AccScience Publishing / JSE / Article
Submit to JSE
Cite this article
37
Views
Journal Browser
Volume | Year
Issue
Search
Forthcoming Issue
Current Issue
View All
News and Announcements
View All
ARTICLE

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

YUANYUAN MA,  SIYUAN CAO
Show Less
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: 4 June 2018 | Accepted: 15 April 2019 | Published: 1 June 2019
© 2019 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/ )
Download PDF
Cite
XML
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)
References
  1. Allen, J.B., 1977. Short term spectral analysis, synthetic and modification by discrete
  2. Fourier transform. IEEE Transact. Acoust., Speech Sign. Proces., 25: 235-238.
  3. Bryce, R.M. and Sprague, K.B, 2012. Revisiting detrended fluctuation analysis. ScientificReports, 2(3): 315-320.
  4. Canales, L., 1984. Random noise reduction. Expanded Abstr., 54th Ann. Internat. SEGMtg., Atlanta: 525-527.
  5. Chen, Y. and Ma, J., 2014. Random noise attenuation by f-x empirical-modedecomposition predictive filtering. Geophysics, 79(3): V81-V91.
  6. Dragomiretskiy, K. and Zosso, D., 2014, Variational mode decomposition. IEEETransact. Sign. Process., 62: 531-544.
  7. Geological Survey U.S., 1981. http://wiki.seg.org/wiki/ALASKA_2D_LAND_LINE_31-81, accessed 2 September 2017.
  8. Grossmann, A. and Morlet, J., 1984. Decomposition of Hardy functions into squareintegrable wavelets of constant shape. SIAM J. Mathemat. Analys., 15: 723-736.
  9. Han, J. and van der Baan, M., 2015. Microseismic and seismic denoising via ensembleempirical mode decomposition and adaptive thresholding. Geophysics, 80(6):KS69-KS80.
  10. Hestenes, M.R., 1969. Multiplier and gradient methods. J. Optimizat. Theory Applicat., 4:303-320.
  11. Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yen, N.-C., Tung,
  12. C.C. and Liu, H.H., 1998. The empirical mode decomposition and the Hilbertspectrum for nonlinear and non-stationary time series analysis. Proc. Mathemat.Physic. Engineer. Sci., 454: 903-995.
  13. Huang, N. and Wu, Z., 2008. A review on Hilbert-Huang transform: Method and itsapplications to geophysical studies. Rev. Geophys., 46: RG2006.
  14. Hurst, H.E., 1951. Long-term storage capacity of reservoirs. Transact. Am. Soc. CivilEngin., 116: 770-779.
  15. Ivanova, K. and Ausloos, M, 1999. Application of the detrended fluctuation analysis(DFA) method for describing cloud breaking. Physica A - Statist. Mechan.Applicat., 274: 349-354.
  16. Jospin, M., Caminal, P., Jensen, E.W., Litvan, H., Vallverdi, M., Struys, M.M., Vereecke,
  17. HE. and Kaplan, D.T., 2007. Detrended fluctuation analysis of EEG as a measureof depth of anesthesia:. IEEE Transact. Biomed. Engineer., 54: 840-846.
  18. Kantelhardt, J.W., Zschiegner, S.A., Koscielny-Bunde, E., Havlin, S., Bunde, A. and
  19. Stanley, H.E, 2002, Multifractal detrended fluctuation analysis of nonstationarytime series. Physica A — Statist. Mechan. Applicat., 316: 87-114.
  20. Leistedt, S., Dumont, M., Lanquart, J.P., Jurysta, F. and Linkowski, P., 2007.
  21. Characterization of the sleep EEG in acutely depressed men using detrendedfluctuation analysis. Clinic. Neurophysiol., 118: 940-950.
  22. Leite, F.S., Rocha, A.F. and Carvalho, J.L., 2010. Matlab software for detrendedfluctuation analysis of heart rate variability. Biosignals 2010 — Internat. Conf.Bio-Insp. Syst. Sign. Process.: 225-229.
