基于ADMM算法优化的矩形网格隐式有限差分波动方程正演模拟  

Forward modeling of wave equation with implicit finite difference method optimizedby ADMM algorithm in rectangular grid

作　　者：王文化 文晓涛[2,3] 吴昊[2,3] 杨吉鑫 匡胤 WANG WenHua;WEN XiaoTao;WU Hao;YANG JiXin;KUANG Yin(School of Computer Science,Chengdu Normal University,Chengdu 611130,China;Key Laboratory of Earth Exploration and Information Technology Ministry of Education,Chengdu University of Technology,Chengdu 610059,China;College of Geophysics,Chengdu University of Technology,Chengdu 610059,China;Institute of Acoustics,Chinese Academy of Sciences,Beijing 100190,China)

机构地区：[1]成都师范学院计算机科学学院,成都611130 [2]成都理工大学地球勘探与信息技术教育部重点实验室,成都610059 [3]成都理工大学地球物理学院,成都610059 [4]中国科学院声学研究所,北京100190

出　　处：《地球物理学报》2025年第2期680-695,共16页Chinese Journal of Geophysics

基　　金：国家自然科学基金项目(42304147,62341202);四川省科技厅自然科学基金项目(2024NSFSC0808);重点研发计划项目(22ZDYF2726);成都师范学院科研项目(YJRC2021-10,CS21ZCY07)共同资助

摘　　要：有限差分(FD)法广泛用于地震勘探领域的波动方程数值模拟.由于存在“饱和效应”,利用Taylor级数展开法(TE)计算高阶FD系数会在高频和粗网格条件下产生明显的数值频散.一般的常系数优化法能在较大波数区间取得更高的数值精度,但缺乏对中、低波数区间的误差约束;此外,它们大多沿单空间方向压制数值频散,因而无法缓解矩形网格模板的数值各向异性.本文基于隐式FD模板发展了一种多空间方向优化的波动方程正演模拟方法,以同时解决数值频散和数值各向异性问题.针对实用性更强的矩形网格单元,本文基于L_(1)范数建立目标函数并增加波传播角约束以减小数值各向异性,然后运用交替方向乘子法(ADMM)求解优化问题从而实现提高模拟精度的目的.理论误差曲线分析表明,相比传统TE方法和其他单向L_(1)范数、L_(2)范数、L_(∞)范数优化方法,本文基于L_(1)范数的多向优化方法在中、低波数区间具有最小的绝对误差,同时能更好的均衡各个方位角之间的误差分布.均匀介质、Marmousi-2地质模型的正演模拟算例均证明本文所提出的方法比其他三种优化方法在减小长时程测试下的误差积累方面更有优势.The Finite Difference(FD)method is widely used for wave equation numerical simulation in the field of seismic exploration.Due to the"saturation effect",using the Taylor-series expansion(TE)method to calculate the higher-order FD coefficients will result in significant numerical dispersion under high frequency and coarse grid conditions.The general constant coefficient optimization method can achieve higher numerical accuracy in the large wavenumber interval,but lacks the error constraint for the middle-and low-wavenumber interval.In addition,most of them suppress numerical dispersion along the single spatial direction,so the numerical anisotropy of the rectangular grid template cannot be alleviated.In this paper,a forward modeling method of wave equation based on implicit FD template is developed to solve both numerical dispersion and numerical anisotropy problems.For the more practical rectangular grid element,the objective function is established based on L_(1) norm and adds wave propagation angle constraints to reduce numerical anisotropy.Then,the alternate direction multiplier method(ADMM)is used to solve the optimization problem to achieve the purpose of improving the simulation accuracy.Theoretical error curve analysis shows that compared with the traditional TE method and other single-direction L_(1) norm,L_(2) norm and L_(∞)norm optimization methods,the multi-direction optimization method based on L_(1) norm in this paper has the smallest absolute error in the low-and middle-wavenumber interval,and can better balance the error distribution among various azimuthal angles.The forward modeling examples of homogeneous model and Marmousi-2 geological model all demonstrate that the method proposed in this paper has more advantages than the other three optimization methods in reducing the accumulation of errors under long-term testing.

关 键 词：隐式有限差分 矩形网格 波动方程正演 常系数优化法 交替方向乘子法 

分 类 号：P631[天文地球—地质矿产勘探]