Estimating velocity anisotropy tomographically from cross well traveltime data is a process that often has two degrees of nonlinearities: the anisotropy itself and the ray bending from one iteration to the next. Under certain conditions one of these nonlinearities can be neglected and the computations related to other one are simplified. For example, assuming weak anisotropy, Pratt and Chapman (1992) and Chapman and Pratt (1992) proposed to do the ray tracing in isotropic media and to use those rays to back project in the anisotropic model. Michelena et al. (1991) simplify the problem even more and present examples where the velocity contrasts are small enough such that the rays traced on the anisotropic model are straight and the only non linearity that remains is in the estimation of the anisotropy. Unfortunately, these simplifications are not valid in general and therefore, the problem needs to be solved by tracing rays appropriately in inhomogeneous anisotropic media.
Methods for dynamic ray tracing in inhomogeneous anisotropic media have been proposed by Cervený (1972), Hanyga (1982), Jech and Psencík (1989) and Gajewski and Psencík (1990), among others. These methods are based on the solution of the dynamic ray tracing equations. In order to solve only the kinematic problem (what is needed to perform traveltime tomography), Byun (1982) and Byun (1984) proposes a different technique based on the application of Snell's law at each interface.
In this paper, I review Byun's procedure for kinematic ray tracing. From the boundary conditions at each interface, I derive the equation that relates the ray parameter p of the incident phase to the angle of the transmitted phase. By using this equation and the equations that relate phase and group velocities, I explain a procedure that uses alternatively both types of velocity to propagate a ray across a layer and to figure out how it changes direction when impinging upon an interface. At the end, I show examples of P-wave ray tracing for a cross-well geometry in different layered transversely isotropic models. In a separate paper (Michelena, 1992), I use this ray tracing procedure to do traveltime tomography in azimuthally anisotropic media.