地震偏移反演成像的迭代正则化方法研究

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.

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

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.