傅里叶有限差分法三维波动方程正演模拟  

Modeling 3-D scalar waves using the Fourier finite-difference method

作　　者：张金海[1] 王卫民[1] 赵连锋[1] 姚振兴[1] 

机构地区：[1]中国科学院地质与地球物理研究所,北京100029

出　　处：《地球物理学报》2007年第6期1854-1862,共9页Chinese Journal of Geophysics

基　　金：中国科学院知识创新工程重要方向项目(KZCX2-YW-101)资助

摘　　要：傅里叶有限差分(FFD)法兼有相位屏法和隐式有限差分法二者的优势,能够处理复杂地质构造中的波传播问题,但在三维情形下,算子的双向分裂会引起明显的方位各向异性误差.本文用Fourier变换计算双向分裂过程中的高阶交叉项,消除了方位各向异性误差.该方法充分利用了FFD法在双域实现的算法结构,明显减少了由于引入误差校正所带来的计算量.将该方法应用于修改后的三维French模型的地震正演问题,并将得到的叠后记录、单炮记录同全波有限差分法的模拟结果进行对比,结果证实了该方法对一次反射波具有较高的模拟精度,在内存需求和计算效率方面则具有更大的优势.Fourier finite-difference （FFD） operator has both of the advantages of Fourier and finite-difference methods, it can handle the wave propagations in complex media with large velocity contrasts and wide propagation angles. In 3-D case,however, two-way splitting may cause artificial azimuthal anisotropy. In this paper, we handle the remnants of the conventional two-way splitting technique by Fourier transforms, and the azimuthal anisotropy is removed. Based on the dual-domain scheme of the FFD method, the proposed algorithm significantly reduces computational cost caused by error correction. Compared with the finite-difference method by the zero-offset records and shot profiles based on 3-D modified French model, the proposed method can properly model the primary reflected waves and is much more attractive in both computational cost and storage demand.

关 键 词：三维正演模拟 傅里叶有限差分 双向分裂 波动方程 

分 类 号：P631[天文地球—地质矿产勘探]