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An improved robust threshold for variational mode decomposition based denoising in the frequency-offset domain

YUANYUAN MA,  SIYUAN CAO
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The State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum, Changping 102249, Beijing, P.R. China,
JSE 2019, 28(3), 277–305;
Submitted: 9 June 2025 | Revised: 9 June 2025 | Accepted: 9 June 2025 | Published: 9 June 2025
© 2025 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

Ma, Y.Y. and Cao, S.Y., 2019. An improved robust threshold for variational mode decomposition based denoising in the frequency-offset domain. Journal of Seismic Exploration, 28: 277-305. We proposed a novel robust denoising method using variational-mode decomposition (VMD) and the detrended fluctuation analysis (DFA) in the frequency- offset (f-x) domain, named robust DFA-VMD. DFA is mainly introduced to solve the problem that VMD requires the number of modes to be predefined. The scaling exponent obtained by DFA is a robust metric to measure the long-range correlations and can be used to adjust the number of intrinsic mode functions (IMFs) automatically. To reconstruct the denoised signal, a scaling exponent is also used as a threshold to identify and remove the noisy modes. We define a novel robust threshold of random noise in seismic data, because the predefined noise boundaries for other time series cannot perform perfectly when dealing with seismic data. The proposed robust DFA-VMD is an almost parameters-free denoising approach and we apply it in the (fx) domain for seismic denoising. We have verified its performance by comparing it with the results from several other methods including (f-x) deconvolution and the conventional DFA- VMD. Two synthetic examples and three field-data examples revealed the effectiveness of the proposed approach in applications to random and coherent noise attenuation.

Keywords
denoising
frequency-offset domain
adaptive filtering
variational mode decomposition (VMD)
detrended fluctuation analysis (DFA)
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing
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