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Automatic differentiation-based weighted instantaneous phase inversion

Mengzi Wang1 ,  Yong Hu1* ,  Zhihan Zhang1 ,  Chunyuan Shi1 ,  Xiaoyuan Liao1
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1 Department of Resources and Geosciences, China University of Mining and Technology, Xuzhou, Jiangsu, China
JSE 2026, 35(2), 025520132 https://doi.org/10.36922/JSE025520132
Submitted: 25 December 2025 | Revised: 28 January 2026 | Accepted: 29 January 2026 | Published: 27 March 2026
© 2026 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

Traditional full waveform inversion objective functions typically rely on discrepancies between waveforms, making full waveform inversion highly dependent on the initial model and the low-frequency components in the seismic data. The instantaneous phase of the seismic signal reflects the kinematic information of seismic waves and has a more linear relationship with the subsurface velocity structure, aiding in the retrieval of low-wavenumber components of velocity models. Conversely, waveform information is instrumental in achieving high-resolution inversion results while maintaining algorithmic stability. In addition, automatic differentiation provides an efficient and accurate mechanism for computing gradients by systematically applying the chain rule across the computational graph, yielding reliable derivative information for optimization. To balance the contributions of waveform and phase information in velocity inversion, within the framework of automatic differentiation, we integrate instantaneous phase and waveform information to propose an automatic differentiation-based weighted instantaneous phase inversion method. Numerical tests using the Marmousi model and the Overthrust model demonstrate that the proposed method achieves more accurate velocity inversion results.

Keywords
Full waveform inversion
Instantaneous phase
Weighted objective function
Automatic differentiation
Cycle skipping
Funding
This research was funded by the National Natural Science Foundation of China (Grant No. 42104116).
Conflict of interest
The authors declare 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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