Exact and Approximate Generalized Ray Theory in Vertically Inhomogeneous Media

The generalized ray method in a vertically inhomogeneous model is formulated without any approximation by homogeneous layers. The solution is obtained as an infinite series in multiply ‘reflected’ waves. Each term can be solved using the exact method or the plane-wave, first-motion or geometrical approximations. It is shown that the first-motion approximation of the series converges rapidly, the ratio of successive terms in the infinite series being-(2l+ 1)(2l)(6/π)2. In addition it is shown that the first-motion approximation, which reduces to the geometrical approximation when the latter is valid, is a useful alternative to geometrical ray theory, being more generally valid and being almost as simple to compute.