A gradient-optimized least-squares reverse time migration based on the safe type-I anderson acceleration

Abstract

Least-squares reverse time migration (LSRTM) can generate preferable images for complex media, but faces substantial computational challenges in field data applications, especially in 3D cases. Many optimization algorithms have been proposed to alleviate this problem, such as the limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) method, the restarted generalized minimal residual method, and Anderson acceleration (AA). AA is a popular gradient optimization algorithm that has been widely used in many fields due to its ability to greatly accelerate the convergence of fixed-point iterations and considerably reduce the computational cost. According to Broyden's method, AA is divided into type-I AA (AA-I) and type-II AA (AA-II), with most implementations favoring AA-II due to residual oscillation issues observed in AA-I during data residual minimization. To address the residual vibration issue of AA-I and expedite the convergence of LSRTM, we apply a safe AA-I method to LSRTM, incorporating Powell-type regularization, re-start checking, and safe guarding steps. The Powell-type regularization guarantees the non-singularity of AA-I, while the re-start checking preserves its strong linear independence, both contributing to the stability of AA-I. The safe guarding steps examine the data residual reduction and accelerate the convergence. Our analysis reveals that the optimal step length for the safe AA-I method is approximately 5 times or 10 times the initial steepest descent (SD) iteration. We also derive an exponential scaling law for the safe AA-I step length. In addition, the safe AA-I has faster data residual convergence speed, less computational cost, and higher quality images than SD, conjugate gradient (CG), AA-II, and LBFGS. The safe AA-I is approximately twice as efficient as the LBFGS. Field validation through land seismic data processing shows that LSRTM based on the safe AA-I delivers enhanced structural resolution with sharper imaging events and improved stratigraphic continuity relative to LBFGS-based implementations.