This paper describes theoretical computations of the dynamic response of the ground to strong earthquakes using both finite-element methods and analytic formulas based upon asymptotic approximations. We use the approximate formulas to calculate the predominant frequency of ground motion at the surface of sediment-filled valleys or 2-D sedimentary basins and compare the results with full-wave numerical results. We find that analytic approximations can be used to obtain good estimates for the fundamental and vertical overtone eigenfrequencies, i.e., for those ray eigentrajectories confined by the modal caustics to the neighborhood of the observation site. We show that, in general, the distribution of eigenfrequencies of resonant sedimentary basins can be understood in terms of the basin's geometry, specifically, the curvatures of the sediment/rock interface determine both the eigenfrequency distribution and the kind of dispersion (normal or anomalous) of surface waves trapped in the basin. To appropriately account for the effect of dispersion, a new formulation is proposed that is of more general validity than the asymptotic approximations.
All computations are performed in the time domain, and synthetic seismograms are constructed that illustrate the interference process leading to resonance. The scope of this paper is limited to the elastic response of 2-D basins and exclusively to SH waves.