Anti-plane (SH) waves diffraction by an underground semi-circular cavity:analytical solution

摘要

Diffraction of a two-dimensional (2D) semi-circular cavity in a half-space under incident SH-waves is studied using the classic wave function expansion method with a new de-coupling technique.This so-called "improved cosine half-range expansion" algorithm exhibits an excellent performance in reducing displacement residual errors at two rim points of concern.The governing equations are developed in a manner that minimizes the residues of the boundary conditions.Detailed derivation and analysis procedures as well as truncation of infinite linear governing equations are presented.The semi-circular cavity model presented in this paper, due to its simple profile, is expected to be used in seismic wave propagation studies as a benchmark for examining the accuracies of various analytical or numerical methods for mixed-boundary wave propagation problems.