基于浸入吸收边界的起伏地表逆时偏移方法  

Reverse-time migration method based on immersed absorbing boundary for undulating surfaces

作　　者：陈汉明 陈柯吉 王玲谦 韩己航 周辉[1,2,3] CHEN HanMing;CHEN KeJi;WANG LingQian;HAN JiHang;ZHOU Hui(College of Geophysics,China University of Petroleum(Beijing),Beijing 102249,China;National Key Laboratory of Petroleum Resources and Engineering,China University of Petroleum(Beijing),Beijing 102249,China;CNPC Key Laboratory of Geophysical Exploration,Beijing 102249,China)

机构地区：[1]中国石油大学(北京)地球物理学院,北京102249 [2]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 [3]中国石油天然气集团有限公司探重点实验室,北京102249

出　　处：《地球物理学报》2025年第3期1069-1086,共18页Chinese Journal of Geophysics

基　　金：国家自然科学基金(42274143,42304120);中石油天然气集团有限公司物探应用基础实验和前沿理论方法研究(2022DQ0604-03);教育部复杂油气藏勘探开发工程研究中心开放课题基金(2462024PTJS008);中国石油天然气集团有限公司十四五前瞻性基础研究项目(2021DJ3506)联合资助.

摘　　要：对起伏地表的地震数据直接进行逆时偏移是避免常规静校正不准对偏移成像影响的有效手段.准确模拟起伏地表条件下的地震波场需要考虑起伏的自由边界,但对于逆时偏移而言,为避免与自由地表相关多次波的干扰,需要采用吸收边界条件.然而,由于矩形网格阶梯近似的问题,适用于水平地表的吸收边界并不能直接用于起伏地表.当考虑起伏地表时,通常将波动方程转换到曲线坐标系下求解,但该方法将成倍地增加计算量,且当地表剧烈起伏时还存在数值求解不稳定的问题.为此,本文基于平面波透射边界条件提出了一种高效的适用于起伏地表的浸入吸收边界条件,实现了声波方程有限差分数值模拟中波场沿地表法向的吸收衰减,有效避免了来自地表的边界反射.浸入吸收边界基于传统的矩形网格剖分,无需网格映射,其实现过程仅涉及少量非整数网格节点的波场插值,计算效率高.以浸入吸收边界为基础,本文进一步发展了起伏地表逆时偏移方法,实现了对起伏地表地震数据的直接偏移成像.二维和三维波场数值模拟算例证实浸入吸收边界条件能有效地吸收来自地表的边界反射,即使当地表存在不可导的奇异点时,浸入吸收边界条件仍能获得良好的吸收效果,且能在长时间的模拟过程中保持稳定.二维合成数据的逆时偏移测试证实基于浸入吸收边界的逆时偏移方法能对地表采集的地震数据直接偏移成像,获得准确的地下构造.Reverse-time migration(RTM)of seismic data in presence of undulating surface is an effective way to avoid the impacts of the standard static correction errors on migration.To simulate realistic seismic wave propagation in presence of undulating surface,one needs to consider the irregular free surface with specific boundary conditions.However,an absorbing boundary condition(ABC),instead of free-surface boundary conditions should be applied in RTM to avoid the interferences caused by the free-surface related multiples.Due to the grid staircase problem,the ABC applicable to horizontal surfaces cannot be used for undulating surfaces,directly.One effective approach to fit the undulating surfaces is to solve seismic wave equations in a curvilinear coordinate but at the price of much higher computational cost.The simulation scheme at a curvilinear mesh could also suffer from numerical instability in the case of a severely rugged surface.To avoid the curvilinear mesh discretization,we develop an efficient immersed absorbing boundary condition(IABC)for finite-difference(FD)modeling of seismic waves in presence of undulating surface.This IABC is based on the plane-wave transmitting boundary condition and it is modified to simulate wavefield absorption along the normal directions of undulating surfaces.Unlike the curvilinear mesh method,IABC is implemented at the rectangular mesh directly.The only increased computational cost by IABC is wavefield interpolation at a few fractional(non-integer)grid nodes,which makes it highly efficient.Based on IABC,we further develop an RTM method to migrate seismic data acquired at undulating surfaces.Two-(2D)and three-dimensional(3D)wave propagation examples confirm that the developed IABC can absorb the boundary reflections from the surface,cleanly.Even when the surface contains non-differentiable singular points,IABC still achieves good absorption effects and does not encounter numerical instability issues in long-time simulations.Several 2D RTM tests with synthetic data verify that the

关 键 词：逆时偏移 起伏地表 浸入边界法 吸收边界条件 有限差分 地震波 

分 类 号：P631[天文地球—地质矿产勘探]