起伏地表QR径向基函数有限差分及其在弹性波逆时偏移中的应用  

QR radius-basis-function finite difference method with irregular topography and its application to elastic reverse time migration

作　　者：段沛然 谷丙洛 李振春[1,2] 李青阳 DUAN PeiRan;GU BingLuo;LI ZhenChun;LI QingYang(School of Geosciences,China University of Petroleum(East China),Qingdao 266580,China;Deep Oil and Gas Key Laboratory,Qingdao 266580,China;Exploration and Development Research Institute of Changqing Oilfield Branch Company Ltd.,PetroChina,Xi'an 710018,China)

机构地区：[1]中国石油大学(华东)地球科学与技术学院,青岛266580 [2]深层油气重点实验室,青岛266580 [3]中国石油长庆油田分公司勘探开发研究院,西安710018

出　　处：《地球物理学报》2024年第3期1181-1207,共27页Chinese Journal of Geophysics

基　　金：国家自然科学基金面上项目(42374151)资助的成果。

摘　　要：弹性波逆时偏移不受倾角和偏移孔径的限制,能够实现任意复杂构造的高精度多波成像,是目前最精确的多分量资料偏移成像方法之一.逆时偏移算法的核心是波场延拓,传统波场延拓以水平基准面为边界条件,基于固定采样步长进行规则网格剖分,采用阶梯近似法处理起伏地表和复杂构造界面时会产生台阶散射,严重影响起伏地表复杂构造的成像精度.基于无网格节点模型,定量分析了弹性波模拟中径向基函数有限差分法的频散关系和稳定性条件.基于此,提出一种基于QR径向基函数的高精度有限差分方法,并提出一种优化的起伏地表自适应节点剖分方法,推导了精确的无网格自由边界条件和弹性波无网格混合吸收边界条件,形成了新的基于无网格的起伏地表弹性波数值模拟方法.此外,本文将此无网格径向基函数有限差分方法应用于精确的纵横波场矢量分解公式,实现了起伏地表弹性波逆时偏移成像.通过对高斯山丘模型,起伏凹陷模型和起伏地表Marmousi-2模型进行数值试算,验证了本文方法的有效性和可行性.Elastic Reverse Time Migration (ERTM) is one of the most accurate migration methods because it is free of dip angle and migration aperture and images complex underground structures with high accuracy. Theoretically, it is one of the most accurate migration imaging methods for multi-wave and multi-component data. It is well understood that wavefield extrapolation is the core of reverse time migration. Because the traditional wavefield extrapolation method is based on the flatten-surface assumption, carries out regular grids based on fixed sampling step size, and uses step approximation to deal with the surface topography, it often brings a loss of precision when dealing with the seismic data acquired in the complex structure with surface topography. We analyze the dispersion relation and stability conditions of Radial Basis Function Finite Difference Method (RBF-FDM) in elastic wave simulation based on mesh-free node distribution. On this basis, we develop the QR-RBF-FDM, design an optimized adaptive node generation method for the model with irregular topography in a flexible and efficient manner, derive the corresponding free boundary condition and hybrid absorbing boundary conditions in elastic modeling, and finally form a new elastic wave simulation method for irregular topography. In addition, the proposed QR-RBF-FDM is used to extrapolate seismic wavefield in mesh-free-based ERTM, where the QR-RBF-FDM is also applied to the P- and S-wave vector decomposition formula. Finally, we validate the proposed method with the Gauss Hill model, the Sag model, and the Marmousi-2 model, and the numerical results demonstrate the feasibility and effectiveness of the proposed method.

关 键 词：起伏地表 无网格 径向基函数有限差分 自由边界 弹性波逆时偏移 

分 类 号：P631[天文地球—地质矿产勘探]