Diffraction of SH-Waves by Subsurface Inclusions of Arbitrary Shape

Abstract

The weighted residual method was applied to the problem of scattering and diffraction of plane SH-waves by an underground inclusion of a different elastic medium and of arbitrary shape in a two-dimensional half-space. Results from the application of the weighted residual approach to the case of an underground circular inclusion closely approximate those obtained using the closed-form solution for underground inclusions. To demonstrate the versatility of the method, it was applied to inclusions of elliptical and square shape. It was shown that significant ground-motion amplification, with respect to the amplitude of the incident waves, occurred due to the presence of an inclusion or cavity. Amplifications were dependent on the size, shape, and depth of the inclusion as well as the frequency and angle of incidence of the incident waves. Amplification profiles for the lower-frequency incident waves were simple with peak values that did not differ significantly from 2, the value expected on the surface of a uniform half-space. As the frequency is increased, amplification profiles become more complicated with worst-case values exceeding 7 for elliptical-shaped inclusions.