A ray theory is developed for an inhomogeneous, anisotropic medium, based on the concept of a wave front as the carrier of a discontinuity in particle velocity. The discontinuity conditions of several field quantities involved are formulated and serve to cast the problem in terms of a partial differential equation. The characteristics of this equation subsequently are identified in terms of rays, represented in parametric form as space curves. The energy transport along the rays is formulated by means of transport equations.

The theory is applied in particular to the case of the transversely (horizontally) isotropic, vertically inhomogeneous medium. Equations for rays and travel times are obtained in the form of integrals, which are suited for serving the purpose of numerical computations.

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