Scattering of elastic waves in heterogeneous media using the direct solution method

Abstract

SUMMARY Multiple scattering is a phenomenon generic to wave propagation in heterogeneous media. In order to study scattering effects caused by inhomogeneities within an elastic medium we use the direct solution method (DSM). This method is based on solving the weak form of the elastic equation of motion. A complete set of trigonometric functions is used as trial functions to study 2-D problems. The computational costs of this method increase with frequency. To partially overcome this problem we use the discrete fast Fourier sine/cosine transforms. One of the problems that arises in the application of discrete solution methods for wave propagation calculations is the presence of reflections from the boundaries of the numerical mesh. We apply absorbing boundary conditions at the edges and corners. We use the stiffness concept for a three-quarter-space (calculated using the indirect boundary element method) to reduce the undesirable reflected waves generated at the corners. We also apply the stiffness concept for a quarter-space to impose free-surface boundary conditions. We consider SH-wave propagation (incident plane waves and line sources) in a 2-D space with natural boundary conditions. Comparisons with analytical solutions for simple problems are shown.