ARTICLE

Wavelet extraction and local seismic phase correction using normalized first-order statistics

DIAKO HARIRI NAGHADEH CHRISTOPHER KEITH MORLEY
Show Less
Petroleum Geophysics, Department of Geological sciences, Chiang Mai University, Chiang Mai, Thailand. diako.h@cmu.ac.th,
JSE 2016, 25(2), 163–176;
Submitted: 9 June 2025 | Revised: 9 June 2025 | Accepted: 9 June 2025 | Published: 9 June 2025
© 2025 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/ )
Abstract

Hariri Naghadeh, D. and Morley, C.K., 2016. Wavelet extraction and local seismic phase correction using normalized first-order statistics. Journal of Seismic Exploration, 25: 163-176. In this paper wavelet phase is extracted using normalized first-order statistics, which are introduced as an indicator of localized seismic signal phase. The analysis demonstrates sharpness of the probability distribution of a discrete time series, which is more robust than that obtained by applying higher-order statistics. The normalized first-order statistical value of the zero phase signal is higher than that of the non-zero phase signal, hence it is used as a signal phase correction controller to produce zero-phase signals. The most important parameter for correctly estimating the phase pertains to the best length of time window used for local phase correction. Incorrect window length creates non-zero phase wavelets. To choose the correct time window length, a continuous wavelet transform is applied, using a Morlet wavelet to decompose signals to wavelets. Based on the time-distance between maximum energy of wavelet coefficients normalized by the scale, it is possible to choose the best window length for local phase correction. Synthetic and real data examples are used to demonstrate the effectiveness of this method in both wavelet extraction and for local correction of signal phase. Results of the seismic phase correction using this method demonstrate superiority over the local Kurtosis and local skewness methods, because of high stability and dynamical range. Normalized first-order statistics permit a short window length not only as a phase correction controller but also as a thin layer detector.

Keywords
normalized first-order statistics
Kurtosis
Morlet wavelet
wavelet phase
skewness
References
  1. Fomel, S. and van der Baan, M., 2014. Local skewness attribute as a seismic phase detector.
  2. Interpretat., 2: SA49-SAS6.
  3. Herrera, H.R. and Mirkov, V.D.B., 2011. Revisiting homomorphic wavelet estimation and phase
  4. unwrapping. CSPG CSEG CWLS Conv., Calgary.
  5. Mansar, S. and Rodriguez, J.M., 1996. Analyzing and zero phasing seismic data using wavelet
  6. transform. Extended Abstr., 58th EAEG Conf., Amsterdam.
  7. Mendel, J.M., 1991. Tutorial on higher-order statistics (spectra) in signal processing and system
  8. theory. Proc. IEEE, 79: 278-305.
  9. Levy, S., Oldenburg, D.W., 1987. Automatic phase correction of common-midpoint stacked data.
  10. Geophysics, 52: 51-59.
  11. Rioul, O. and Vetterli, M., 1991. Wavelets and signal processing. IEEE Signal Proc., 8(4): 14-38.
  12. Robinson, E.A. and Treitel, S., 1980. Geophysical Signal Analysis. Prentice-Hall, Englewood
  13. Cliffs, NJ.
  14. Sinha, S., Partha, S.R., Phil, A.D. and Castagna, J.P., 2005. Spectral decomposition of seismic
  15. data with continuous-wavelet transform. Geophysics, 70(6): V11-V18.
  16. van der Baan, M., 2008. Time-varying wavelet estimation and deconvolution by Kurtosis
  17. maximization. Geophysics, 73(2): V11-V18. doi: 10.1190/1.2831936.
  18. van der Baan, M. and Fomel, S., 2009. Non-stationary phase estimation using regularized local
  19. Kurtosis maximization. Geophysics, 74(6): A75-A80. doi: 10,1190/1.3213533.
  20. White, R.E., 1988. Maximum Kurtosis phase correction. Geophys. J. Internat., 95: 371-389.
Share
Back to top
Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing