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ISSN 2542-1905 (Online)

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Runnova A. E., Artemiev A. E., Koronovskii A. A., Pavlov A. N., Hramov A. E. Progress and prospect of wavelet transform application to the analysis of nonstationary nonlinear dates in contemporary geophysics. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, iss. 3, pp. 3-23. DOI: 10.18500/0869-6632-2010-18-3-3-23

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Progress and prospect of wavelet transform application to the analysis of nonstationary nonlinear dates in contemporary geophysics

Runnova Anastasia Evgenevna, Saratov State University
Artemiev Aleksandr Evgenevich, Saratov State University
Koronovskii Aleksei Aleksandrovich, Saratov State University
Pavlov Aleksej Nikolaevich, Saratov State University
Hramov Aleksandr Evgenevich, Immanuel Kant Baltic Federal University

The presented paper is an analytical review of the methods and examples of applications of the continuous and discrete wavelet transform in geophysical study. The possibility of the extension of application of the wavelet-based methods in geophysics is also considered.

  1. Grossman A, Morlet J. Decomposition of Hardy functions into square integrable wavelets of constant shape. SIAM J. Math. Anal. 1984;15(4):723–736. DOI: 10.1137/0515056.
  2. Addison PS. The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science Engineering, Medicine and Finance. Bristol: Institute of Physics Publishing; 2002.
  3. Dobeshi I. Ten Lectures on Wevelets. Moscow-Izhevsk: Regular and chaotic dynamics; 2001. 464 p. (in Russian).
  4. Torrence C, Compo GP. A Practical Guide to Wavelet Analysis. Bulletin of the American Meteorological Society. 1998;79(1):61–78. DOI: 10.1175/1520-0477(1998)079<0061:APGTWA>2.0.CO;2.
  5. Wavelets in Physics. Edited by van der Berg JC. Cambridge: Cambridge University Press; 2004.
  6. Aldroubi A, Unser M. Wavelets in Medicine and Biology. CRC-Press; 1996. 640 p.
  7. Koronovsky AA, Khramov AE. Continuous Wavelet Analysis and its Applications. Moscow: Fizmatlit; 2003. (in Russian).
  8. Hramov AE, Koronovskii AA, Ponomarenko VI, Prokhorov MD. Detection of synchronization from univariate data using wavelet transform. Phys. Rev. E. 2007;75(5):056207. DOI: 10.1103/PhysRevE.75.056207.
  9. Sosnovtseva OV, Pavlov AN, Brazhe NA, Brazhe AR, Erokhova LA, Maksimov GV, Mosekilde E. Interference microscopy under double-wavelet analysis: a new approach to studying cell dynamics. Phys. Rev. Lett. 2005;94(21):218103. DOI: 10.1103/PhysRevLett.94.218103.
  10. Koronovskii AA, Khramov AE. Wavelet bicoherence analysis as a method for investigating coherent structures in an electron beam with an overcritical current. Plasma Physics Reports. 2002;28(8):666–681. DOI: 10.1134/1.1501324.
  11. Piskun PV. Software and algorithmic support of continuous wavelet transformation in the processing and interpretation of geophysical fields. Moscow: MSU; 2006. 102 p. (in Russian).
  12. Piskun PV, Petrov AV, Zinovkin SV. Computer technology Koskad SEIS for complex analysis of seismic and well information. In: Abstracts of the VII International Scientific and Practical Conference «Geomodel – 2005». 2005:42 (in Russian).
  13. Astafieva NM. Wavelet analysis: basic theory and some applications. Phys. Usp. 1996;39(11):1085–1108.
  14. Dremin IM, Ivanov OV, Nechitailo VA. Wavelets and their uses. Phys. Usp. 2001;44(5):447–478.
  15. Stakhovsky IR. Wavelet analysis of seismic time series. Dokl. Akad. Nauk. 1996;350(3):393–396 (in Russian).
  16. Mallat SG. Multiresolution approximations and wavelet orthonormal bases of L2(R). Trans. Amer. Math. Soc. 1989;315(1):69–87.
  17. Wirtki K. El Niño—The Dynamic Response of the Equatorial Pacific Oceanto Atmospheric Forcing. Journal of Physical Oceanography. 1975;5:572–584. DOI: 10.1175/1520-0485(1975)005<0572:ENTDRO>2.0.CO;2.
  18. Rayner NA, Horton EB, Parker DE, Folland CK, Hackett RB. Version 2.2 of the global sea-ice and sea surface temperature data set 1903–1994. CRTN 74, Hadley Centre for Climate Prediction and Research; 1996.
