Skip to main content
Log in

NMR Log Data De-noising Method Based on a Variable Order Wavelet Packet Domain Adaptive Filtering

  • Published:
Applied Magnetic Resonance Aims and scope Submit manuscript

Abstract

To improve the de-noising effects of low signal to noise ratio (SNR) nuclear magnetic resonance (NMR) log data, improve the calculating precision of the porosity parameters of the reservoirs, this paper attempts to apply the wavelet packet domain adaptive filtering algorithm to de-noise the NMR log data. First of all, the algorithm is interpreted in detail. And then, the de-noise off phenomenon is analyzed in the de-noising process of simulant and NMR echo data using the wavelet (packet) domain adaptive filtering algorithm. The factors affecting the occasion of the phenomenon are studied systematically, and a variable order processing scheme is proposed to eliminate the influence of the existence of the de-noise off phenomenon on the inversed T2 spectra. As a result, the effectiveness of the algorithm is verified by the application in the numerical simulation and NMR log data, respectively. The results indicated that, comparing with wavelet domain adaptive filtering algorithm, wavelet packet domain adaptive filtering algorithm is more suitable for low SNR-NMR echo data de-noising.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. C. M. Edwards, S. Chen, Society of Petrophysicists and Well Log Analysts 37th Annual Logging Symposium. RR (1996)

  2. O.A. Ahmed, M.M. Fahmy, IEEE T. Med. Imaging. 20, 1018–1025 (2001)

    Article  Google Scholar 

  3. R.H. Xie, Y.B. Wu, K. Liu, L.Z. Xiao, J. Geophys. Eng. (2014). doi:10.1088/1742-2132/11/3/035003

    Google Scholar 

  4. N. Serban, Comput. Stat. Data. An. 54, 1051–1065 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  5. Q.M. Xie, L.Z. Xiao, L.J. Cheng, J.F. Liu, H.Y. Li, F. Deng, Appl. Magn. Reson. 44, 1381–1391 (2013)

    Article  Google Scholar 

  6. L.Z. Xiao, