二维波动方程偏移的一种实用算法及其在小型计算机上的实现

A PEACTJCAL 2-D MIGRATION ALGORITHM AND ITS REALIZATION ON SMALL COMPUTER

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.

This paper deals with in some detail the principle and algorithm of the 2-D wave equation migration suitable for small dip-angle and its realization on small computer. It re-examined in the first place the mathematical and physical foundamental of this method presented by Claerbout, and then, derived a universally valid formula for the determination of reflection, migration from the equivalent mechanism. Several formulae corresponding with certain specific coordinate transformation were worked out attended by. It was pointed out that the results ought to be equivalent for both the equations of upward and downward waves as long as the migration conditions were suitable. Unlike the derivation of the convolution from the Z-transformation, this paper examined the implicit solution of the difference equation in a different way. It examined the solution from the view point of matrix and this kind of solution was called the approximate quickning pursuit method. Comparing with the classic pursuit method,the work hours of calculating is only 1/2 or so of that of the classic method. As for the practical parameters, the order of error and the speed of attenuation are all within the limits of allowance. Besides, the influence of the boundary conditions and the elimination of this influence were discussed as well. The calculation scheme of the realization of migration on computer Model 719, the practical technique of segment upon segment handling and margin joining were also examined. Parameters and indexes corresponding to the processing program were given. The trial and error tests of the program mentioned above have been made for both the theoretical model and the practical seismic data and some results were given at the end of this paper. Theoretical models adopted are: digital models (sine function horizontal wavelet) and synthetic models (single boundary with 15°syncline and 30°step). Seismic data adopted are the marine analog recordings, inclu- ding: typical diffractions, rotary waves, dipping layers and faults. Resultant of the trial and error test has fully proved that the algorithm and the program are both correct. Fine quality resultant of migration has been obtained for both theoretical model and practical data processing.The task as indicated above was for the providing of special software for the analogue data processing on computer Model 719, but it can be extended to digital data processing and computers of other types.