Least-squares reverse time migration in frequency domain based on Anderson acceleration with QR factorization

Least-squares reverse time migration (LSRTM) has become a popular research topic and has been practically applied in recent years. LSRTM can generate preferable images with high signal-to-noise ratio (SNR), high resolution, and balanced amplitude. However, LSRTM faces substantial computational challenges when dealing with large amounts of data. Anderson acceleration (AA) is recognized for its simplicity in implementation and its potential to reduce computational costs. By incorporating QR factorization into AA, computational efficiency can be further enhanced. We propose the use of AA with QR factorization (AA-QR) for LSRTM in the frequency domain to accelerate convergence and reduce computational cost. Numerical experiments utilizing the sunken model, the salt model, and the Marmousi model indicate that an optimal memory size for AA-QR is 10, and the step length can be set to five times the initial iteration step length of the steepest descent (SD) method. Compared to the SD method, conjugate gradient (CG) method, limited-momory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) method, and AA, the AA-QR approach not only converges faster but also delivers superior imaging quality. Additionally, AA-QR remains robust under noisy conditions, producing high-resolution images. As such, AA-QR presents a viable alternative to LBFGS for gradient update in LSRTM.