Sparsity‐promoting least‐squares reverse time migration via preconditioned Bregmanized operator splitting

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 l1‐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.