by defects is discussed by means of first-order perturbation theory. The defect is treated as a point defect of excess mass, either at the surface or some fixed distance below it. Scattering is into other Rayleigh waves or into bulk waves. Expressions are given for the scattering probability and for the relative scattering into these two groups of modes. For a point defect at the surface, scattering varies as the fifth power of frequency, and scattering into other Rayleigh waves is the dominant process. For point defects distributed through the volume of the solid, scattering varies as the fourth power of frequency. Expressions are also given for a line of defects normal to the surface and of finite length. For an infinite line, scattering varies as the cube of the frequency. Horizontal line defects and vertical sheets of defects have been treated in the doctoral dissertation of one of the authors (R.G.S.). These results are summarized.