Accelerating full waveform inversion using HSS solver and limited memory conjugate gradient method

Full waveform inversion (FWI) consists in finding an accurate optimal model of the subsurface from local measurements of the seismic wavefield. This aim is achieved by minimizing the difference between the observed and predicted data, starting from an initial estimation of the subsurface parameters. One challenge for FWI is its intensive large-scale wavefield simulations, which seriously restricts its wide applications. Additionally, due to the ill-posedness of FWI problem, when the nonlinear conjugate gradient method is employed, the current gradient often lies in the space spanned by the previous directions, resulting in very slow convergence. In this paper, a limited memory version conjugate gradient method equipped with the scalable HSS-structured multifrontal solver is applied to efficiently solve the FWI problem. A hierarchically preconditioned scheme is considered to enhance the robustness of the inversion algorithm. Numerical experiments including 2D and 3D are illustrated to show the performances of this high efficient inversion algorithm.