Variable seismic motions of P-wave scattering by a layered V-shaped canyon of the second stratification type

Abstract

Seismic waves scattering especially waves SH by different topographies has been widely studied in the field of earthquake engineering. However, most of these studies mainly focus on the topographies with the ideal assumption (elastic, isotropic and homogeneous) of uniform medium or the first stratification type of canyon (canyon that is not crossing by layer-interfaces). Compared with SH wave scattering, there exists a challenge to derive the theoretical solution for the scattering of P or SV wave especially by relative complicated canyon with non-uniform medium, which is defined as the second stratification type or type II here. The paper focuses on the study on the two-dimensional scattering of plane P waves by a symmetrical V-shaped canyon embedded in a two-layered elastic half-plane of type II. The challenge is to deal with three issues simultaneously, namely satisfaction of boundary conditions in the vertical direction, more complex reflections and more coordinate system transformations. Here more cylindrical coordinate systems and the skew coordinate transformation formulas need to be defined and used so as to satisfy the boundary conditions along the canyon surface, in which coordinate transformation and its solution process become more complex. The derived solution of symmetrical V-shaped canyon is rigorous theoretically and reliable, and further demonstrate that it is affected directly by the second layered type of symmetrical V-shaped canyon. Moreover, the effects of the layer medium, the incident frequencies and incident angles on the ground motion also are investigated by the double-layer considering nonhomogeneous cases. This study shows that inhomogeneous-material, frequencies of incident waves and the existence of the canyon result in conspicuous even non-ignorable effect on variability of surface ground motions.