Optimal Transport with a New Preprocessing for Deep-Learning Full Waveform Inversion

Full waveform inversion (FWI) has been implemented using deep learning techniques as an analogue recurrent neural network for geophysics. However, the cycle-skipping issue, from which the conventional FWI suffers, troubles the deeplearning aided FWI as well if the least-square loss function is used to measure the misfit between observed and synthetic data. We propose to use a Wasserstein distance loss function combined with a newly designed preprocessing transform, named integration affine scaling, for the inversion. This transform transfers the seismograms into probability densities, and significantly improves the inversion results. Numerical results show that the proposed method outperforms its counterparts in mitigating cycle-skipping, in comparison with other loss functions including the least-square, the absolute, and the quadratic Wasserstein distance losses.