The formal integral solution for an arbitrary ray in a plane parallel-layered, vertically inhomogeneous elastic medium is evaluated using a modified third-order saddle point method. The result, which reduces to the Airy function solution where the latter is valid, is shown to be more generally valid and just as simple to compute.

In addition, it is shown that the phase shift due to caustics is intimately related to the occurrence of turning points along the ray. An expression is derived explicitly relating this phase shift to the number of turning points and to whether the ray is on a direct or reverse travel-time branch.

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