In this study we relax the strong limiting condition of parallel layering which is usually assumed in seismic modeling by allowing dipping boundaries. We start with the derivation of generalized ray theory in a wedge-shaped medium with free and rigid boundaries. Then, through the development of the method of equivalent models and de-Hoop contours, we extend the theory to dipping structure with elastic boundaries. The effect of a dipping interface over a half-space for the case of a line source is shown by a series of numerical models which include various angles of dip and source-to-receiver distances. Results for a line source situated below the layer indicate that, when the layer thickens toward the receiver, one obtains a wave form similar to the case where the source is actually in the layer. These features are produced by the combination of forward and backward traveling rays which can have super-critical reflections.

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