高效的成像域最小二乘逆时偏移  

An efficient least-squares reverse time migration in image domain

作　　者：陈生昌[1] 李代光 金成玫 CHEN ShengChang;LI DaiGuang;JIN ChengMei(School of Earth Sciences,Zhejiang University,Hangzhou 310027,China)

机构地区：[1]浙江大学地球科学学院,杭州310027

出　　处：《地球物理学报》2022年第8期3098-3107,共10页Chinese Journal of Geophysics

基　　金：国家自然科学基金项目(U19B2008,41874133)资助。

摘　　要：最小二乘偏移相对于常规偏移可以获得具有更高保真性和空间分辨率的偏移成像结果.本文在成像域利用空间反褶积提出了一种高效的最小二乘逆时偏移方法.给定具有地震波运动学准确的光滑偏移速度模型(仅考虑基于标量波方程的偏移),常规逆时偏移可视为是一种对有关地下反射率的线性反演问题的粗糙求解.在成像域,常规逆时偏移成像结果是最小二乘逆时偏移成像结果与Hessian矩阵的空变积分.Hessian矩阵中的列向量可视为成像域中成像点的点扩散函数.由于偏移速度模型光滑性和地震数据观测系统的多次覆盖,在一定大小的局域内的成像点的点扩散函数具有很大的相似性,因此该局域内的常规逆时偏移结果可近似表示为最小二乘逆时偏移结果与Hessian矩阵的空不变褶积,进而提出基于局域空不变反褶积的成像域最小二乘逆时偏移方法.利用空不变反褶积的波数域伪广义逆方法可稳定高效地实现对空不变反褶积的计算.局域的大小是最小二乘逆时偏移计算效率和效果之间的折中.把本文提出的方法应用于合成和实际地震数据均取得了理想的效果.The results of least-squares migration have higher fidelity and spatial resolution than that of conventional migration.In this paper,an efficient method for least-squares reverse time migration in imaging domain(IDLSRTM)is proposed by using spatial de-convolution.Given a smooth velocity model with accurate kinematics of seismic wave used for migration(only the migration based on scalar wave equation is considered),the conventional reverse time migration(RTM)can be viewed as one kind of rough solution to the linear inversion problem of subsurface reflectivity.In image domain,the conventional reverse time migration results are a spatial-variant integral of the least-squares reverse time migration results and Hessian matrix.Different column vectors in the Hessian matrix can be regarded as the point spread functions of different imaging points in imaging domain.Because of the smoothness of migration velocity model and the multi-fold of seismic data acquisition system,the point spread functions of imaging points in a certain local region have well similarity.Therefore,the conventional reverse time migration results can be approximately represented as a spatial-invariant convolution between the least-square reverse time migration results and the Hessian matrix in the local region,and then a least-square reverse time migration method in image domain based on the local region spatial-invariant de-convolution is proposed.The spatial-invariant de-convolution can be efficiently and stably realized by using the pseudo-generalized inverse approach to spatial-invariant de-convolution in wavenumber domain.The size of local region is a trade-off between the efficiency and the effect of the least-square reverse time migration.The method proposed in this paper is applied to synthetic and field seismic data,ideal results are obtained.

关 键 词：成像域 最小二乘逆时偏移 高效 点扩散函数 局域 空不变反褶积 波数域 

分 类 号：P631[天文地球—地质矿产勘探]