  23. Li, F., Zhang, B., Verma, S. and Marfurt, KJ., 2017. Seismic signal denoising usingthreshold variational mode decomposition. Explor. Geophys.doi.org/10.1071/EG17004
  24. Li, F., Zhao, T., Qi, X., Marfurt, KJ. and Zhang, B, 2016. Lateral consistency preserved
  25. Variational Mode Decomposition (VMD). Expanded Abstr., 86th Ann. Internat.SEG Mtg., Dallas: 1717-1721.
  26. Liu, W., Cao, S. and Chen, Y., 2016. Applications of variational mode decomposition inseismic time-frequency analysis. Geophysics, 81(5): V365-V378.
  27. Liu, W., Cao, S. and He, Y., 2015. Ground roll attenuation using variational modedecomposition. Extended Abstr., 77th EAGE Conf., Madrid: Th P6 06.
  28. Liu, W., Cao, S. and Wang, Z., 2017. Application of variational mode decomposition toseismic random noise reduction. J. Geophys. Engineer., 14: 888-899.
  29. Liu, Y., Yang, G., Li, M. and Yin, H,, 2016. Variational mode decomposition denoisingcombined the detrended fluctuation analysis. Sign. Process., 125: 349-364.
  30. Magrin-Chagnolleau, I. and Baraniuk, R., 1999. Empirical mode decomposition basedtime-frequency attributes. Expanded Abstr., 69th Ann. Internat. SEG Mtg.,Houston: 1949-1952.
  31. Mandic, D., Wu, Z. and Huang, N.E., 2013. Empirical mode decomposition based time-frequency analysis of multivariate signals: The power of adaptive data analysis.IEEE Sign. Process., 30(6): 74-86.
  32. Mert, A. and Akan, A, 2014. Detrended fluctuation thresholding for empirical modedecomposition based denoising. Digital Signal Processing, 32, no.2, 48-56.
  33. Peng, C.K., Buldyrev, S.V., Havlin, S., Simons, M., Stanley, H.E. and Goldberger, A.L,
  34. Mosaic organization of DNA nucleotides. Phys. Rev. E Statist. Phys. Plasm.
  35. Fluids Relat. Interdiscipl. Topics, 49: 1685-1689.
  36. Peng, C.K., Havlin, S., Stanley, HE. and Goldberger, A.L, 1995. Quantification ofscaling exponents and crossover phenomena in nonstationary heartbeat time series.Chaos, 5: 82-87.
  37. Stockwell, R.G., Mansinha, L. and Lowe, R.P., 1996. Localization of the complexspectrum. The S-transform. IEEE Transact. Sign. Process., 44: 998-1001.
  38. Telesca, L., Lapenna, V., Macchiato, M. and Hattori, K, 2007. Nonuniform scalingbehavior in ultralow-frequency geomagnetic data in relationship with seismicity.
  39. Expanded Abstr., 77th Ann. Internat. SEG Mtg., San Antonio: 1167-1171.
  40. Torres, M., Colominas, M., Schlotthauer, G. and Flandrin, P., 2011. A completeensemble empirical mode decomposition with adaptive noise. IEEE Internat. Conf.Acoust., Speech Sign. Process.: 4144-4147.
  41. Upadhyay, A. and Pachori, R.B., 2015. Instantaneous voiced/non-voiced detection inspeech signals based on variational mode decomposition. J. Franklin Inst., 352:2679-2707.
  42. Wu, Z. and Huang, N.E., 2004. A study of the characteristics of white noise using theempirical mode decomposition method. Proc. Mathemat., Phys. Engineer. Sci,460: 1597-1611.
  43. Wu, Z. and Huang, N.E., 2009. Ensemble empirical mode decomposition: A noise-assisted data analysis method. Adv. Adapt. Data Analys., 1: 1-41.
  44. Xiong, H. and Shang, P., 2017. Detrended fluctuation analysis of multivariate time series.
  45. Communicat. Nonlin. Sci. Numer. Simulat., 42: 12-21.
  46. Yu, S. and Ma, J., 2018. Complex variational mode decomposition for slop-preservingdenoising. IEEE Transact. Geosci. Remote Sens., 56: 586-897.
Share
Back to top
Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here
Accept