A trust-region Newton method for frequency-domain full waveform inversion

Exploiting Hessian information greatly enhances the convergence of full waveform inversion. A theoretically simple way to incorporate these second-order derivatives is to minimize the misfit using Newton methods. In practice however the pure Newton method is too computationally intensive to implement, because it requires inverting the Hessian operator. In addition, the misfit is not necessarily quadratic, thus the exact Newton direction is not necessarily appropriate. Consequently, it is natural to turn to inexact Newton methods, where the search direction is constructed iteratively to approximate the pure Newton direction. The bottleneck of these methods lies in the compromise to find between a direction built in few iterations, but which hardly takes the Hessian into account and a nearly exact direction which is very expensive to compute. In this work we present an inexact Newton method based on a particular trust-region algorithm, in the context of frequency-domain full waveform inversion. A numerical test is performed on the Marmousi model to compare convergence speeds with a line search based inexact Newton algorithm. This illustrates that the trust-region method is more robust and provides faster convergence for an adequate choice of trust-region parameters.