Resonance analysis of a 2D alluvial valley subjected to seismic waves

The T-matrix formalism and an ultrasonic experiment are developed to study the scattering of in-plane waves for an alluvial valley embedded in a two-dimensional half-space. The solution of the in-plane scattering problem can be determined by the T-matrix method, where the basis functions are defined by the singular solutions of Lamb's problems with surface loading in both horizontal and vertical directions. In the experiment, a thin steel plate with a semicircular aluminum plate attached on the edge is used to simulate the two-dimensional alluvial valley in the state of plane stress. Based on the spectra of displacement signals measured at the free edge of the scatterer, the resonance frequencies where the peaks appear can be identified. It can be shown that the nondimensional resonance frequency is one of the characteristic properties of the scattering system. Furthermore, it is noted that the nondimensional resonance frequencies measured experimentally are in good agreement with those calculated theoretically.