Reflection and transmission of surface waves in laterally varying media

Abstract

SUMMARY The T-matrix description of surface wave scattering is viewed in a reflection/transmission context reminiscent of problems involving elastic wave propagation in stratified media. This approach exploits the orthogonality properties of the surface wave basis functions and permits a description of surface wave propagation in environments exhibiting a degree of quasi-concentric multilayering about a vertical axis. In the first case we consider a multilayered environment where the individual layers are laterally homogeneous and where the layer boundaries need not be circularly cylindrical. The reflection/transmission treatment incorporates all higher order scattering processes and may be used to examine both scattering from multilayered obstacles and the outward evolution of a wavefield from a source acting along the vertical coordinate axis. We then examine the form taken by the reflection/transmission matrices where arbitrary lateral variations in material properties are confined to a broad cylindrical band surrounding the vertical axis. The total response is assembled by considering the band as a succession of infinitesimally thin, heterogeneous shells in welded contact. This treatment relies on the use of invariant embedding techniques and the expansion of the Green's function for a stratified medium in terms of surface wave basis functions. It is demonstrated that the theory is the 3-D extension of coupled mode techniques used to model surface wave propagation in strictly 2-D waveguides. The theory is applied to investigate the effect of near-source, continuously varying heterogeneity on surface wave radiation patterns in the far-field. The general character of the transmitted wavefield agrees with that expected from arguments based on geometrical optics. Despite the suggestive behaviour of the surface wave basis functions in the near-field, wavetype coupling by continuously varying heterogeneity is not especially efficient in this regime. This implies that large transverse components of displacement frequently observed on regional seismograms from explosive sources are the result of other mechanisms, for example abrupt changes in structure or anisotropy.