预条件弹性介质最小二乘逆时偏移

相对于纵波勘探，多波地震勘探能够得到更多的地下介质信息，弹性波逆时偏移（Elastic reverse time migration，ERTM）是当前偏移方法中较为精确的方法。最小二乘逆时偏移成像基于反演理论，可为岩性储层评价提供更加保真的高分辨率反射系数成像剖面，成为当前成像方法的研究热点和发展趋势。从建立线性一阶速度-应力弹性波方程出发，应用伴随状态法得到了逆时偏移数据重构算法，并引入最小二乘理论，利用汉森矩阵的逆对梯度进行预处理，实现了预条件弹性介质最小二乘逆时偏移成像算法（Preconditioning elastic least-squares reverse time migration，P-ELSRTM）。在实现算法的基础上，对SEG/EAGE二维盐丘模型进行测试。结果表明：与常规弹性波最小二乘逆时偏移（Elastic leastsquares reverse time migration，ELSRTM）相比，P-ELSRTM成像分辨率更高，保幅性更好，收敛速度更快。另外，P-ELSRTM对含有随机噪音的观测数据适应性更强。

Preconditioning elastic least-squares reverse time migration

Compared to P-wave seismic exploration,multi-wave seismic exploration can attain more information of underground medium. Elastic reverse time migration is a more accurate method for imaging. Leastsquares inverse time migration(LSRTM)treats the migration imaging as an inversion problem in the sense of least squares, which is a correction of the migration imaging process and results, and can provide reflectance images with higher resolution for lithologic reservoir estimation,which has become the trend of imaging method. Based on the establishment of a linear first-order velocity-stress elastic wave equation,the application of adjoint state method helped to reconstruct the reverse-time migration algorithm,and by introducing the theory of leastsquares and using the inverse of approximate Hessian matrix to precondition the gradient,preconditioning elastic least-squares reverse time migration(P-ELSRTM)was implemented. The numerical tests on SEG/EAGE 2-D salt dome model show that compared with the conventional elastic least-squares reverse time migration(ELSRTM), P-ELSRTM can image with higher resolution,better amplitude preservation and faster convergence. In addition,P-ELSRTM is more adaptable to seismic data with random noise.