直达波旅行时线性插值算法

Direct wave travel time linear interpolation algorithm

文中首先简要介绍了初至波旅行时LTI算法,并分析了该法的计算结果包含非直达波旅行时的原因,由此提出通过对射线方向进行控制实现直达波旅行时计算的方法。直达波旅行时计算步骤与初至波旅行时LTI算法的计算步骤基本一样,只有两个不同之处:其一,旅行时赋初值不同,对震源点以外的节点,初至波旅行时LTI算法赋予大于该节点初至波旅行时的值,而直达波旅行时LTI算法则赋予大于该节点直达波旅行时的值;其二,在每次更新节点旅行时的过程中,一旦发现有波从某个低速地层传向某个高速地层,则在以后的计算中,判断射线是否是从该高速层指向该低速层,如果是则舍去该射线的旅行时。平层速度模型和具有起伏速度界面的多层模型算例说明,本文提出的直达波旅行时LTI迭代算法简单而有效,反射波射线追踪算例说明基于该算法可以进行大角度反射波射线追踪。

At first in this paper the direct wave travel time LTI algorithm was briefly introduced, then the reason for the algorithm’s calculation results to involve non-direct wave travel time was analyzed, so a new algorithm to calculate the direct wave travel time was realized by controlling ray’s direction. The calculation steps for the direct wave travel time are almost the same as the steps for the first break travel time LTI algorithm except the two different aspects as below. The first aspect is the different initial value for the travel time, for the nodes other than the source point, a value which is larger than the value of the first break travel time at the node was assigned in first break travel time LTI algorithm, while a value which is larger than the value of the direct weave travel time at the node was assigned in direct wave travel time LTI algorithm, the other different aspect exists in the process of refreshing the travel time for the nodes, that is once wave ray was found propagating from low velocity layer to high velocity layer, then the travel time for the wave ray would be ignored in the next calculations. Calculation example for horizontal layer velocity model and multi-layer model with rugged velocity subsurface show that the direct wave travel time LTI iterative algorithm is sample but effective, reflection ray tracing calculation example demonstrated that large angle reflection wave ray tracing can be conducted by using the algorithm.