Ground motions around a deep semielliptic canyon with a horizontal edge subjected to incident plane SH waves

We study scattering of antiplane shear waves induced by a deep semielliptic canyon with a horizontal edge. We employ the region-point-matching technique to cope with the problem considered. Through an auxiliary boundary, a part of the circumference of a semiellipse, the whole analyzed region is divided into two subregions. We express the displacement fields in terms of Mathieu functions. We unify two distinct elliptic coordinates via a simple coordinate transformation relation. Integration of the coordinate transformation relation into the region-point-matching technique simplifies the procedure for constructing simultaneous equations. Imposing the continuity conditions and traction-free ones, we obtain the expansion coefficients. Frequency-domain results demonstrate ground motion variability based on several key factors. Ground surface responses under seismic shaking are also simulated in the time domain.     

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

A series solution of the plane SH-waves incident on a partially filled semi-circular alluvial valley imbedded in a half-space is presented. Based on the region-matching method, the analysed region is decomposed into two subregions by the interface between two media. The antiplane displacement field of each subregion is expressed in terms of an infinite series of cylindrical wavefunctions with unknown expansion coefficients. After imposing the traction-free condition on the curved valley surface and the matching conditions on the interface with the aid of Graf's addition theorem, the unknown coefficients are obtained. Both the frequency- and time-domain responses are evaluated. In the theoretical derivation of this work, two classical exact series solutions are also included, so the present series solution is more general than those given before. Visible effects of different physical parameters on ground surface motions are illustrated in graphical form.     

An analytical approach for the scattering of SH waves by a symmetrical V-shaped canyon: shallow case

Based on the application of the region-matching technique, an analytical approach is presented for the scattering of plane SH waves from a shallow symmetrical V-shaped canyon, and then a series solution is derived. The analysed region is divided into an enclosed and an open region by introducing a semi-circular auxiliary boundary. In each region, the displacement field can be expressed as infinite sum of appropriate wavefunctions satisfying partial boundary conditions, respectively. The unknown coefficients can be determined by enforcing the continuity conditions in connection with the Graf's addition formula. The frequency- and time-domain responses are both evaluated and displayed for several physical parameters. From graphical results, the effects of the canyon depth on surface ground motion are conspicuous. The proposed series solutions can serve as benchmark for numerical methods, in particular for those at much higher frequencies.