Huber inversion-based reverse-time migration with de-primary imaging condition and sparse constraint in curvelet domain

Summary LSRTM formulates RTM in the least-squares inversion framework to obtain the optimal reflectivity image. It can produce images with more balanced amplitudes, higher resolution, and fewer artefacts than RTM. However, three problems still exist: (1) inversion can be dominated by strong events in the residual; (2) low-wavenumber artefacts in the gradient affect convergence speed and imaging results; (3) High-wavenumber noise is also enhanced as iteration increase. To solve these three problems, we improved LSRTM: firstly, we used Huber-norm as the objective function to emphasize the weak reflectors during the inversion; secondly, we adapted the de-primary imaging condition to suppress the low-wavenumber noise above strong reflectors and the partial false high-wavenumber reflectors in the gradient; thirdly, we applied the L1-norm sparse constraint in the curvelet domain as the regularization term to suppress the high-frequency migration artefacts and reduce the sidelobes around the reflectors. As the new inversion scheme is a nonlinear and non-smooth inversion problem, we used the preconditioned nonlinear conjugate-gradient method and a modified iterative soft thresholding method to solve it. The numerical example of the Sigsbee2A model demonstrates that the Huber inversion-based RTM can produce high-quality images by mitigating migration artefacts and boosting the illumination of weak reflectors.