地震偏移反演成像的迭代正则化方法研究  

On iterative regularization methods for migration deconvolution and inversion in seismic imaging

作　　者：王彦飞[1] 杨长春[1] 段秋梁[1] 

机构地区：[1]中国科学院地质与地球物理研究所,北京100029

出　　处：《地球物理学报》2009年第6期1615-1624,共10页Chinese Journal of Geophysics

基　　金：国家重点基础研究发展规划(973)项目(2005CB422104);国家自然科学基金项目(10871191)共同资助

摘　　要：利用伴随算子L^＊，直接的偏移方法通常导致一个低分辨率或模糊的地震成像．线性化偏移反演方法需求解一个最小二乘问题．但直接的最小二乘方法的数值不稳定，为目视解译带来困难．本文建立约束正则化数学模型，研究了地震偏移反演成像问题的迭代正则化求解方法．首先对最小二乘问题施加正则化约束，接着利用梯度迭代法求解反演成像问题，特别是提出了共轭梯度方法的混合实现技巧．为了表征该方法的可实际利用性，分别对一维，二维和三维地震模型进行了数值模拟．结果表明该正则偏移反演成像方法是有效的，对于实际的地震成像问题有着良好的应用前景．In this paper, we consider continuous solution methods for migration deconvolution imaging in seismic inverse problems. Direct migration methods, using the adjoint operator L＊ , usually yield a lower resolution or blurred image. Linearized migration deconvolution requires solving a least-squares migration （LSM） problem. However, we notice that the direct LSM method is unstable in computation which is a severe obstacle for visual explanation. We study regularized mathematical model. We first formulate the problem by incorporating regularizing constraints, and then employ iterative gradient methods for migration deconvolution and imaging. A hybrid gradient technique for ill-posed migration in verse problem is proposed. To show the potential for application of the proposed method, we use synthetic one-, two- and three-dimensional seismograms for seismic migration inversion. Numerical performance indicates that the proposed method is very promising for practical seismic migration imaging.

关 键 词：偏移反演 正则化 最优化 

分 类 号：P631[天文地球—地质矿产勘探]