Multiple scattering of surface waves from discrete obstacles

Abstract

The surface wave T‐matrix formulation which describes scattering from a discrete obstacle embedded in a stratified medium is extended to accommodate scattering from two or more obstacles. By exploiting the translation properties of the vector cylindrical wave functions and employing the definition of the surface wave T‐matrix for a single obstacle it is possible to construct a composite T‐matrix for a two‐obstacle configuration in terms of the individual T‐matrices. This procedure can be extended, recursively, to incorporate N obstacles. The scattered field contributions from each obstacle including the entire hierarchy of multiple scattering interactions are clearly identifiable in the resulting expression. The formulation is applied to several two‐obstacle configurations over a range of ka to investigate the implications of multiple scattering interactions for regional phases such as Lg propagating in the Earth's crust and upper mantle. The results indicate that the significance of multiple scattering is dependent upon the size of the scatterers, their separation and orientation with respect to the incident wave. Multiple scattering is less pronounced for small scatterers (ka < 1.0) and is most significant at separations under a wavelength. For obstacles of ka∼ 1.0, pair interactions result in deviations from the zeroth‐order field of less than 10 per cent in the forward scattered power. The effects of multiple scattering are limited to still smaller separations for point scatterers; however the nature of their multipole representations suggests that scattered Love waves may be generated more efficiently through pair interactions than Rayleigh waves in the low‐frequency limit. Consideration of multiple scattering becomes essential as the size of the obstacle increases. Large obstacles (ka∼ 10.0) behave as lenses by focusing the majority of scattered energy along a narrow corridor about the forward direction. If two obstacles are aligned parallel to the direction of the incident wave the power in the first‐order pair interaction is comparable to the total power scattered from a single obstacle for a wide range of separations. Copyright © 1992, Wiley Blackwell. All rights reserved