The truncated Newton method for Full Waveform Inversion

Abstract

Full Waveform Inversion (FWI) is a promising seismic imaging method. It aims at computing quantitative estimates of the subsurface parameters (bulk wave velocity, shear wave velocity, rock density) from local measurements of the seismic wavefield. Based on a particular wave propagation engine for wavefield estimation, it consists in minimizing iteratively the distance between the predicted wavefield at the receivers and the recorded data. This amounts to solving a strongly nonlinear large scale inverse problem. This minimization is generally performed using gradient-based methods. We investigate the possibility of applying the truncated Newton (TrN) method to this problem. This is done through the development of general second-order adjoint state formulas that yield an efficient algorithm to compute Hessian-vector products, and the design of an adaptive stopping criterion for the inner conjugate gradient (CG) iterations. Numerical results demonstrate the interest of using the TrN method when multi-scattered waves dominate the recorded data.