Seismic signal denoising using thresholded variational mode decomposition
Fangyu Li 1 Bo Zhang 2 4 Sumit Verma 3 Kurt J. Marfurt 11 ConocoPhilips School of Geology and Geophysics, The University of Oklahoma, Norman, OK 73019, USA.
2 Department of Geological Sciences, The University of Alabama, Tuscaloosa, AL 35487, USA.
3 Department of Physical Sciences, The University of Texas of the Permian Basin, Odessa, TX 79762, USA.
4 Corresponding author. Email: bzhang33@ua.edu
Exploration Geophysics 49(4) 450-461 https://doi.org/10.1071/EG17004
Submitted: 8 January 2017 Accepted: 12 June 2017 Published: 11 August 2017
Abstract
Noise reduction is important for signal analysis. In this paper, we propose a hybrid denoising method based on thresholding and data-driven signal decomposition. The principle of this method is to reconstruct the signal with previously thresholded intrinsic mode functions (IMFs). Empirical mode decomposition (EMD) based methods decompose a signal into a sum of oscillatory components, while variational mode decomposition (VMD) generates an ensemble of modes with their respective centre frequencies, which enables VMD to further decrease redundant modes and keep less residual noise in the modes. To illustrate its superiority, we compare VMD with EMD as well as its derivations, such as ensemble EMD (EEMD), complete EEMD (CEEMD), improved CEEMD (ICEEMD) using synthetic signals and field seismic traces. Compared with EMD and its derivations, VMD has a solid mathematical foundation and is less sensitive to noise, while both make it more suitable for non-stationary seismic signal decomposition. The determination of mode number is key for successful denoising. We develop an empirical equation, which is based on the detrended fluctuation analysis (DFA), to adaptively determine the number of IMFs for signal reconstruction. Then, a scaling exponent obtained by DFA is used as a threshold to distinguish random noise and signal between IMFs and the reconstruction residual. The proposed thresholded VMD denoising method shows excellent performance on both synthetic and field data applications.
Key words: adaptive filtering, detrended fluctuation analysis (DFA), empirical mode decomposition (EMD), seismic signal denoising, variational mode decomposition (VMD).
References
Bekara, M., and van der Baan, M., 2009, Random and coherent noise attenuation by empirical mode decomposition: Geophysics, 74, V89–V98| Random and coherent noise attenuation by empirical mode decomposition:Crossref | GoogleScholarGoogle Scholar |
Berthouze, L., and Farmer, S. F., 2012, Adaptive time-varying detrended fluctuation analysis: Journal of Neuroscience Methods, 209, 178–188
| Adaptive time-varying detrended fluctuation analysis:Crossref | GoogleScholarGoogle Scholar |
Chen, Z., Ivanov, P. C., Hu, K., and Stanley, H. E., 2002, Effect of nonstationarities on detrended fluctuation analysis: Physical Review E, 65, 041107
| Effect of nonstationarities on detrended fluctuation analysis:Crossref | GoogleScholarGoogle Scholar |
Chkeir, A., Marque, C., Terrien, J., and Karlsson, B., 2010, Denoising electrohysterogram via empirical mode decomposition: PSSNIP Biosignals and Biorobotics Conference, 4–6 January 2010, Vitoria, Brazil, 32–35.
Colominas, M. A., Schlotthauer, G., and Torres, M. E., 2014, Improved complete ensemble EMD: A suitable tool for biomedical signal processing: Biomedical Signal Processing and Control, 14, 19–29
| Improved complete ensemble EMD: A suitable tool for biomedical signal processing:Crossref | GoogleScholarGoogle Scholar |
Donoho, D. L., and Johnstone, J. M., 1994, Ideal spatial adaptation by wavelet shrinkage: Biometrika, 81, 425–455
| Ideal spatial adaptation by wavelet shrinkage:Crossref | GoogleScholarGoogle Scholar |
Dragomiretskiy, K., and Zosso, D., 2014, Variational mode decomposition: IEEE Transactions on Signal Processing, 62, 531–544
| Variational mode decomposition:Crossref | GoogleScholarGoogle Scholar |
Fang, Y. M., Feng, H. L., Li, J., and Li, G. H., 2011, Stress wave signal denoising using ensemble empirical mode decomposition and an instantaneous half period model: Sensors, 11, 7554–7567
| Stress wave signal denoising using ensemble empirical mode decomposition and an instantaneous half period model:Crossref | GoogleScholarGoogle Scholar |
Gan, Y., Sui, L., Wu, J., Wang, B., Zhang, Q., and Xiao, G., 2014, An EMD threshold denoising method for inertial sensors: Measurement, 49, 34–41
| An EMD threshold denoising method for inertial sensors:Crossref | GoogleScholarGoogle Scholar |
Gilles, J., 2013, Empirical wavelet transform: IEEE Transactions on Signal Processing, 61, 3999–4010
| Empirical wavelet transform:Crossref | GoogleScholarGoogle Scholar |
Han, J., and van der Baan, M., 2013, Empirical mode decomposition for seismic time-frequency analysis: Geophysics, 78, O9–O19
| Empirical mode decomposition for seismic time-frequency analysis:Crossref | GoogleScholarGoogle Scholar |
He, B., and Bai, Y., 2016, Signal-noise separation of sensor signal based on variational mode decomposition: 2016 8th IEEE International Conference on Communication Software and Networks (ICCSN), 132–138.
