利用矩阵分解理论的双程波方程叠前深度偏移方法  

Two-way wave equation prestack depth migration using the matrix decomposition theory

作　　者：尤加春 曹俊兴[1] 王俊[1] YOU JiaChun;CAO JunXing;WANG Jun(School of Geophysics,Chengdu University of Technology,Chengdu 610059,China)

机构地区：[1]成都理工大学地球物理学院,成都610059

出　　处：《地球物理学报》2020年第10期3838-3848,共11页Chinese Journal of Geophysics

基　　金：中国博士后科学基金面上项目资助(2019M653357);国家自然科学基金(41430323);国家自然科学基金联合基金项目(U1562219)联合资助.

摘　　要：叠前深度偏移理论及方法一直是地震数据成像中研究的热点问题.业界对单程波叠前深度偏移方法和逆时深度偏移开展了深入的研究,但对双程波方程波场深度延拓理论及成像方法的研究还鲜有报道.本文以地表记录的波场值为基础,利用单程波传播算子估计波场对深度的偏导数,为在深度域求解双程波方程提供充分的边界条件,并提出利用矩阵分解理论实现双程波方程的波场深度外推.通过对强速度变化介质中传播波场的计算,与传统的单程波偏移方法相比,本文提出的偏移方法计算的波场与常规有限差分技术计算的波场相一致,证明了本方法计算的准确性.通过对SEAM模型的成像,在相同的成像参数下,与传统的单程波偏移算法和逆时深度偏移算法方法相比,本文提出的偏移方法能够提供更少的虚假成像和更清晰的成像结果.本文所提偏移算法具有深度偏移和双程波偏移的双重特色,推动和发展了双程波叠前深度偏移的理论和实践.Study on the theory and method of prestack depth migration has always been a focused topic in seismic data imaging.The one-way wave equation depth migration and reverse time migration methods have been deeply studied,while less research on wavefield depth extrapolation and imaging based on two-way wave equation is reported.Based on the wavefield recorded at the surface,we use a one-way wave propagator to estimate the derivative wavefield,which provides sufficient boundary conditions for solving two-way wave equation in the depth domain and propose a matrix decomposition scheme to perform wavefield depth extrapolation based on two-way wave equation.Through the calculations of wavefields in the medium with strong velocity changes,it is proved that the down-going waves obtained by the proposed method are consistent with that achieved by the conventional finite difference technique.Compared with the one-way GSP method,this numerical experiment verifies the accuracy and stability of the proposed two-way wave depth migration algorithm.In imaging the SEAM model,we can see that the proposed imaging method is able to provide a clear result with less artifacts compared with the results produced by the conventional GSP and RTM methods.Our proposed method has the characteristics of depth migration and two-way wave equation migration,which is of great significance in theory and practice.

关 键 词：双程波方程 边界条件 波场深度外推 矩阵分解 

分 类 号：P631[天文地球—地质矿产勘探]