  Full-waveform inversion (FWI) is an imaging approach for modeling velocity
structure by minimizing the misfit between recorded and predicted seismic
waveforms. 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/elastic PDEs and neural network
layers to update the weights and biases 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.
