Least-Squares Reverse Time Migration With Curvelet-Domain Preconditioning Operators

Least-squares reverse time migration (LSRTM) is an amplitude-preserving seismic imaging technique that aims at finding the subsurface reflectivity model. It is often performed iteratively using an inversion algorithm, such as the conjugate gradient method. Such an implementation requires a huge amount of calculation as it may converge slowly. Preconditioning plays a crucial role in seismic inverse problems. In this study, we propose a novel preconditioning method for LSRTM. The proposed method estimates a new guided curvelet-domain deblurring filter for one-step LSRTM and preconditioned LSRTM. Then, the filter is applied to migrated images and gradients in LSRTM. Such a deblurring filter acts as a curvelet-domain local linear approximation of the least-squares functional inverse Hessian, which can improve the image quality and accelerate the convergence. Numerical tests on the synthetic model and a field data example demonstrate that the preconditioning operator can effectively accelerate the convergence of LSRTM. One-step LSRTM can obtain comparable image quality to that of conventional iterative LSRTM with only a single iteration. The comparison of the convergence curves demonstrates that the curvelet-domain preconditioning operators accelerate the convergence of LSRTM. Furthermore, the preconditioned LSRTM achieves better image quality than the conventional LSRTM. We compare preconditioning operators based on diagonal and local linear approximations. The preconditioning operator based on the local linear approximation has more robust performance and more stable convergence curves than the diagonal-based approximation.