应用自适应变网格紧致差分的地震波数值模拟及逆时偏移  

Seismic numerical simulation and reverse time migration with adaptive variable-grid and compact difference method

作　　者：陈亮 黄建平[1] 王自颖 慕鑫茹 CHEN Liang;HUANG Jianping;WANG Ziying;MU Xinru(School of Geosciences,China University of Petroleum(EastChina),Qingdao,Shandong266580,China)

机构地区：[1]中国石油大学(华东)地球科学与技术学院,山东青岛266580

出　　处：《石油地球物理勘探》2023年第3期641-650,712,共11页Oil Geophysical Prospecting

基　　金：国家重点研发计划项目“膏盐层屏蔽下的超深层复杂构造成像技术”(2019YFC0605503);国家自然科学基金项目“油气勘探地球物理”(41922028);国家自然科学基金创新团体项目“油气成藏机理”(41821002);青岛海洋科学与技术试点国家实验室山东省专项“崎岖海底地震波传播机理与深层复杂构造成像”(2021QNLM020001-5)联合资助。

摘　　要：紧致有限差分(Compact Difference,CD)格式相对于中心有限差分(Finite Difference,FD)格式具有计算精度高、边界处理简单等优点,其中,规则网格四阶CD格式所需计算节点数少,计算精度高,但使用该格式求解声波方程时需求解大型稀疏对角矩阵方程组,当模型较大时,该格式计算效率较低,同时用于存储和计算对角矩阵方程组的内存需求也较大。自适应变网格策略能够通过优化网格剖分,有效降低模型网格数,从而达到提高计算效率、降低内存占用的目的。文中推导了求解二维声波方程的时间二阶中心差分、空间四阶CD的离散格式,并应用于正演模拟;通过引入自适应变网格策略,推导了修正声波方程,发展了高效、高精度的自适应变网格紧致差分逆时偏移成像方法。数值实验表明:该方法可实现复杂构造的高效、高分辨率成像;与规则细网格剖分方法相比,在保证精度的前提下,该方法可将Marmousi模型的成像效率提高约33.7%。Compared with the central finite difference(FD)scheme,the compact difference(CD)scheme has the advantages of high computational accuracy and simple boundary processing.Specifically,the fourth-order CD scheme based on a regular grid requires fewer computational nodes and has higher computational accuracy.However,it is required to solve large sparse diagonal matrix equations when using this scheme to solve the acoustic wave equation.When the model is large,the fourth-order CD scheme is less computationally efficient,and the memory requirement for storing and computing the diagonal matrix equations is large.The adaptive variable-grid strategy can improve computational efficiency and reduce memory consumption by optimizing the grid discretization and effectively reducing the number of grid points.This paper first derives a discrete scheme that uses the second-order FD scheme in time and the fourth-order CD scheme in space to solve the two-dimensional acoustic wave equation.Then the scheme is applied to forward modeling.As a result,the paper derives the modified acoustic wave equation based on the adaptive variable-grid strategy and develops a high-efficiency and high-accuracy reverse time migration method with adaptive variable-grid CD scheme.Numerical experiments show that the proposed method can image complex structures efficiently with high-resolution.Compared with the regular fine grid discretization method,the proposed method can improve the imaging efficiency of the Marmousi model by about 33.7%without accuracy loss.

关 键 词：紧致差分 自适应变网格 数值模拟 逆时偏移 计算效率 计算精度 

分 类 号：P631[天文地球—地质矿产勘探]