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Fully automatic differentiation with coupling deep neural networks for full-waveform inversion

Pengyuan Sun1,2 ,  Jun Zheng3 ,  Jingyi Zhao3 ,  Ying Yang3 ,  Yufeng Wang3*
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1 BGPInc. National Petroleum Corporation, Zhuozhou, Hebei, China
2 National Engineering Research Center of Oil and Gas Exploration Computer Software, Zhuozhou, Hebei, China
3 Hubei Subsurface Multi-Scale Imaging Key Laboratory, China University of Geosciences, Wuhan, Hubei, China
JSE, 025410085 https://doi.org/10.36922/JSE025410085
Submitted: 11 October 2025 | Revised: 27 October 2025 | Accepted: 28 October 2025 | Published: 19 November 2025
© 2025 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License ( https://creativecommons.org/licenses/by/4.0/ )
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Abstract

Seismic full-waveform inversion (FWI) is a powerful technique used in geophysical exploration to infer subsurface properties. However, FWI often suffers from challenges such as cycle skipping and sensitivity to uncertainties in seismic observations. This study aims to tackle these challenges by developing a novel fully automatic differentiation (AD) strategy for seismic FWI, coupling U-Net-based reparameterization inspired by the deep image prior concept into a reformulated wave equation simulation framework utilizing recurrent neural networks (RNNs). We demonstrate that the U-Net reparameterization serves as a form of implicit regularization for FWI, mitigating the ill-posed nature of the inversion problem and enhancing the stability of the optimization process. In addition, the RNN reformulation offers a flexible approach for backpropagating the FWI misfit, allowing the gradient with respect to the velocity parameters to be computed using the AD capabilities inherent in deep learning frameworks. Through extensive experiments on synthetic datasets, we showcase the regularization effect of our proposed method, leading to improved inversion results in terms of accuracy and robustness. This study offers a promising avenue for enhancing the reliability and accuracy of FWI through the lens of deep learning methodologies.

Keywords
Full-waveform inversion
U-Net
Deep image prior
RNN-based FWI
Funding
This work was financially supported by the National Natural Science Foundation of China Program (42327803, 42304121, 42574154, U2344218), the Open Fund of National Engineering Research Center of Oil and Gas Exploration Computer Software, and the Natural Science Foundation of Wuhan (2025040601020137).
Conflict of interest
The authors declare that they have no competing interests.
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Journal of Seismic Exploration, Print ISSN: 0963-0651, Published by AccScience Publishing
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