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本文较详细地探讨了小倾角二维波动方程偏移的原理、算法及其在小型计算机上的实现.文章首先简略回顾了克莱鲍特所提出的该方法的数学物理原理,并基于等效机制导出确定归位反射层的统一公式以及在几种具体坐标变换下的相应公式,指出无论对上行波或下行波方程,只要采用适当的归位条件,结果应当是等价的.与采用z变换导出褶积法不同,本文从矩阵角度出发对差分方程的一种隐式解法:快速近似追赶法进行了探讨.与经典追赶法相比,该算法的计算工作量仅为经典追赶法的一半左右,就实用参数而言,误差的量级及衰减速率是完全允许的.同时,简略讨论了这种算法的边界条件影响及处理办法.探讨了在国产小型719计算机上具体实现偏移的计算方案、分段重迭处理和边部拼接的实际技巧,并给出了相应程序的处理参数及有关指标.对上述方法程序,曾就理论模型和生产剖面进行了试算验证.本文最后给出了这方面的部分结果.理论模型包括:数字模型(正弦函数水平子波)和合成模型(15度向斜,30度阶梯的单界面模型).实际资料为海上模拟带记录,包括:较典型的绕射波,回转波以及倾斜层和断层.试算结果充分表明方法和程序是正确的,无论在理论模型和生产剖面上都取得了相当明显的偏移效果.以上工作当时是为提供适于模拟带资料生产的专用软件,针对7
In this paper, the principle and algorithm of two-dimensional wave equation migration with small dip angle and its implementation on a small computer are discussed in detail.First, the mathematical and physical principle of this method proposed by Claybottom is briefly reviewed, and based on the equivalent Mechanism to derive a unified formula to determine the homing layer and the corresponding formulas under several specific coordinate transformations, pointing out that the results should be equivalent as long as the appropriate homing conditions are used, regardless of the upgoing or downgoing wave equations, Different from the transformation-derived convolution method, this paper discusses an implicit solution to the difference equation from the matrix point of view: fast approximate chasing method.Compared with the classical chasing method, the computational workload of this algorithm is only about half of the classical chasing method , For the practical parameters, the error magnitude and the decay rate are completely allowed.At the same time, the paper briefly discusses the influence of the boundary condition and the treatment method.It also discusses the calculation scheme of the offset in the domestic small 719 computer , Subdivision overlap and edge splicing practical skills, and gives the corresponding program processing parameters and related indicators.For the above method procedures, the theoretical model Type and production profile were tested and verified.The partial results in this paper are given at the end of the paper.The theoretical models include: digital model (sine wave function horizontal wavelet) and synthetic model (15 degree syncline, 30 degree step single interface model The actual data are recorded for the offshore simulation zone and include: typical diffractions, gyroscopes, and inclined and fault zones, and the trial results show that the method and procedure are correct, both in theoretical and production profiles Quite obvious offset effect.The above work was to provide suitable for simulation data with the production of special software for 7