Transient elastic waves in a wedge-shaped layer

TLDR: In this paper, generalized ray integrals for multi-reflected rays in the top layer are formulated by using two rotated coordinate systems, one for each interface, and are expressed in terms of local wave slowness along each interface.

Abstract: The theory of generalized ray is applied to analyzing transient elastic waves in a layered half-space with non-parallel interface. The propagation, reflection and refraction of longitudinal (P-) and transverse (SV-) waves which are generated by a line source in the surface layer of a two layer model are considered, each of the two homogeneous and isotropic layers having different density and inverse of wave speeds. Generalized ray integrals for multi-reflected rays in the top layer are formulated by using two rotated coordinate systems, one for each interface, and are expressed in terms of local wave slowness along each interface. Through a series of transformations of the local slowness, all ray integrals are expressible in a common slowness variable. Special attention is given to wave mode changes during reflection. The arrival time of each ray is then determined from the stationary value of the phase function with common slowness of the ray integral. Arrivals of head waves corresponding to rays refracted at a fast bottom are calculated from proper branch points of the Cagniard-mapping.