Full Waveform Inversion through a Double-Sweeping Inexact Newton Method

An efficient method is proposed to accurately approximate the gradient and the Hessian operator for the full-waveform inversion (FWI) in large-scale problems. The key idea is an approximate solver called double-sweeping solver, which divides the domain into smaller slabs and sequentially solves the wavefields through a downward and an upward sweeping. The sequential solution is facilitated by approximating the continuity conditions that suppress the multiples, thus relaxing long-range coupling between the subdomains. The double-sweeping solver is incorporated into an inexact Gauss-Newton approach to perform FWI, where the gradient and the Hessian vector multiplication are computed more efficiently. Through numerical experiments, we show that the convergence of FWI with respect to the number of iterations does not degrade when the double-sweeping approximation is used. Given that the double-sweeping solver is computationally cheaper than full-wave simulation, the proposed method is more efficient than the standard FWI. This paper contains the complete formulation of the proposed methodology as well as an illustration of its effectiveness to problems of varying complexity including the inversion of the Marmousi model from the Geophysics community.