Sensitivity of frequency-dependent traveltimes to laterally heterogeneous, anisotropic Earth structure

This paper describes a study of the resonance phenomenon of a 2-D alluvial valley embedded in a half-space and subjected to an incident plane SH wave. The scattered wave and refracted wave are expressed as a series of basis functions, and both the scattered and refracted coefficients can be related to the incident wave by the so-called T-matrix method. By using singular-value decomposition and solving the eigenvalue problem, one can decouple the effects of all resonance modes. Therefore, the amplification factor of each partial eigenwave can be found, and used to determine the resonance frequencies of each normal mode and its overtones. The motion of the ground subjected to the incident plane SH wave and the mode shape of each single normal mode are determined and discussed for semicircular and semi-elliptical alluvial valleys.