Application of a preconditioned truncated Newton method to Full Waveform Inversion

Full Waveform Inversion (FWI) is a powerful seismic imaging method, based on the iterative minimization of the distance between simulated and recorded wavefields. The inverse Hessian operator related to this misfit function plays an important role in the reconstruction scheme. As conventional methods use direct approximations of this operator, we investigate an alternative optimization scheme: the truncated Newton method. This two-nested-loops algorithm is based on the resolution of the Newton linear system through a matrix-free iterative solver at each outer iteration. On the 2D BP 2004 model widely used as a benchmark for FWI, the contrasts in wave velocities between salt structures and the upper water layer generate high amplitude multiple reflections. These multiple reflections strengthen the need for quite accurate approximation of the inverse Hessian operator and the truncated Newton method is shown to outperform than more conventional algorithms (l-BFGS, nonlinear conjugate gradient).