Safe Anderson type-I least-squares reverse time migration based on a coefficient-optimized 25-point difference scheme

Least-squares reverse time migration (LSRTM) is widely used in seismic imaging for high-resolution subsurface imaging, particularly in complex geological structures. This technique helps reveal detailed subsurface features that are crucial for fields such as oil and gas exploration and geotechnical studies. However, the iterative nature of LSRTM and its reliance on the least-squares approach result in high computational costs, making it challenging for large-scale applications. To address this challenge, this article proposes a safe Anderson-type-I LSRTM, built upon an enhanced 25-point finite difference scheme. This method incorporates a coefficient-optimized 25-point frequency-domain finite difference scheme, alongside Powell regularization, restart checking, and safety protection steps, which are applied to Anderson acceleration type I in order to improve stability and accelerate convergence. Model tests demonstrate that the proposed safe Anderson type-I LSRTM, based on the improved 25-point finite difference scheme, results in faster data residual convergence, higher imaging signal-to-noise ratio, superior resolution, clearer imaging of the in-phase axis, and a closer match between the imaging and the true reflection coefficient model, compared to the steepest descent method, conjugate gradient method, and limited-memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS) method. This method significantly enhances the practical feasibility of LSRTM for large-scale, high-resolution seismic imaging.