波动理论深度偏移快速算法研究与实现

Fast algorithm for wave equation depth migration

1. 地矿部海洋地质综合研究大队, 上海200120;2. 同济大学海洋地质系, 上海200092

Integrated Research Party of Marinc Gcology, Ministry of Gcology and Mincral Rcsourees, Shanghai City, Internal Postcodc: 200120

为了使复杂地质构造地区的地震资料正确成像, 最终需要应用精确复杂的偏移方法。优良的偏移方法, 不仅能适应较大地层倾角变化, 而且要求算法的适应范围更广泛．能够处理大的速度变化。随着越来越多地采用多次偏移迭代速度分析方法, 要求偏移方法趋向于快速计算过程。本文主要研究深度偏移快速计算方法和在中小型计算机上的具体实现。在推导了全倾角波动偏移的方程式后, 应用“函数替代法”和“变量分裂法”概括出了全倾角波动理论深度偏移方程组。采用微分方程差分化方法, 获得全倾角深度偏移差分方程, 并提出了一种新的差分方程矩阵单边化求解方法, 简化了差分计算过程, 降低了对计算机内存容量的要求。同时, 针对计算边界条件的设置, 应用了一种新的矩阵快速近似追赶算法, 加快了计算求解过程, 提高了计算效率。文章的最后, 提供了采用快速算法编制的处理软件对模型资料和实际地震测线进行处理的实际记录。计算过程和处理资料结果表明：本文提出的新的深度偏移快速算法理论正确, 计算过程稳定, 计算效率高, 处理效果良好。更有意义的是, 这种计算方法能够在中小型计算机上实现, 有利于深度偏移技术的推广应用。

Sophisticated techniques for migration are nceded in the final stage of data processing to image scismic data prceisely in arcas of structural complexity, which are required to be adaptable to formation dips and scismic velocities with variation in relatively large scales. Morcover, high-speed algorithm for implementing migration are in expectation since through which multiple iterative velocity analysis is incrcasingly cmployed.The topic of the paper is related to a fast algorithm for depth migration and how it operatcs on a mcdium or mini computer. After the derivation of a wave equation for migration in full dip scale, a equation system for depth migration in full dip scale is yiolded by means of " function substitution" and "variable separation", from which a set of differential cquation is built as a result of differencing. The prucedurc for solving such a equation system can be greatly simplified by trans forming its coefficicnt matrix to be unilatcral. In this way,the storage capacity necessary for operation might thus be reduccd. In cooperation with the boundary conditions established, a new algorithm approximate to the " specdup algorithm " is employed to expedite the computational process.In the latter part of the paper,some cxamples concerning the above-mentioned fast algorithm applied to both modeling and real scismic data with its associated program modules are prescnted.Practice shows that the algorithm is correct in principle, stable and efficient in operation and acceptable in result. It's worth mentioning that the algorithm can be operated on cither medium or mini computers, which is advantageous to the popularization of depth migration technique.