Scattering of cylindrical SH waves induced by a symmetrical V-shaped canyon: near-source topographic effects

The series solution of wave functions for 2-D scattering and diffraction of cylindrical SH waves induced by a symmetrical V-shaped canyon is proposed herein to account for near-source topographic effects. A line source of cylindrical waves is employed to reveal the influence of source on topographic effects. According to the region-matching method, the half-space having a symmetrical V-shaped canyon is divided into two subregions by using a circular-arc auxiliary boundary. Hence, two cylindrical coordinate systems for the two subregions are defined. In each coordinate system, the wavefield is represented by means of the separation of variables method, in terms of the series of both Bessel functions and Hankel functions with unknown complex coefficients. Two more cylindrical coordinate systems are built for the source and its image with respect to the free surface. Then both of the wavefields in the two subregions are represented in the same coordinate system by using the Graf addition theorem. The unknown coefficients of the wavefields are solved by satisfying the continuity conditions of the auxiliary boundary. By comparing our cylindrical wave results with plane wave results in the literature, we find that near-source topographic effects are different from far-field topographic effects. The ground motion at a particular site could be amplified for a near source even if it is reduced for the incidence of plane waves without real sources. To show the effect of the source on the topographic amplification of ground motions, a parametric analysis is carried out in the frequency domain. Surface and subsurface transient responses in the time domain demonstrate the phenomenon of cylindrical wave propagating and scattering. It is found that the topographic effect is a function of incident wave sources, and near-source topographic effects are strongly affected by source locations. Whether the ground motion at a particular site is amplified or not and how strong the amplification or reduction is can be altered by the source location.