Scattering of shallow asymmetric V-shaped canyon under cylindrical SH waves

Previous studies mostly used plane waves as the source input to study the influence of topography effects without considering the source distance. However, the influence of source effect on topography amplification cannot be ignored. This study presents a series solution for the scattering of cylindrical SH waves by a shallow asymmetric V-shaped canyon, and the effect of the location of the source on the topography magnification is investigated. The presented formulations in this paper first divide the asymmetric shallow V-shaped canyon into enclosed and open regions using the region-matching method. The free wavefield of cylindrical SH wave is solved by the image theory, and the wavefield in the enclosed and open regions is obtained based on the separation of variable method. The Graf’s formula is derived to unify the wavefield coordinates of the two regions, and the unknown coefficients of the wavefield are solved by the continuity condition of the boundary. Then, the proposed solution is verified by comparisons with published data for two cases (e.g. those pertaining to the symmetrical V-shaped canyon of cylindrical SH waves and the asymmetric shallow V-shaped canyon of plane SH waves). Finally, the effect of the source position, the width, and the dimensionless frequency of the asymmetric V-shaped canyon on the surface displacement amplification is discussed. It is found that the difference of displacement amplitude between asymmetric canyon and symmetric canyon can reach 270.2