The dynamic Green's function due to an impulse in an infinite anisotropic medium under anti-plane deformation is derived by the method of Smirnov [1] for two-dimensional wave equation. The Green's function is inversely proportional to the time t and an effective dynamic shear modulus. It is shown that the tractions on the planes passing through the source point vanish identically. Based on the free-space Green's function, the Green's functions for wedges, semi-infinite media and strips are obtained.

This paper is to develop the background phase subtraction method to determine the resonance frequency of a two-dimensional alluvial valley subjected to an incident plane SH-wave. The scattered wave due to the alluvium can be expressed in a series of basis functions, and the associated coefficients are related to the coefficients of free field by the so-called T-matrix method. By applying the resonance scattering theory, the effects among all normal modes can be decoupled and hence one can obtain the phase shift of each eigen partial wave. Similarly, the phase shift of each eigen partial wave due to a canyon with the same geometrical shape of the alluvium can be determined, and is recognized as the background effect. Furthermore, based on the phase represented scattering matrix, the resonance frequencies of each normal mode and its overtones can be determined by the subtraction of the associated phase dependent function due to the canyon from that due to the alluvium.