Ray tracing algorithms in three-dimensional laterally varying layered structures
Ray tracing algorithms in three-dimensional laterally varying layered structures
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DOI：
10.1007/978-94-009-3899-1_5
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发表时间：
1987
影响因子：
6.1
通讯作者：
V. Červený
中科院分区：
文献类型：
--
作者：
V. Červený
这一章简要回顾了我的高频地震体波在三维横向变化的各向同性层状结构中传播的追踪和旅行时计算的现有方法。主要关注初值射线追踪，其中所考虑的单个射线由其初始点和该点上的射线的初始方向来指定。详细讨论了求解初值轨迹的数值方法、解析方法和单元方法。本文给出了用二次慢度(L/V2)代替传播速度V的“二次慢度”模型中光线追踪的简单算法。在第6节中，光线追踪系统被重写为任意曲线正交系，在第7节中被重写为球面坐标系。在所有这些情况下，光线跟踪系统由适当的反射/传输定律补充，允许执行光线跟踪和走时计算，即使在任意曲线的情况下也是如此。动态光线跟踪和传播矩阵的简要回顾在第8-10节中给出。动态射线追踪和传播子矩阵最近在地震学中得到了重要应用。例如，它们可以方便地计算旅行时间场的二阶导数，只需重新设置射线沿线的空间导数和射线“近轴”附近的走时场。光线传播矩阵还可用于简单地计算任意傍轴光线，并解析地求解任意傍轴光线的边值光线追踪问题。完全解析解
This chapter presents a concise review of reeent methods of my tracing and traveI time computations of high-frequency seismic body wave propagating in three-dimensional laterally varying isotropic layered structures. Large attention is devoted mainly to initial value ray tracing, in which a single ray under consideration is specified by its initial point and by the initial direction of the ray at that point. The numerieal, analytic and cell approaches to the soIution of initial value my tracing are discussed in detail. Particularly simple algorithms are obtained for the ray tracing in the" quadratie slowness" model, in which the quadratic sIowness (l/V2) is used instead of the propagation velocity V. In Section 6, the ray tracing system is rewritten into an arbitrary curvilinear orthogonaI coordinate system, and in Section 7 into a spherical coordinate system. In all these cases, the ray tracing system is supplemented by the appropriate reflection/transmission laws which allow to perform the ray tracing and the traveI time computations even aeross arbitrary eurved interjaees.A short review of the dynamie ray tracing and propagator matriees is given in Sections 8-10. Dynamic ray tracing and the propagator mattiees have recently found important applleations in seismology. For example, they can be used to compute easily the second derivatives of the traveI time field with respeet to the spatial derivatives along the rayand the travel time field in the" paraxial" neighbourhood of the ray. Ray propagator mattiees can be also used to compute simply any paraxial rayand to solve analytieally any boundary value ray tracing problem for paraxial rays. The complete analytic soIution