  Full-waveform inversion (FWI) is an accurate imaging approach for modeling
velocity structure by minimizing the misfit between recorded and predicted
seismic waveforms. However, the strong non-linearity of FWI resulting from
fitting oscillatory waveforms can trap the optimization in local minima. We
propose a neural-network-based full waveform inversion method (NNFWI) that
integrates deep neural networks with FWI by representing the velocity model
with a generative neural network. Neural networks can naturally introduce
spatial correlations as regularization to the generated velocity model, which
suppresses noise in the gradients and mitigates local minima. The velocity
model generated by neural networks is input to the same partial differential
equation (PDE) solvers used in conventional FWI. The gradients of both the
neural networks and PDEs are calculated using automatic differentiation, which
back-propagates gradients through the acoustic PDEs and neural network layers
to update the weights of the generative neural network. Experiments on 1D
velocity models, the Marmousi model, and the 2004 BP model demonstrate that
NNFWI can mitigate local minima, especially for imaging high-contrast features
like salt bodies, and significantly improves the inversion in the presence of
noise. Adding dropout layers to the neural network model also allows analyzing
the uncertainty of the inversion results through Monte Carlo dropout. NNFWI
opens a new pathway to combine deep learning and FWI for exploiting both the
characteristics of deep neural networks and the high accuracy of PDE solvers.
Because NNFWI does not require extra training data and optimization loops, it
provides an attractive and straightforward alternative to conventional FWI.