Hestenes, M. R., 1969, Multiplier and gradient methods: Journal of Optimization Theory and Applications, 4, 303–320
| Multiplier and gradient methods:Crossref | GoogleScholarGoogle Scholar |
Horvatic, D., Stanley, H. E., and Podobnik, B., 2011, Detrended cross-correlation analysis for non-stationary time series with periodic trends: EPL (Europhysics Letters), 94, 18007
| Detrended cross-correlation analysis for non-stationary time series with periodic trends:Crossref | GoogleScholarGoogle Scholar |
Hu, K., Ivanov, P. C., Chen, Z., Carpena, P., and Stanley, H. E., 2001, Effect of trends on detrended fluctuation analysis: Physical Review E, 64, 011114
| Effect of trends on detrended fluctuation analysis:Crossref | GoogleScholarGoogle Scholar | 1:STN:280:DC%2BD38%2FisVOltw%3D%3D&md5=b7b83b9ad20a4dd3b1437eef03928e8eCAS |
Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., and Liu, H. H., 1998, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 454, 903–995
Kabir, M. A., and Shahnaz, C., 2012, Denoising of ECG signals based on noise reduction algorithms in EMD and wavelet domains: Biomedical Signal Processing and Control, 7, 481–489
| Denoising of ECG signals based on noise reduction algorithms in EMD and wavelet domains:Crossref | GoogleScholarGoogle Scholar |
Lahmiri, S., and Boukadoum, M., 2014, Biomedical image denoising using variational mode decomposition: IEEE Biomedical Circuits and Systems Conference (BioCAS) Proceedings, 340–343.
Li, C., Zhan, L., and Shen, L., 2015, Friction signal denoising using complete ensemble EMD with adaptive noise and mutual information: Entropy, 17, 5965–5979
| Friction signal denoising using complete ensemble EMD with adaptive noise and mutual information:Crossref | GoogleScholarGoogle Scholar |
Li, F., Zhang, B., Zhai, R., Zhou, H., and Marfurt, K. J., 2017, Depositional sequence characterization based on seismic variational mode decomposition: Interpretation, 5, SE97–SE106
| Depositional sequence characterization based on seismic variational mode decomposition:Crossref | GoogleScholarGoogle Scholar |
Liu, W., Cao, S., and He, Y., 2015, Ground roll attenuation using variational mode decomposition: 77th Annual International Conference and Exhibition, EAGE, Extended Abstracts, Th P6 06.
Liu, W., Cao, S., and Chen, Y., 2016a, Applications of variational mode decomposition in seismic time-frequency analysis: Geophysics, 81, V365–V378
| Applications of variational mode decomposition in seismic time-frequency analysis:Crossref | GoogleScholarGoogle Scholar |
Liu, Y., Yang, G., Li, M., and Yin, H., 2016b, Variational mode decomposition denoising combined the detrended fluctuation analysis: Signal Processing, 125, 349–364
| Variational mode decomposition denoising combined the detrended fluctuation analysis:Crossref | GoogleScholarGoogle Scholar |
Mert, A., and Akan, A., 2014, Detrended fluctuation thresholding for empirical mode decomposition based denoising: Digital Signal Processing, 32, 48–56
| Detrended fluctuation thresholding for empirical mode decomposition based denoising:Crossref | GoogleScholarGoogle Scholar |
Peng, C. K., Buldyrev, S. V., Havlin, S., Simons, M., Stanley, H. E., and Goldberger, A. L., 1994, Mosaic organization of DNA nucleotides: Physical Review, 49, 1685–1689
| 1:CAS:528:DyaK2cXksFamsr8%3D&md5=1fc9bd03a43c1eead8068056adeaf630CAS |
Schuster, G. T., 2007, Basics of seismic wave theory: notes for the lecture courses: University of Utah.
Torres, M. E., Colominas, M. A., Schlotthauer, G., and Flandrin, P., 2011, A complete ensemble empirical mode decomposition with adaptive noise: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 4144–4147.
Verma, S., Guo, S., Ha, T., and Marfurt, K. J., 2016, Highly aliased groundroll suppression using a 3D multiwindow KL filter: application to a legacy Mississippi Lime survey: Geophysics, 81, V79–V88
| Highly aliased groundroll suppression using a 3D multiwindow KL filter: application to a legacy Mississippi Lime survey:Crossref | GoogleScholarGoogle Scholar |
Wu, Z., and Huang, N. E., 2009, Ensemble empirical mode decomposition: a noise-assisted data analysis method: Advances in Adaptive Data Analysis, 1, 1–41
| Ensemble empirical mode decomposition: a noise-assisted data analysis method:Crossref | GoogleScholarGoogle Scholar |