A theoretical approach to multiple scattering of surface waves by shallow cavities in a half-space

The current theoretical work investigates multiple scattering of surface waves from shallow cavities at the surface of an elastic half-space. The multiple scattered field is shown to be equivalent to the field generated by the application of a distribution of tractions, obtained from the incident wave, on the surfaces of the cavities. Using a self-consistent method, an analytical approach is proposed to derive an explicit set of equations which approximate the multiple scattered field. Its far-field displacement amplitude is then calculated and verified by numerical calculation obtained by the boundary element method (BEM). The analytical and BEM results are graphically presented and show excellent agreement when the depths of cavities are small compared to the wavelength. The improvement of the proposed approach relative to a first order approximation is reported and its limitations are discussed based on the results of comparison.