SH‐wave propagation in a continuously inhomogeneous half‐plane with free‐surface relief by BIEM

Abstract

The anti‐plane strain elastodynamic problem for a continuously inhomogeneous half‐plane with free‐surface relief subjected to time‐harmonic SH‐wave is studied. The computational tool is a boundary integral equation method (BIEM) based on analytically derived Green's function for a quadratically inhomogeneous in depth half‐plane. To show the versatility of the proposed BIE method, it is considered SH‐wave propagation in an inhomogeneous half‐plane with free surface relief presented by a semi‐circle, semi‐elliptic and triangle canyon. The inhomogeneous in depth half‐plane is modeled in two different ways: (i) the material properties vary continuously in depth and BIEM based on Green's function is used; (ii) the material properties vary in a discrete way and the half‐plane is presented by a set of homogeneous layers with horizontal interfaces and a hybrid technique based on wave number integration method (WNIM) and BIEM is applied. The equivalence of these two different models is shown. The simulations reveal a marked dependence of the wave field on the material inhomogeneity and the potential of the BIEM based on the Green's function for half‐plane to produce highly accurate results by using strongly reduced discretization mesh in comparison with the conventional boundary element technique using fundamental solution for the full plane.