Nowadays the least‐squares reverse time migration has become the most used migration method because of its accuracy in amplitude recovery and high‐resolution imaging, specifically its priority to image the beneath of structural domes such as salt domes. However, errors in the migration velocity model, inadequate physics of modelling/migration and too sparse data decrease the quality of the migrated image. Sparsity constraints help to mitigate the shortcomings of the least‐squares reverse time migration and stabilize the migration image, but the computational burden of sparse solvers is still a big challenge. In this paper, we propose a fast sparsity‐promoting least‐squares reverse time migration algorithm based on the Bregmanized operator splitting algorithm. In particular, we solve the least‐squares reverse time migration with $l_1$‐norm regularization to increase the image resolution while removing the artefacts which cannot be suppressed by the traditional least‐squares reverse time migration. Also we develop a preconditioned Bregmanized operator splitting algorithm where iteratively using of a preconditioner decreases the computational burden. The proposed method is applied to a few sets of synthetic data, and results are compared with reverse time migration or least‐squares reverse time migration to verify its superiority. Numerical tests demonstrate that the proposed preconditioned Bregmanized operator splitting algorithm converges to the desired migration image in a small number of iterations.

中文翻译：

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通过预处理的Bregmanized运算符拆分来促进稀疏性的最小二乘最小二乘反向时间迁移

如今，最小二乘逆时偏移已经成为最常用的偏移方法，这是因为其幅度恢复和高分辨率成像的准确性，尤其是对诸如盐穹顶之类的结构穹顶下方进行成像的优先级。但是，迁移速度模型中的错误，建模/迁移的物理性不足以及数据太稀疏会降低迁移图像的质量。稀疏约束有助于减轻最小二乘逆时偏移的缺点并稳定偏移图像，但是稀疏求解器的计算负担仍然是一个很大的挑战。本文提出了一种基于Bregmanized算子分裂算法的快速稀疏促进最小二乘逆时偏移算法。特别是，我们用${升}_{\mathrm{1个}}$规范规范化，以提高图像分辨率，同时消除传统最小二乘逆时偏移无法抑制的伪像。我们还开发了预处理的Bregmanized运算符拆分算法，其中迭代使用预处理器可减少计算负担。将该方法应用于几套合成数据，并将结果与​​逆时偏移或最小二乘逆时偏移进行比较，以验证其优越性。数值测试表明，所提出的预处理Bregmanized算子分裂算法可以在少量迭代中收敛到所需的迁移图像。