Surface motion of a semi-elliptical alluvial valley for incident plane SH waves

Abstract By using the exact analytical solution for the two-dimensional SH-wave propagation in and around an elastic inclusion whose cross section corresponds to one half of an ellipse, we have examined those aspects of the resulting ground motion that are of special interest for earthquake engineering and strong-motion seismology. Computed amplitudes and phases of periodic ground motion display complicated wave-interference phenomena that lead to nearly-standing wave patterns, abrupt changes in the amplification of incident motions along the free surface of the alluvial valley and strong dependence of the overall motions on the incidence angle of SH waves. By comparing the amplification patterns derived from the exact model with the amplifications computed on the basis of an equivalent single-layer model excited by the vertically incident shear waves, we have demonstrated that this approximate representation may lead to meaningful results only if the wavelength of incident waves is longer than the characteristic dimension of the alluvial valley. Although simple, we expect that the model presented in this paper might explain qualitatively the vibrations of some alluvial valleys excited by SH components of strong ground motion.