LAUSR

Full waveform inversion (FWI) is traditionally designed as an iterative non-linear optimization problem. Thus, it is subject to scaling problems due to inappropriate choice of model parametrization. It is well known that the conventional gradient-based direction update of the parameters, although widely reported and used, does not have the correct physical units; thus, it needs to be properly weighted to provide an adequate model update. The purpose of this work is to examine this issue and to provide an alternative computation to the update directions for the multi-parameter FWI by taking into account the transformation properties of the Hessian and its approximations, since the Hessian contains information related to parameter scaling. To put in evidence the benefits of this approach, we present applications to mono-parameter acoustic and multi-parameter elastic FWI using the 2D Marmousi-2 synthetic model. The proposed direction of update properly scales the estimated models and provides a much faster convergence rate.