矩形网格上的隐式四向分解差分算法及其在VTI偏移中的应用

Four-way splitting implicit finite-difference algorithm on rectangular grids and its application to VTI migration

(CGGVeritas公司,美国得克萨斯休斯敦 TX 77072)

CGGVeritas, Houston TX77072, USA

采用传统的双向分裂算法隐式差分求解单程波方程会导致严重的数值各向异性问题，而目前的四向分解格式只适用于正方形网格。针对这个问题，构造了矩形网格上的四向分解格式，同时采用李氏修正项来减少数值频散和倏逝波噪声。进一步，将这个方法推广到求解VTI介质中的单程波偏移。利用数值计算验证了该方法的可行性。同已有的各种VTI介质单程波偏移方法相比，该方法计算时占用内存小、速度快，且能对速度剧烈变化地区的地质构造比较精确地成像。

The conventional implicit finite-difference algorithm by two-way splitting causes severe numerical anisotropy when applied to one-way wave equation migration. However, the present four-way splitting mode is just suitable to uniform grid. Therefore, we propose a new four-way splitting method which adapts to any rectangular grids and uses Li’s correction to reduce the numerical dispersion and evanescent energy. Further, we generalized it to one-way wave migration of VTI medium. Numerical examples prove the feasibility of this method. Comparing to the published VTI migration methods, our method requires less memory storage, computes fast, and can handle strong lateral velocity variations.