Generalized ray theory for dipping structure
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.
Additional InformationCopyright © 1977, by the Seismological Society of America. Manuscript received January 26, 1977. The authors thank D. Kosloff for providing us the results of finite element method for comparison. They also thank H. Kanamori, D. Harkrider, and C. Langston for reading the manuscript and giving constructive suggestions. This research was supported in part by the National Science Foundation under Grant ENV76-10506 and in part by the Advanced Projects Research Agency at the Department of Defense and was monitored by the Air Force Office of Scientific Research under Contract F44620-72-C-0078.
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