Physics-guided full waveform inversion using Encoder-Solver convolutional neural networks

Full Waveform Inversion (FWI) is an inverse problem for estimating the wave velocity distribution in a given domain, based on observed data on the boundaries. The inversion is computationally demanding because we are required to solve multiple forward problems, either in time or frequency domains, to simulate data that are then iteratively fitted to the observed data. We consider FWI in the frequency domain, where the Helmholtz equation is used as a forward model, and its repeated solution is the main computational bottleneck of the inversion process. To ease this cost, we integrate a learning process of an Encoder-Solver preconditioner that is based on convolutional neural networks (CNNs). The Encoder-Solver is trained to effectively precondition the discretized Helmholtz operator given velocity medium parameters. Then, by re-training the CNN between the iterations of the optimization process, the Encoder-Solver is adapted to the iteratively evolving velocity medium as part of the inversion. Without retraining, the performance of the solver deteriorates as the medium changes. Using our light retraining procedures, we obtain the forward simulations effectively throughout the process. We demonstrate our approach to solving FWI problems using 2D geophysical models with high-frequency data.