Analytic Studies of Seismic Waves in 3-D Structures

波在层状介质中的传播已经得到了卓有成效的研究， 几十年来，在物理学和其他领域有许多应用。 在大多数情况下，这种建模的基本限制是 它无法处理结构的横向变化。 最近的一 现在的发现表明，分析方法，发展和广泛 用于具有平面平行界面的层，可以扩展到 平面界面不平行的情况。 因此，似乎有可能发展一种广义射线理论 用于楔形层堆叠中的波传播。 层 界面可以有任意的倾角和走向，允许研究 真正三维结构中的波。 这些方法可以 从并行分层到非并行分层， 源于一个基本的和众所周知的旅行之间的关系， 时间、范围和垂直慢度之和（按图层加权 厚度）。 值得注意的是，这种关系，如此熟悉， 纯粹的深度依赖结构，在三个方面几乎没有变化- 维度案例 我们建议探索新的广义方法来研究波 与随机倾斜界面相关的传播。

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.