Recent advances in evaluating Green's functions for multi-layered media and half-space problems

Recent extensions in the computation of Green's functions for multi-layered media and half-space problems are reported. For anisotropic problems, a two-level asymptotic singularity extraction is combined with extended Sommerfeldrelated identities and the weighted average approach to provide additional acceleration and smoothing of Sommerfeld integrals for efficient simplex interpolation. For lossy anisotropic media, the associated identities must be appropriately continued into the complex plane. For the special case of half-space problems, two novel approaches are examined. The first uses double exponential quadrature to integrate directly between known singularities rather than detouring contours around singularities before reaching the so-called Sommerfeld tail region where the weighted average method can be used. The second technique instead deforms the integration path into a quasi-steepest-descent path, and seems particularly useful for large transverse source and observation point separations.