Applications of variational mode decomposition in seismic time-frequency analysis

ABSTRACTWe have introduced a novel time-frequency decomposition approach for analyzing seismic data. This method is inspired by the newly developed variational mode decomposition (VMD). The principle of VMD is to look for an ensemble of modes with their respective center frequencies, such that the modes collectively reproduce the input signal and each mode is smooth after demodulation into baseband. The advantage of VMD is that there is no residual noise in the modes and it can further decrease redundant modes compared with the complete ensemble empirical mode decomposition (CEEMD) and improved CEEMD (ICEEMD). Moreover, VMD is an adaptive signal decomposition technique, which can nonrecursively decompose a multicomponent signal into several quasi-orthogonal intrinsic mode functions. This new tool, in contrast to empirical mode decomposition (EMD) and its variations, such as EEMD, CEEMD, and ICEEMD, is based on a solid mathematical foundation and can obtain a time-frequency representation that is less sens...

[1]  Tianyou Liu,et al.  Seismic spectral decomposition and analysis based on Wigner–Ville distribution for sandstone reservoir characterization in West Sichuan depression , 2010 .

[2]  Sylvain Meignen,et al.  An Alternative Formulation for the Empirical Mode Decomposition , 2012, IEEE Transactions on Signal Processing.

[3]  Dominique Zosso,et al.  Variational Mode Decomposition , 2014, IEEE Transactions on Signal Processing.

[4]  Ingrid Daubechies,et al.  A Nonlinear Squeezing of the Continuous Wavelet Transform Based on Auditory Nerve Models , 2017 .

[5]  Norden E. Huang,et al.  Ensemble Empirical Mode Decomposition: a Noise-Assisted Data Analysis Method , 2009, Adv. Data Sci. Adapt. Anal..

[6]  G. Zhang,et al.  Seismic Data Analysis Using Synchrosqueezeing Wavelet Transform - A Case Study Applied to Boonsville Field , 2015 .

[7]  María Eugenia Torres,et al.  Improved complete ensemble EMD: A suitable tool for biomedical signal processing , 2014, Biomed. Signal Process. Control..

[8]  Gabriel Rilling,et al.  On empirical mode decomposition and its algorithms , 2003 .

[9]  Yangkang Chen,et al.  Time-Frequency Analysis of Seismic Data Using Synchrosqueezing Wavelet Transform , 2014 .

[10]  Yangkang Chen,et al.  Random noise attenuation using local signal-and-noise orthogonalization , 2015 .

[11]  Mirko van der Baan,et al.  Spectral estimation—What is new? What is next? , 2014 .

[12]  Siyuan Cao,et al.  Ground Roll Attenuation Using Variational Mode Decomposition , 2015 .

[13]  Ram Bilas Pachori,et al.  Instantaneous voiced/non-voiced detection in speech signals based on variational mode decomposition , 2015, J. Frankl. Inst..

[14]  Lalu Mansinha,et al.  Localization of the complex spectrum: the S transform , 1996, IEEE Trans. Signal Process..

[15]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[16]  C. Robert Pinnegar,et al.  The S-transform with windows of arbitrary and varying shape , 2003 .

[17]  John P. Castagna,et al.  Examples of wavelet transform time‐frequency analysis in direct hydrocarbon detection , 2002 .

[18]  Mirko van der Baan,et al.  Applications of the synchrosqueezing transform in seismic time-frequency analysis , 2014 .

[19]  Yanxue Wang,et al.  Research on variational mode decomposition and its application in detecting rub-impact fault of the rotor system , 2015 .

[20]  Sergey Fomel,et al.  Seismic data decomposition into spectral components using regularized nonstationary autoregression , 2012 .

[21]  Yanghua Wang,et al.  Seismic time-frequency spectral decomposition by matching pursuit , 2007 .

[22]  Sergey Fomel,et al.  Seismic data analysis using local time‐frequency decomposition , 2013 .

[23]  Nelly Pustelnik,et al.  A multicomponent proximal algorithm for Empirical Mode Decomposition , 2012, 2012 Proceedings of the 20th European Signal Processing Conference (EUSIPCO).

[24]  D. Okaya,et al.  Frequency‐time decomposition of seismic data using wavelet‐based methods , 1995 .

[25]  Patrick Flandrin,et al.  A complete ensemble empirical mode decomposition with adaptive noise , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[26]  Mirko van der Baan,et al.  Empirical mode decomposition for seismic time-frequency analysis , 2013 .

[27]  Khaled H. Hamed,et al.  Time-frequency analysis , 2003 .

[28]  I. Daubechies,et al.  Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool , 2011 .

[29]  Patrick Flandrin,et al.  On the existence of discrete Wigner distributions , 1999, IEEE Signal Processing Letters.

[30]  Dennis Gabor,et al.  Theory of communication , 1946 .

[31]  Jont B. Allen,et al.  Short term spectral analysis, synthesis, and modification by discrete Fourier transform , 1977 .

[32]  P. Anno,et al.  Spectral decomposition of seismic data with continuous-wavelet transform , 2005 .

[33]  Stéphane Mallat,et al.  Matching pursuits with time-frequency dictionaries , 1993, IEEE Trans. Signal Process..

[34]  M. Hestenes.  Multiplier and gradient methods , 1969 .