Full waveform inversion based on hybrid conjugate gradient with Newton direction

Abstract

Summary The full waveform inversion (FWI) suffers from low computational efficiency. The main reasons are slow convergence speed and unstable convergence. We mainly use optimization methods to solve the problem of low computational efficiency. Nowadays, we commonly use the following two optimization methods: L-BFGS method and hybrid conjugate gradient (HCG) method. l-BFGS method has fast convergence speed but unstable convergence, while HCG method has stable convergence but slower convergence speed. We introduce the N-HCG method into FWI. The method is based on the HCG method and uses Newton direction to approximate the optimal result. This method combines the advantages of both L-BFGS and HCG methods, and has the characteristics of fast and stable convergence. In the mathematical neighborhood, the method is called the hybrid conjugate gradient method with the proposed Newton direction correction (N-HCG). In the model test of acoustic wave FWI, we demonstrate that the method can substantially improve the computational efficiency of the full waveform inversion.