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

Abstract

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 is still under the great computational pressure in processing field data. Anderson acceleration (AA) is widely popular for its ease of implementation and reduced computational effort. The QR factorization can be applied to AA to improve computational efficiency. We propose to use AA with QR factorization (AA-QR) for LSRTM in frequency domain to speed up the convergence and save computational cost. Through the numerical experiments using the sunken model, the salt model, and the Marmousi model, we find that the suitable memory size for AA-QR is 10 and the step length of AA-QR can be referred to 5 times 1st iteration step length of steepest descent (SD) method. Compared with SD method, conjugate gradient (CG) method, the limited-momory Broyden–Fletcher–Goldfarb–Shanno (LBFGS) method and AA, AA-QR can converges faster and has better imaging quality. Under noisy condition, AA-QR also can converge well and obtain high-resolution images. AA-QR can be used as an alternative to LBFGS when LSRTM chooses the gradient update algorithm.