Multipathing, reciprocal traveltime fields and raylets
Multipathing, reciprocal traveltime fields and raylets
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多路径、互易走时场和光线
DOI：
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发表时间：
2010
期刊：
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通讯作者：
J. Hauser
中科院分区：
文献类型：
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作者：
N. Rawlinson;M. Sambridge;J. Hauser
本文提出了一种计算非均匀介质中地震波后至的新理论。我们引入了“小射线”的概念，它是由正向和倒数走时场的联合性质定义的源和接收器之间的一段较晚到达的射线路径。我们证明了任意非均匀介质中单个源和接收器之间的所有射线都可以被划分为一组唯一的射线，其中任何一个射线都可以用来构造完整的两点路径。射线的一个特别有用的性质是它们对应于求和曲线中的平稳曲线。（正向和反向）走时字段，即添加第一个从某个点A到某个点B的第一（或第二，或甚至更晚）到达旅行时字段。我们发现，许多射线，每个对应于一个较晚到达的阶段，只需要较早到达的旅行时字段的建设。描述光线性质的理论是本文的主要结果。一个实际的结果是，在非均匀介质中，源和接收器之间的许多后来到达可以从两个初至走时场中找到，一个来自源，另一个（倒数场）来自接收器。构造后至波的理论和方法在二维数值实验中得到了验证，但在三维中没有变化。我们使用一个简单的基于网格的程函求解器来计算前向和倒数的初至走时场，并验证我们的结果与基于射线的波前建设（WFC）技术。在一个涉及简单波前三重化（或燕尾）的测试中，所有三个到达都被检索出来。在另一个具有严重速度不均匀性的例子中，在总共37个波至中找到了16个。理论表明，将来自源和接收器的二阶和高阶走时场组合起来可以产生所有的射线，因此可以产生所有的后期波至。在实践中，只有初至走时字段通常是可用的，在这种情况下，我们描述了一个简单的程序，找到任何剩余的到达使用中间人工源连同他们的初至走时字段。射线波的性质及其在联合走时场中的表现形式是一个以前未被认识到的特征，并提供了一种新的新方法来计算后来到达的波。
SUMMARY A new theory for the calculation of later seismic arrivals in heterogeneous media is presented. We introduce the concept of a ‘raylet’, which is a segment of a later arriving ray path between source and receiver defined by joint properties of forward and reciprocal traveltime fields. We show that all rays between a single source and receiver in arbitrary heterogeneous media can be divided into a unique set of raylets, any one of which can be used to construct the complete two-point path. A particularly useful property of raylets is that they correspond to stationary curves in the summed (forward and reciprocal) traveltime fields, i.e. adding the first (or second, or even later) arriving traveltime field from some point A to the first (or second, or even later) arriving traveltime field from some point B. We show that many raylets, each corresponding to a later arriving phase, require only earlier arrival traveltime fields for their construction. The theory describing the properties of raylets is the primary result of the paper. One practical consequence is that many later arrivals between source and receiver in heterogeneous media can be found from just two first-arrival traveltime fields, one from the source and the other (the reciprocal field) from the receiver. The theory and a method for constructing later arrivals is demonstrated though numerical experiments in 2-D but holds without change in 3-D. We use a simple grid-based eikonal solver to compute forward and reciprocal first-arrival traveltime fields, and validate our results with a ray-based wave front construction (WFC) technique. In one test involving a simple wave front triplication (or swallowtail), all three arrivals are retrieved. In another example featuring severe velocity heterogeneities, 16 out of a total of 37 arrivals are found. The theory shows that combining second and higher order traveltime fields from source and receiver yields all raylets and hence all later arrivals. In practice only first-arrival traveltime fields are usually available and for this case we describe a simple procedure to find any remaining arrivals using intermediate artificial sources together with their first-arrival traveltime fields. The properties of raylets and their manifestation in the joint traveltime field appears to be a previously unrecognized feature and provides a novel new approach to the calculation of later arrivals.