Surface motion of a half-space with triangular and semicircular hills under incident SH waves

Abstract

Wave propagation in a half-space with complex surface configuration is often encountered in fields like seismology and ocean engineering. This article presents a theoretical study of multiple scattering of SH waves by two hills of different geometries (a triangle and a semicircle) on a solid half-space. The standing waves in the triangular and semicircular hills are constructed by the fractional-order Bessel function method and Fourier integral transform method, respectively. The unknown coefficients of the standing waves are determined via the region-matching method. It is shown that the apexes of the hills are very sensitive to the external dynamic load because of multiple incidences; in particular, the apex of the triangular hill exhibiting maximum amplitude is most susceptible to the external load. Furthermore, the effect of the interaction between the triangular and semicircular hills is evaluated. It is found that the amplitudes on the showdown zone that connects the two hills have been largely amplified due to the interaction between the two hills. The mutual interaction between the hills should not be neglected if the distance between them is less than O(100) times the typical dimension of the hill.