Analytic Studies of Seismic Waves in 3-D Structures

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Wave propagation in layered media has been fruitfully studied for several decades, with many applications in geophysics and other fields. The fundamental limitation of this type of modelling, in most cases, is its inability to handle lateral variations of structure. A recent discovery now indicates that analytical methods, developed and widely used for layers with plane parallel interfaces, can be extended to the case of plane interfaces that are not parallel. Consequently, it appears possible to develop a generalized ray theory for wave propagation in a stack of wedge-shaped layers. Layer interfaces can have arbitrary dip and strike, permitting the study of waves in truly three-dimensional structures. The methods that can be so generalized, from parallel layering to non-parallel, are those that derive from a fundamental and well-known relationship between travel- time, range, and a sum over vertical slownesses (weighted by layer thickness). It is remarkable that this relationship, so familiar in purely depth-dependent structures, is virtually unchanged in the three- dimensional case. We propose to explore the newly generalized methods to study wave propagation associated with randomly dipping interfaces.