  19. Mac Kenzie D. New Scientist. 1987;16:16.
  20. Shaowu W. Reconstruction of El Niflo event chronology for the last 600 year period. Acta Meteorologica Sinica. 1992;6(1):47–57.
  21. Hudgins L., Friehe L.A., Mayer M.E. Wavelet transforms and atmopsheric turbulence. Physical Review Letters. 1993;71(20):3279–3282. DOI: 10.1103/PhysRevLett.71.3279.
  22. Sonechkin DM, Datsenko NM, Ivashchenko NN. Izvestiya VUZ. Applied nonlinear dynamics. 1996;4(4-5):108. (in Russian).
  23. Mandea M, Balasis G. The SGR 1806-20 magnetar signature on the Earth's magnetic field. Geophys. J. Int. 2006;167(2):586–591. DOI: 10.1111/j.1365-246x.2006.03125.x.
  24. Corso G, Kuhn PS, Lucena LS, Thom ZD. Seismic ground roll time–frequency filtering using the gaussian wavelet transform. Physica A. 2003;318(3):551–561. DOI: 10.1016/S0378-4371(02)01379-1.
  25. Naveau P, Oh H. Polynomial Wavelet Regression for Images With Irregular Boundaries. IEEE Transactions on Image Processing. 2004;13(6):773–781. DOI: 10.1109/tip.2003.821345.
  26. Yuen DA, Vincent AP, Kido M, Vecsey L. Geophysical applications of multidimensional filtering with wavelets. Pure and Applied Geophysics. 2002;159(10):2285–2309. DOI: 10.1007/s00024-002-8736-5.
  27. Petrov AV, Nikitin AA, Piskun PV, Zinovkin SV. In: Abstracts of the VIII International Scientific and Practical Conference «Geomodel – 2006». 2006:315. (in Russian).
  28. Albora M, Bal A, Ucan ON. A New Approach for Border Detection of the Dumluca (Turkey) Iron Ore Area: Wavelet Cellular Neural Networks. Pure and Applied Geophysics. 2007;164(1):199–215. DOI: 10.1007/s00024-006-0156-5.
  29. Svetov BS, Piskun PV. Spectral-spatial analysis (span) of electrical data. Geophysics. 2005;4:43–48. (in Russian).
  30. Gholami A, Siahkoohi HR. A two-step wavelet-based regularization for linear inversion of geophysical data. Geophysical Prospecting. 2009;57(5):847–862. DOI: 10.1111/j.1365-2478.2008.00751.x.
  31. Gholami A, Siahkoohi HR. Simultaneous constraining of model and data smoothness for regularization of geophysical inverse problems. Geophys. J. Int. 2009;176:151–163.
  32. Kumar P, Foufoula-Georgiou E. Wavelet analysis for geophysical applications Reviews of Geophysics. 1997;35(4):385–412. DOI: 10.1029/97RG00427.
  33. Kritski A, Vincent P, Yuen DA, Carlsen T. Adaptive wavelets for analyzing dispersive seismic waves. Geophysics. 2007;72:V1–V11.
  34. Gusev VA, Koronovskii AA, Hramov AE. Adaptive wavelets applied to the analysis of nonlinear systems with chaotic dynamics. Technical Physics Letters. 2003;29(9):776–779.
  35. Sitnikova E, Hramov AE, Koronovskii AA, Luijtelaar EL. Sleep spindles and spike–wave discharges in EEG: Their generic features, similarities and distinctions disclosed with Fourier transform and continuous wavelet analysis. Journal of Neuroscience Methods. 2009;180(2):304–316. DOI: 10.1016/j.jneumeth.2009.04.006.
  36. Koronovskii AA, Hramov AE. Continuous Wavelet Analysis: Application to Nonlinear Dynamics Problems. Saratov: GosUNTs «College»; 2002. (in Russian).
  37. Koronovskii AA, Hramov AE. An introduction to continuous wavelet analysis for nonlinear dynamics specialists. Izvestiya VUZ. Applied Nonlinear Dynamics. 2001;9(4-5):3–49 (in Russian).
  38. Koronovskii AA, Hramov AE. An effective wavelet analysis of the transition to chaos via intermittency. Technical Physics Letters. 2001;27(1):1–5. DOI: 10.1134/1.1345150.
  39. Koronovskii AA, Khramov AE. Analysis of phase chaotic synchronization using continuous wavelet analysis. Letters in the Life Sciences. 2004;14:29–36 (in Russian).
  40. Gurvich II, Boganik GN. Seismic exploration. Moscow: Nedra; 1980. 551 p. (in Russian).
  41. Yilmas O. Seismic Data Analysis. V. I, II. USA: Tulsa, Society of Exploration Geophysicists; 2001. DOI: 10.1190/1.9781560801580.
  42. Vorobyev VI, Gribunin VG. Theory and Practice of the Wavelet Transform. St. Petersburg: VUS; 1999. 204 p. (in Russian).
  43. Reine C., Van der Baan N., Clark R. The robustness of seismic attenuation measurements using fixed and variable-window time-frequency transforms. Geophysics. 2009;74(2):WA123–WA135. DOI: 10.1190/1.3043726.
