Least-squares reverse-time migration with modified total-variation regularization

Least-squares reverse-time migration images may contain significant artifacts when data are too sparse. We develop a new least-squares reverse-time migration method with a modified total-variation regularization scheme to improve the image quality and reduce image artifacts. The modified total-variation regularization is a hybrid regularization scheme, taking advantages of the Tikhonov regularization and the total-variation regularization. To improve the convergence and robustness of our new method, we decouple the original optimization problem into two simple subproblems: a least-squares reverse-time migration subproblem with the Tikhonov regularization and a L²-total-variation denoising subproblem. We solve these two subproblems separately using the preconditioned conjugate-gradient and split Bregman iterative methods. We validate the improved imaging capability of our new method using synthetic surface seismic data for a 2D geophysical model constructed using geologic features found at the Soda Lake geothermal site. Our numerical examples demonstrate that the new method significantly improves the image quality and reduce image artifacts for noise-free and noisy data compared with those obtained using conventional least-squares reveres-time migration.