Regularization by Denoising for the Least-Squares Reverse Time Migration With Source Encoding

The least-squares reverse time migration (LSRTM), through iterative minimization of residuals between seismic observational and simulated data, can produce high-quality imaging results. However, it comes at the expense of high computational costs due to many wave-equation simulations in each iteration. To enhance the inversion efficiency of LSRTM, we embraced the source encoding strategy, merging multiple seismic shot gathers into several supergather shots, thereby reducing the scale of the seismic imaging problem. This, however, introduced severe crosstalk noise in imaging results. To mitigate the issue of crosstalk noise in source-encoded LSRTM, we proposed an improved multisource LSRTM method with a nonsubsampled Shearlet transform (NSST) scheme based on the regularization by denoising (RED) framework, which was named as RED-LSRTM. Employing the RED strategy, the NSST denoising engine can be flexibly integrated into the inversion process. Specifically, an NSST denoising operator is integrated into the gradient update step to optimize the solution of the inverse problem, effectively combining gradient optimization with inversion denoising, and enabling the suppression of crosstalk noise throughout the iteration. Numerical tests on the Layer model, the Salt model, and the Marmousi model validated that NSST-based RED-LSRTM effectively enhanced the imaging quality of simultaneous-sources inversion by alleviating more migration artifacts and suppressing more crosstalk noise when compared with standard LSRTM. Owing to its simplicity, flexibility, and effectiveness, our proposed method provides a reliable choice for mitigating crosstalk noise in an inversion of the simultaneous source or blended seismic data.