求解二阶解耦弹性波方程的低秩分解法和低秩有限差分法  

Solving second-order decoupled elastic wave equation using low-rank decomposition and low-rank finite differences

作　　者：袁雨欣 胡婷[1,2,3,4] 王之洋[1,2,3] 郭鹏 刘洪[1,2,3,4] YUAN YuXin;HU Ting;WANG ZhiYang;GUO Peng;LIU Hong(Institute of Geology and Geophysics,Chinese Academy of Sciences,Beijing 100029,China;Institute of Earth Science,Chinese Academy of Sciences,Beijing 100029,China;Key Laboratory of Petroleum Resources Research,Institute of Geology and Geophysics,Chinese Academy of Sciences,Beijing 100029,China;University of Chinese Academy of Sciences,Beijing 100049,China;Lanzhou Institute of Seismology,China Earthquake Administration,Lanzhou 730000,China)

机构地区：[1]中国科学院地质与地球物理研究所,北京100029 [2]中国科学院地球科学研究院,北京100029 [3]中国科学院油气资源研究院重点实验室,北京100029 [4]中国科学院大学,北京100049 [5]中国地震局兰州地震研究所,兰州730000

出　　处：《地球物理学报》2018年第8期3324-3333,共10页Chinese Journal of Geophysics

基　　金：国家自然科学基金项目(41630319);中国博士后科学基金(2016M591244);国家重点研发计划深地专项项目(2016YFC0601101);中国石油集团"弹性波地震成像技术合作研发课题"联合资助

摘　　要：时间域的波场延拓方法在本质上都可以归结为对一个空间-波数域算子的近似.本文基于一阶波数-空间混合域象征,提出一种新的方法求解解耦的二阶位移弹性波方程.该方法采用交错网格,连续使用两次一阶前向和后向拟微分算子,推导得到了解耦的二阶位移弹性波方程的波场延拓算子.由于该混合域象征在伪谱算子的基础上增加了一个依赖于速度模型的补偿项,可以补偿由于采用二阶中心差分计算时间微分项带来的误差,有效地减少模拟结果的数值频散,提高模拟精度.然而,在非均匀介质中,直接计算该二阶的波场延拓算子,每一个时间步上需要做N次快速傅里叶逆变换,其中N是总的网格点数.为了减少计算量,提出了交错网格低秩分解方法;针对常规有限差分数值频散问题,本文将交错网格低秩方法与有限差分法结合,提出了交错网格低秩有限差分法.数值结果表明,交错网格低秩方法和交错网格低秩有限差分法具有较高的精度,对于复杂介质的地震波数值模拟和偏移成像具有重要的价值.Seismic wavefield extrapolation is an important part of seismic imaging and full waveforminversion.Theoretically,the problem of wave extrapolation in the time domain can be reduced into analyzing numerical approximation to the space-wavenumber mixed-domain symbol.In this paper,we propose a novel method to solve decoupled second-order elastic wave equation.We successively employ backward and forward first-order pseudo differential operators to derive a wave extrapolation operator for second-order decoupled elastic wave propagation.The mixed-domain symbol incorporates the accurate spectral evaluation of spatial derivatives and the time-marching adjustment to ensure that the solution is exact for homogeneous wave propagation for time steps of an arbitrarily large size.Considering its straightforward implementation in heterogeneous media,it needs to do Ntimes inverse fast Fourier transform（FFT）every time step,here Nis the total size of the model grid.In order to reduce computational cost,we propose a staggered-grid low-rank（SGL）method,which can be applied to large time step wave extrapolation.We also propose a staggeredgrid low-rank finite-difference（SGLFD）method by combining the staggered low-rank method and finite-difference to reduce numerical dispersion.The 2 Dnumerical experiments demonstrate that these two methods can improve the accuracy of modeling results compared with the ordinary staggeredgrid finite difference method.

关 键 词：波场延拓 波数-空间混合域象征 交错网格低秩分解方法 交错网格低秩有限差分法 

分 类 号：P631[天文地球—地质矿产勘探]