ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Pavlov A. N., Runnova A. E. Method of empirical modes and wavelet­filtering: application in geophysical problems. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 1, pp. 3-13. DOI: 10.18500/0869-6632-2011-19-1-3-13

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
57.087
DOI: 
10.18500/0869-6632-2011-19-1-3-13

Method of empirical modes and wavelet­filtering: application in geophysical problems

Autors: 
Pavlov Aleksej Nikolaevich, Saratov State University
Runnova Anastasia Evgenevna, Saratov State University
Abstract: 

Theoretical bases of empirical mode decomposition being one of the new methods of time-frequency analysis of processes with time-varying characteristics are discussed. It is shown that application of this approach together with wavelet-filtering allows one to study in details the structure of multicomponent registered signals recorded in prospecting seismology.

Key words: 
Instantaneous frequency
empirical mode decomposition
wavelet-analysis
seismic prospecting
Reference: 
  1. Peng CK, Havlin S, Stanley H, Goldberger A. Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos. 1995;5(1):82–87. DOI: 10.1063/1.166141.
  2. Muzy JF, Bacry E, Arneodo A. The multifractal formalism revisited with wavelets. Int. J. Bifurcation Chaos. 1994;4(2):245–302. DOI: 10.1142/S0218127494000204.
  3. Daubechies I. Ten Lectures on Wavelets. Philadelphia: S.I.A.M.; 1992. 350 p. DOI: 10.1137/1.9781611970104.
  4. Meyer Y. Wavelets: Algorithms and Applications. Philadelphia: S.I.A.M.; 1993. 133 p.
  5. Mallat SG. A Wavelet Tour of Signal Processing. New York: Academic Press; 1998. 805 p. DOI: 10.1016/B978-0-12-374370-1.X0001-8.
  6. Addison PS. The Illustrated Wavelet Transform Handbook: Applications in Science, Engineering, Medicine and Finance. Bristol; Philadelphia: IOP Publishing; 2002. 472 p.
  7. Flandrin P. Some aspects of non-stationary signal processing with emphasis on time-frequency and time-scale methods. In: Combes JM, Grossmann A, Tchamitchian P, editors. Wavelets. Springer, Berlin; 1989. P. 68–98. DOI: 10.1007/978-3-642-97177-8_4.
  8. Flandrin P. Time-Frequency and Time-Scale Analysis. San Diego: Academic Press; 1999. 386 p.
  9. Anisimov AA, Pavlova ON, Tupicyn AN, Pavlov AN. Wavelet-analysis of chirps. Izvestiya VUZ. Applied Nonlinear Dynamics. 2008;16(5):3–11 (in Russian). DOI: 10.18500/0869-6632-2008-16-5-3-11.
  10. Kaiser G. A Friendly Guide to Wavelets. Boston: Birkhauser; 1994. 300 p. DOI: 10.1007/978-0-8176-8111-1.
  11. Koronovskii AA, Khramov AE. Continuous Wavelet Analysis and Its Applications. Moscow: Fizmatlit; 2003. 176 p. (in Russian).
  12. Zhang Q, Benveniste A. Wavelet networks. IEEE Trans. Neural Networks. 1992;3(6):889–898. DOI: 10.1109/72.165591.
  13. Zhang J, Walter GG, Miao Y, Lee WN. Wavelet neural networks for function learning. IEEE Trans. Signal Proc. 1995;43(6):1485–1497. DOI: 10.1109/78.388860.
  14. Huang NE, Shen Z, Long SR, Wu MC, Shih HH, Zheng Q, Yen NC, Tung CC, and Liu HH. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. London Ser. A. 1998;454(1971):903–995. DOI: 10.1098/rspa.1998.0193.
  15. Coughlin KT, Tung KK. 11-year solar cycle in the stratosphere extracted by the empirical mode decomposition method. Adv. Space Res. 2004;34(2):323–329. DOI: 10.1016/j.asr.2003.02.045.
  16. Neto EPS, Custaud MA, Cejka CJ, Abry P, Frutoso J, Gharib C, Flandrin P. Assessment of cardiovascular autonomic control by the empirical mode decomposition. Method. Inform. Med. 2004;43(1):60–65.
  17. Wu Z, Huang NE. A study of the characteristics of white noise using the empirical mode decomposition method. Proc. R. Soc. London Ser. A. 2004;460(2046):1597–1611. DOI: 10.1098/rspa.2003.1221.
  18. Huang NE, Shen Z, Long SR. A new view of nonlinear water waves: the Hilbert spectrum. Annu. Rev. Fluid Mech. 1999;31:417–457. DOI: 10.1146/annurev.fluid.31.1.417.
  19. Huang NE, Shen SSP, editors. Hilbert–Huang Transform and Its Applications. Singapore: World Scientific; 2005. 324 p. DOI: 10.1142/5862.
  20. Flandrin P, Goncalves P.  Empirical mode decompositions as data-driven wavelet-like expansion. Int. J. Wavelets Multiresolut. Inform. Process. 2004;2(4):477–496. DOI: 10.1142/S0219691304000561.
  21. Flandrin P, Rilling G, Goncalves P.  Empirical mode decomposition as a filter bank. IEEE Signal Process. Lett. 2004;11(2):112–114. DOI: 10.1109/LSP.2003.821662.
  22. Filatova AE, Artemev AE, Koronovskii AA, Pavlov AN, Hramov AE. Progress and prospect of wavelet transform application to the analysis of nonstationary nonlinear dates in contemporary geophysics. Izvestiya VUZ. Applied Nonlinear Dynamics. 2010;18(3):3–23 (in Russian). DOI: 10.18500/0869-6632-2010-18-3-3-23.  
Received: 
12.03.2010
Accepted: 
12.03.2010
Published: 
29.04.2011
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