  44. Alekseev VI. Reports at the 10th scientific and practical conference «Modern geophysical technologies in JSC «Khanty-Mansiysk Geophysics» and prospects for their use to improve the efficiency of prospecting, exploration and development of oil and gas fields». 2008:111. (in Russian).
  45. Zemtsova DP, Nikitin AA, Piskun PV. Wavelet analysis of the wave field in solving seismic exploration problems. In: Abstracts of the VII International Scientific and Practical Conference «Geomodel – 2005», Gelendzhik. 2005:68–69 (in Russian).
  46. Nikitin AA. Geophysics. New methods of processing geophysical data and their well-known analogues. 2006;4:11–15 (in Russian).
  47. Nikitin AA, Petrov AV. Basic procedures of transient fields data processing and interpretation. Geophysics. 2007;3:63–70 (in Russian).
  48. Nikitin AA, Zinovkin SV, Petrov AV, Piskun PV. Adaptive techniques for identifying heterogeneous geological objects in geophysical fields. Izv VUZ. Geology and Exploration. 2006;3:50–56 (in Russian).
  49. Khachai OA, Kuksa YuI, Khachai OYu. Wavelet analysis of magnetovariational monitoring in a seismically active area. Geophysics. 2003;5:66–69 (in Russian).
  50. Broadhead MK, Aramco S, Dhahran N. The impact of random noise on seismic wavelet estimation. The Leading Edge. 2008;27:226–230.
  51. Ampilov YuP, Seismic interpretation: experience and problems. Moscow: «Geoinformmark»; 2004. 276 p. (in Russian).
  52. Chopra S, Marfurt KJ. Seismic attribute mapping of structure and stratigraphy: Society of Exploration Geophysicists, Distinguished Instructor Short Course Series. USA: Tulsa; 2006.
  53. Chopra S, Marfurt K.. Seismic attributes for prospect identification and reservoir characterization: Society of Exploration Geophysicists. OK: Tulsa; 2007.
  54. Liner C, Li C, Gersztenkorn A, Smythe J. SPICE: A new general seismic attribute. SEG Technical Program Expanded Abstracts; 2004. DOI: 10.1190/1.1845256.
  55. Boroschek RL, Comte DY. Amplitude and frequency characteristics of the 2001 Southern Peru, Mw = 8.4 earthquake records. J. Seismol. 2006;10:353–369. DOI: 10.1007/s10950-006-9021-3.
  56. Domingues MO, Mendes OJ, Mendes da Costa A. On wavelet techniques in atmospheric sciences. Advances in Space Research. 2005;35:831–842. DOI: 10.1016/j.asr.2005.02.097
  57. Alekseev VI, Bobryshev AN. Wavelet analysis of seismic images. Geophysics. 2009;3:12–15 (in Russian).
  58. Piskun PV, Nikitin AA, Zemtsova DP. Abstracts of VI Geophysical Readings named in honour of Fedynsky VV. GEON Center; 2004. (in Russian).
  59. Masyukov AV, Masyukov VV, Shlenkin SI. A family of efficiently computed integral wavelet transforms. Mathematical methods in geophysics: Proceedings of the International Conference; 2003. (in Russian).
  60. Kopilevich EA, Afanasyev ML, Petrov AYu. Model substantiation of forecasting of filtration-capasitive properties of reservoirs in crosswell space. Oil Industry. 2006;9:10–15 (in Russian).
  61. Davydova EA, Kopilevich EA, Mushin IA. Spectral-temporal method for mapping typical geological sections. Doklady Earth Sciences. 2002;385A(6):718–720.
  62. Kopilevich EA, Davydova EA, Samarkin MA. Noise immunity and frequency resolution of the spectral-temporal method of mapping geological section types according to seismic data. Geophysics. 2004;2:21–24 (in Russian).
  63. Strutz T., Muller E. Adaptive Wavelet Transformation for Image Coding Using a Forecast Decomposition Selection. Picture Coding Symposium’97, 10–12 September. Berlin. Germany. 1997:67–72.
  64. Strutz T, Schwarz H, Muller E. Predictive Image Coding With Adaptive Wavelet Transform. Proceedings of SPIE. 1997;3164:279–290.
  65. Frick P, Baliunas SL, Galyagin D, Sokoloff D, Soon W. Wavelet analysis of stellar chromospheric activity variations. The Astrophisical Journal. 1997;483(1):426–434. DOI: 10.1086/304206.
  66. Novikov LV. Adaptive wavelet analysis of signals. Scientific Instrumentation. 1999;9(2):30–37 (in Russian).
  67. Bondarev VI, Krylatkov SM. Foundation of processing and interpretation of seismic data. Yekaterinburg: Ural State Mining Univ. Publ.; 2001. 193 p. (in Russian)
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