基于波前相位方向横向各向同性介质的快速纵横波场分解  

Fast P/S wavefield decomposition for vertical transverse isotropic media based on wavefront phase direction

作　　者：方鑫宇 姚刚 郑青青 张平民 吴迪[1,2,5] 钮凤林 FANG XinYu;YAO Gang;ZHENG QingQing;ZHANG PingMin;WU Di;NIU FengLin(State Key Laboratory of Petroleum Resources and Engineering,China University of Petroleum(Beijing),Beijing 102249,China;Key Lab of Geophysical Exploration of CNPC,China University of Petroleum(Beijing),Beijing 102249,China;Unconventional Petroleum Research Institute,China University of Petroleum(Beijing),Beijing 102249,China;College of Science,China University of Petroleum(Beijing),Beijing 102249,China;College of Geophysics,China University of Petroleum(Beijing),Beijing 102249,China;School of Earth and Space Sciences,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]中国石油大学(北京)油气资源与工程全国重点实验室,北京102249 [2]中国石油大学(北京)中国石油天然气集团公司物探重点实验室,北京102249 [3]中国石油大学(北京)非常规油气科学技术研究院,北京102249 [4]中国石油大学(北京)理学院,北京102249 [5]中国石油大学(北京)地球物理学院,北京102249 [6]中国科学技术大学地球和空间科学学院,合肥230026

出　　处：《地球物理学报》2025年第4期1472-1486,共15页Chinese Journal of Geophysics

基　　金：国家自然科学基金(U23B20159,42074129);中石油集团前瞻性基础性项目“物探岩石物理与前沿储备技术研究”(2022DQ0604-02)资助。

摘　　要：各向异性波场分离不仅可以识别复杂介质中的纵横波,还可以提高逆时偏移成像的质量和全波形反演的精度.因此,研究各向异性波场分离很有意义.基于伪亥姆霍兹分解算子可以很好的实现各向异性波场的纵横波分离,然而,这类方法普遍需要在空间域对矢量各向异性泊松方程进行求解,因此,计算量较大.为了提高计算效率,本文提出了基于波前相位方向的垂直横向各向同性(Vertical Transverse Isotropy,VTI)介质纵横波场高效分解方法.该方法在波数域对各向异性泊松算子的倒数进行一阶泰勒近似从而构建新的辅助波场.在空间-波数域使用快速傅里叶变换对辅助波场进行求解,显著提高了纵横波解耦的计算效率.同时,为了保证波场分离的精度,本文采用基于波前相位方向的一阶伪亥姆霍兹分解算子实现纵横波分离.数值算例和理论分析表明本文方法与大多数波场分离方法相比,很好的平衡了波场分离精度和计算效率的问题,既能保证波场分离的精度,又能大幅提高计算效率.Anisotropic wavefield separation can not only identify P-waves and S-waves in complex media,but also improve the imaging quality of elastic wave reverse time migration and the accuracy of full waveform inversion.Therefore,it is of great significance to study the anisotropic wavefield separation.The pseudo-Helmholtz decomposition operator can effectively achieve the separation of P-waves and S-waves in anisotropic wavefields.However,such methods generally require solving the vector anisotropic Poisson equation in the spatial domain,consequently resulting in substantial computational costs.In order to improve computational efficiency,this paper proposes an efficient wavefield decomposition method for vertical transverse isotropic(VTI)media based on the wavefront phase direction.This method constructs a new auxiliary wavefield by applying a firstorder Taylor approximation to the reciprocal of the anisotropic Poisson operator in the wavenumber domain.Solving the auxiliary wavefield using the fast Fourier transform in the space-wavenumber domain significantly improves the computational efficiency of P-and S-wave decoupling.At the same time,to ensure the accuracy of wavefield separation,this study employs a first-order pseudo-Helmholtz decomposition operator based on the wavefront phase direction to achieve P-and S-wave separation.Numerical examples and theoretical analysis show that,compared with most wavefield separation methods,the method proposed in this paper can well balance the issues of wavefield separation accuracy and computational efficiency.It can not only ensure the accuracy of wavefield separation but also significantly improve computational efficiency.

关 键 词：横向各向同性介质 伪亥姆霍兹分解 波前相位方向 空间-波数域 辅助波场 

分 类 号：P631[天文地球—地质矿产勘探]