The fast multi-pole indirect BEM for solving high-frequency seismic wave scattering by three-dimensional superficial irregularities

Taking full advantage of the indirect boundary element method (IBEM) and fast multi-pole expansion algorithm, this paper proposes a fast multi-pole indirect boundary element method (FM-IBEM) to solve the scattering of high-frequency seismic waves by three-dimensional (3-D) superficial irregularities or heterogeneity in a solid half-space. First, IBEM utilizes an exact dynamic Green's function for a full-space to construct the scattered wave field. Subsequently, by employing plane waves expansion of 3-D potential functions of compressional and shear waves, the multi-pole expansion and local expansion coefficients were derived. Implementation of FM-IBEM is presented in detail for wave-scattering problems. Numerical examples illustrate that the proposed FM-IBEM can reduce the memory required by more than an order of magnitude and also greatly improve the computing efficiency, retaining excellent accuracy as well. Ultimately, several high-frequency plane wave scattering problems of 3-D superficial irregularities in a solid half-space are illustrated, and several important scattering characteristics are described based on the high-precision numerical results.