摘要
由于地层结构和性质的复杂性,很难将它们概括为一类或几类物理模型。对于复杂的地震物理模型,也很难建立与之相应的数学模型。因此,本文在论文[1]、[2]的基础上,首先进行了在地震勘探中应用射线法的物理基础的讨论,并得出了基本上肯定的回答。然后用射线法计算模拟地研究了多层介质中三维地震运动学的正演问题。设每层介质是均匀的,各向同性的,具有常数的纵波和横波波速,其分界面是连续曲面,采用二元函数分片光滑逼近它们,给出了透射波和反射波在各层中射线的方向余弦和走时的计算公式,解决了射线与分界面的分片曲面块的交点求取问题,从而建立了多层介质中透射波和反射波时间场的算法,并计算出和分析了三层平行倾斜层和带有断层的二层平行倾斜层的反射波时距曲面。
Abstract
Because of the complexity of the stratum in its structures and characters, it's difficult to group them into one or more physical models, For the complex seismic physical models, it's not easy to set up the mathe-matic models corresponding to them. For this reason, we,firstly grounded on References [1] and [2], had a discussion on the physical fundamentals of ray-tracing for its application to seismic exploration. The positive results were obtained. Then, we explore the possible ways for solving the kinematic forward problem of 3-D seismic in multilayered medium in terms of the computer simulation of ray-tracing. In the examination, we have made the following assumptions: the medium of each layer is homogeneous and isotropic; the Vp and Vs of each layer are in constant; and each of the interfaces is a continuous one. Under such preconditions, the piecewise smoothing approximation of bivariate function was adopted. Consequently, the direction cosine and the X-T formula for the transmitted and reflected raypaths of each layer could thus be obtained and the problem of extracting the intersection points of raypaths with the piecewise intersurfaces could also be solved. The algorithm for the transmitted and the reflected time field calculation was settled up on this account. The reflection time surfaces of three parallel slant layers and of two parallel slant layers with faults have been calculated and inspected as well.
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