基于非平稳滤波算子的成像域最小二乘偏移

Least-squares migration in image domain using nonstationary matching filter

岩性油气藏储层的精确描述需要宽带波阻抗的成像结果。假设已经得到准确的背景阻抗,可以采用最小二乘叠前深度偏移(LS-PSDM)估计高保真、高分辨率的反射系数,进而采用合理的深度域反演方法,将背景阻抗和宽带反射系数融合成宽带波阻抗成像结果。LS-PSDM有数据域和成像域两种求解方法。数据域LS-PSDM由于其高昂的计算代价以及较慢的收敛速率,通常不能很好地应用于实际生产中;成像域LS-PSDM的关键是估计线性算子Hessian矩阵的逆,对常规成像结果去模糊,提高成像质量。由于Hessian矩阵规模庞大,无法直接进行计算及存储,研究了成像域最小二乘叠前深度偏移Hessian矩阵逆的近似估计方法:在总变差正则化约束下求解非平稳匹配滤波算子,近似Hessian矩阵的逆。将计算得到的非平稳滤波算子直接作用到常规成像结果上,即得到成像域LS-PSDM的反演结果。该方法极大程度降低了LS-PSDM的计算代价,并且计算稳定,适用于各类偏移算子。局部Sigsbee模型以及Marmousi模型的数值试验结果表明,求得的非平稳滤波算子能够较好地实现Hessian矩阵逆的功能,得到的成像域LS-PSDM结果相较于常规偏移成像结果具有更均衡的振幅,分辨率也有一定提高。根据该方法求解成像域LS-PSDM得到的高保真、高分辨率的反射系数为宽带波阻抗成像提供了重要的数据基础。

Accurate description of lithologic reservoirs requires broadband wave impedance inversion imaging.Assuming that accurate background impedance is obtained,least squares prestack depth migration (LS-PSDM) can be used to estimate high-fidelity and high-resolution reflection coefficients,and then the broadband reflection coefficients can be fused into background impedance to obtain broadband wave impedance using a reasonable depth domain inversion method.LS-PSDM can be realized in data domain and image domain.LS-PSDM in data domain is usually not applied in practical production due to its high calculation cost and slow convergence rate.The key of LS-PSDM in imaging domain is the explicit computation of inverse Hessian which can deblur the conventional imaging results.It is of practical significance to analyze the Hessian approximation methods because full Hessian is too huge to compute and save.In this paper,the inverse of Hessian is estimated using nonstationary matching filters under total variation regularization.The nonstationary matching filters are operated on conventional migration image to obtain LS-PSDM result in image domain.This method could save the computational cost of LS-PSDM,and also is stable and applicable for various migration operators.Numerical experiments on part of Sigsbee model and Marmousi model illustrated that the solved nonstationary matching filters approximated the inverse Hessian well,and the LS-PSDM in image domain yielded better imaging with more balanced amplitude and higher resolution compared with conventional migration images.The true-amplitude and high-resolution reflectivity estimated by the proposed LS-PSDM in image domain can provide data foundation for broadband impedance inversion.