An indirect method for computing troublesome coefficients in the boundary integral equation method

Abstract

The boundary integral equation (BIE) method is ideal for modeling scattering of waves from arbitrarily shaped objects embedded in unbounded domains. Its singular or ‘‘self’’-coefficients require special numerical treatment because the kernel of the integral equation exhibits the singularity of the Green’s function for a fundamental point source. Regularization for direct numerical integration is particularly complicated for elastic waves in layered media where the Green’s function is a tensor whose elements cannot be written in closed form. Here the singular coefficients are computed indirectly, by inferring their values from a family of related propagation scenarios whose solutions are known in advance by virtue of Huygens’ principle. The method can be applied quite generally to compute other potentially troublesome coefficients, which may occur in thin platelike objects, for example, when one boundary element lies close and parallel to another on the opposite face, or in horizontally stratified media when one element lies directly above another, making the Green’s function poorly convergent. The method is verified here for scattering from elastic spheres (low to moderate ka), and is demonstrated for scattering from an ice keel in floating sea ice, and for a sphere half-buried in seafloor sediments.