Theory of generalized rays for SH-waves in dipping layers

The theory of generalized rays is applied to analyze transient waves in a layered half-space with non-parallel interfaces. The propagation, transmission, reflection, and refraction of SH waves which are generated by a line source in the surface layer of a three-layer model are considered, each of the two overlaying layers having a different dipping angle.Generalized ray integrals for multi-reflected rays in the top layer and for rays that are transmitted into the lower layer and then refracted back into the top layer are formulated by using three 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 slownesses, all ray integrals are expressible in a common slowness variable. The arrival time of each ray undergoing multiple reflections and transmissions is then determined from the stationary value of the phase function with common slowness of the ray integral. Inverse Laplace transform of these ray integrals are completed by Cagniard's method.