Integrating deep neural networks with full-waveform inversion: Reparameterization, regularization, and uncertainty quantification

Abstract

Full-waveform inversion (FWI) is an accurate imaging approach for modeling the velocity structure by minimizing the misfit between recorded and predicted seismic waveforms. However, the strong nonlinearity of FWI resulting from fitting oscillatory waveforms can trap the optimization in local minima. We have adopted a neural-network-based full-waveform inversion (NNFWI) method 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 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 determine that NNFWI can mitigate local minima, especially for imaging high-contrast features such as salt bodies, and it 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 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.

Effectiveness and computational efficiency of absorbing boundary conditions for full-waveform inversion

“…In principle, then, any particular model poses its own set of challenges to those techniques. Here, we consider widely used models, such as the SEG/EAGE and Marmousi models, as examples of realistic models (Chi et al, 2014;Sun and Demanet, 2020;Zhu et al, 2022;Buchatsky and Treister, 2021).…”

Adaptive Feedback Convolutional‐Neural‐Network‐Based High‐Resolution Reflection‐Waveform Inversion

“…Therefore, we set the threshold to be 655, one percent of the total number of model grid points (65536), to balance the quality of the model basis and the computational cost. For the velocity model containing large‐scale salt bodies or reservoirs, the CNN‐domain FWI (He & Wang, 2021; Wu & McMechan, 2018, 2019; Zhu et al., 2022) to focus the inversion mainly to the prior features in the starting velocity model (e.g., salt bodies, reservoir, etc.) as regularization might be more appropriate than the CNN‐RWI.…”

“…Thus, their method can effectively train a less‐overfitted CNN to invert for the velocity model profile. Another method to train CNN based on a given starting velocity model, rather than a random velocity model set, is to apply CNN as a functional approximator to reparameterize and then replace a given starting velocity model to automatically capture its salient features as prior information in the CNN‐domain FWI (He & Wang, 2021; Wu & McMechan, 2018, 2019; Zhu et al., 2022). Then, the CNN‐domain FWI iteratively constrains the inversion mainly to these captured features in CNN hidden layers, as an implicit regularization, to minimize the data residuals.…”

Differentiable Gaussianization Layers for Inverse Problems Regularized by Deep Generative Models

“…Observed Without With Recently, deep-learning-based models have shown great promise for augmenting various inverse problems [3,9,20,32,36,38,42,47,50,53,54,58,59,64]. In particular, deep generative models, such as VAEs [29], GANs [19], and normalizing flows [15,16,28,48], which directly learn from training data distributions, are a powerful and versatile prior.…”