A multiple-scattering scheme for modelling surface wave propagation in isotropic and anisotropic, three-dimensional structures

We present a method to model the propagation of surface waves in Cartesian structures showing isotropic and anisotropic 3-D heterogeneities. It is assumed that the background structure is laterally homogeneous and that the heterogeneities act as secondary sources, producing multiple scattering and coupling between the surface wave modes of the background structure. No far-field approximation is made, enabling in particular the heterogeneities to be located in the vicinity of the source or receiver. The heterogeneities may be strong and extended 3-D bodies or perturbations of layer boundaries. Several applications are presented, including comparison to an exact solution for a cylindrical heterogeneity. The multiple-scattering series is shown to converge for strong heterogeneities of 10 per cent in S-wave velocity over several wavelengths. We analyse the influence of anisotropy and show in particular that some elastic coefficients, which are non-zero in mantle structures with crystals oriented in a non-horizontal flow, are able to distort the surface wave polarizations strongly.