Least-squares migration with a blockwise Hessian matrix: A prestack time-migration approach
Least-squares migration with a blockwise Hessian matrix: A prestack time-migration approach
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使用分块 Hessian 矩阵的最小二乘偏移：叠前时间偏移方法
DOI：
10.1190/geo2018-0533.1
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发表时间：
2019-07
期刊：
影响因子：
3.3
通讯作者：
Jianfeng Zhang
中科院分区：
文献类型：
--
作者：
Bowu Jiang;Jianfeng Zhang
本文提出了一种基于Hessian矩阵的叠前时间偏移显式逆方法。一个完整的Hessian矩阵被分成一系列的计算易处理的小尺寸的矩阵使用本地化的方法，从而显着减少了逆的大小。该方案通过将成像体划分为一系列与块Hessian矩阵相关的子体来实现，该块Hessian矩阵控制偏移结果与相应反射率之间的映射关系。所提出的分块LS-PSTM可以以面向目标的方式实现。我们用来修改Hessian矩阵的局部化方法可以消除源自分块实现的边界效应。利用PSTM的解卷积成像条件和解析的绿色函数，推导出了与炮检距相关的Hessian矩阵的显式表达式。这避免了估计源小波的挑战性任务。此外，偏移道集可以生成与所提出的方案。块Hessian矩阵的较小尺寸使得可以将全变差正则化并入反演中，从而显著地衰减噪声。我们揭示了所提出的块式LS-PSTM与合成和现场数据集。获得了高质量的野外共反射点道集。
We have developed an explicit inverse approach with a Hessian matrix for the least-squares (LS) implementation of prestack time migration (PSTM). A full Hessian matrix is divided into a series of computationally tractable small-sized matrices using a localized approach, thus significantly reducing the size of the inversion. The scheme is implemented by dividing the imaging volume into a series of subvolumes related to the blockwise Hessian matrices that govern the mapping relationship between the migrated result and corresponding reflectivity. The proposed blockwise LS-PSTM can be implemented in a target-oriented fashion. The localized approach that we use to modify the Hessian matrix can eliminate the boundary effects originating from the blockwise implementation. We derive the explicit formula of the offset-dependent Hessian matrix using the deconvolution imaging condition with an analytical Green’s function of PSTM. This avoids the challenging task of estimating the source wavelet. Moreover, migrated gathers can be generated with the proposed scheme. The smaller size of the blockwise Hessian matrix makes it possible to incorporate the total-variation regularization into the inversion, thus attenuating noises significantly. We revealed the proposed blockwise LS-PSTM with synthetic and field data sets. Higher quality common-reflection-point gathers of the field data are obtained.
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