Scattering of SH Waves by a Truncated Semi-Elliptic Canyon

Abstract

ABSTRACTIn this study, the region-point-matching technique (RPMT) is applied to examine the scattering problem of truncated semi-elliptic canyons under plane SH-wave excitation. The partition of the entire analyzed region into two subregions is carried out via an introduction of the elliptic-arc auxiliary boundary. Taking advantage of appropriate wavefunctions in elliptic coordinates, the expression of antiplane motions for each subregion can be obtained. To accomplish the indispensable coordinate shift, thecoordinate-transformed relation, intended as a substitute for the addition theorem involving Mathieu functions, is well utilized. Integration of thecoordinate-transformed relationinto the RPMT brings about the rapid construction of simultaneous equations. Effects of pertinent parameters on steady-state and transient surface motions are demonstrated. Computed results show that, for horizontal incidence, the potential high level of ground shaking may occur near the illuminated upper corner of the canyon. In such a small localized region, due to the occurrence of constructive interference between the reflected waves from the horizontal ground surface and the scattered waves from the corners of the canyon, the peak amplifaction may be at least two times that of free-field response.