Imaging of elastic seismic data by least‐squares reverse time migration with weighted L2‐norm multiplicative and modified total‐variation regularizations
Imaging of elastic seismic data by least‐squares reverse time migration with weighted L2‐norm multiplicative and modified total‐variation regularizations
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DOI：
10.1111/1365-2478.12849
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发表时间：
2019-09
影响因子：
2.6
通讯作者：
Z. Ren;Zhenchun Li
中科院分区：
文献类型：
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作者：
Z. Ren;Zhenchun Li
最小二乘逆时偏移有可能产生高质量的地球图像。与声学方法相比，弹性最小二乘逆时偏移可以有效解决模式转换问题，并提供速度/阻抗和密度扰动模型。然而，弹性最小二乘逆时偏移是一个不适定问题，并且缺乏唯一性。此外，其解也不稳定。我们开发了两种新的基于加权 L2 范数乘法和改进的全变分正则化的弹性最小二乘逆时偏移方法。在所提出的方法中，原始最小化问题被分为两个子问题，并且图像和辅助变量交替更新。改进的全变分正则化方法分别通过高效的反演工作流程和 split-Bregman 迭代方法解决了两个子问题：Tikhonov 正则化问题和 L2 全变分正则化问题。乘法正则化方法通过高效的反演工作流程和嵌套方式的非线性共轭梯度方法更新图像和辅助变量。我们使用合成和现场地震数据验证了所提出的方法。数值结果表明，与传统方法相比，所提出的正则化方法提高了迁移剖面的分辨率和保真度，并表现出优异的抗噪声能力。此外，对于噪声数据，基于修正总变分的方法比基于乘法正则化的方法具有更高的精度。所提出的两种方法的计算成本与传统的最小二乘逆时偏移方法的计算成本大致相同，因为辅助变量的反演不需要额外的前向计算。
Least‐squares reverse time migration has the potential to yield high‐quality images of the Earth. Compared with acoustic methods, elastic least‐squares reverse time migration can effectively address mode conversion and provide velocity/impendence and density perturbation models. However, elastic least‐squares reverse time migration is an ill‐posed problem and suffers from a lack of uniqueness; further, its solution is not stable. We develop two new elastic least‐squares reverse time migration methods based on weighted L2‐norm multiplicative and modified total‐variation regularizations. In the proposed methods, the original minimization problem is divided into two subproblems, and the images and auxiliary variables are updated alternatively. The method with modified total‐variation regularization solves the two subproblems, a Tikhonov regularization problem and an L2‐total‐variation regularization problem, via an efficient inversion workflow and the split‐Bregman iterative method, respectively. The method with multiplicative regularization updates the images and auxiliary variables by the efficient inversion workflow and nonlinear conjugate gradient methods in a nested fashion. We validate the proposed methods using synthetic and field seismic data. Numerical results demonstrate that the proposed methods with regularization improve the resolution and fidelity of the migration profiles and exhibit superior anti‐noise ability compared with the conventional method. Moreover, the modified‐total‐variation‐based method has marginally higher accuracy than the multiplicative‐regularization‐based method for noisy data. The computational cost of the proposed two methods is approximately the same as that of the conventional least‐squares reverse time migration method because no additional forward computation is required in the inversion of auxiliary variables.