Full waveform inversion with an adjoint scheme for time-dependent inverse wave problems in nonlinear media

The solution of time-dependent inverse wave problems in nonlinear media is considered, using Full Waveform Inversion (FWI). The goal is the identification of parameters related to the nonlinear material behavior. The adjoint method is employed for the efficient calculation of the functional gradient. A general formulation of the method at the semi-discrete level is presented. Two specific models are used to experiment with this formulation: a miniature model that lacks physical meaning, and a model of the deflection of a membrane made of a softening material. The method is specialized to these two models, and numerical experiments demonstrate its performance in each case. Computational aspects that are considered include assessing the success of the identification, and evaluating the performance of the method in the presence of measurement noise.