SH waves scattering from a partially filled semi-elliptic alluvial valley

The scattering of SH waves induced by a partially filled semi-elliptic alluvial valley is explored via the region-point-matching technique (RPMT). Appropriate radial and angular Mathieu functions are well utilized to express the antiplane displacement fields. With the aid of the coordinate-transformed relation, which is intended as a substitute for the addition theorem (involving multiple summations of Mathieu functions), the application of the RPMT facilitates the rapid construction of simultaneous equations. Enforcement of zero-stress conditions on the curved valley surface and continuity conditions on the soil-bedrock interface leads to the determination of unknown coefficients. Comparisons with published data for several limiting cases (e.g. those pertaining to the truncated semi-circular canyon, the partially filled semi-circular alluvial valley, the totally empty semi-elliptic canyon and the fully filled semi-elliptic alluvial valley) show good agreement. Effects of pertinent parameters on steady-state surface motions are demonstrated. Transient changes in surface displacement amplitude are also included.