中文摘要：

在改进后的最短路径算法（MSPM）中引入分区多步计算技术实现了二维层状起伏介质中的多次透射、反射及转换波波前传播的数值模拟，以及相应的走时和射线路径的跟踪计算．其原理是将二维复杂层状模型按速度界面分成若干个独立的计算区域，采用分步计算技术进行多次波的跟踪计算．基于多次波是通过速度界面的简单入射、透射、反射及转换波按一定规律的不同组合，因此可实施分区多步计算技术．通过某一上、下层界面的透射（或透射转换）波实际上是由上层得到的下行波加上由该界面透射的下行波组成，若为转换波则使用不同的速度模型；而经过某一界面的反射（或反射转换）波实际上是由某层内计算得到的下行（或上行）波再加上由该界面反射的上行（或下行）波组成．这样即可得到分区独立计算，并通过速度界面分步连接达到跟踪多次波的目的．计算结果表明MSPM算法下的分区多步计算技术具有单步SPM算法中的诸多优点，即：算法简单、数值计算稳键、计算精度高、速度快及全球解等，因而是解决多次波跟踪计算行之有效的方法．

英文摘要：

The purpose of this study aims at introducing the multistage scheme incorporating with a modified shortest path method （MSPM） for tracking multiple arrivals and simulating wavefront evolutions composed of any kind of combinations of transmissions, conversions and reflections in 2D layered media. The principle is first to divide the layered model into several different computational domains, and then to use the multistage technique to trace the multiple arrivals. It is possible to realize the multiple arrival tracking with the multistage technique because the multiple arrivals are the different combinations of the simple incident, transmitted, reflected and converted waves via velocity boundaries （or discontinuities）. By treating each separate layer that the wavefront enters as an independent computational domain, one can simulate wavefront transmission and mode conversion by reinitializing it in the adjacent layer, and wavefront reflection （and/or conversion） by reinitializing it in the incident layer. Numerical tests and error analysis indicate that the multistage MSPM method retains the basic characteristics of the single-stage MSPM approach, that is algorithm simplex, numerical stability, high computational accuracy, fast, global solution and etc. Therefore it is a practical algorithm for tracking multiple arrivals.