Response of a shallow asymmetric V-shaped canyon to antiplane elastic waves

This study focuses on the theoretical aspect of topographic scattering induced by a shallow asymmetric V-shaped canyon under plane shear horizontal-wave incidence. An analytical approach, based on the region-matching technique, is applied to derive a rigorous series solution, which is more general than that in a previous study. For the wave functions constrained in two angular directions, a novel form of Graf's addition formula is derived to arbitrarily shift the local coordinate system. Barrier geometry, angle of incidence and wave frequency are taken as the most significant parameters in exploring the topographic effects of localized concave free surfaces on ground motions. Both surface and subsurface motions are presented. Comparisons with previously published results and boundary-element solutions show good agreement. Frequency-domain results indicate that, for the high-frequency case at a low grazing angle (corresponding to the potential case in teleseismic propagation), the high levels of amplified motions occur mostly on the illuminated side of the canyon. When the windward slope is steeper, the peak amplitude values, at least 2.4 times larger than those of free-field responses, tend to increase. Time-domain simulations display how a sequence of scattered waves travel and attenuate at regional distances.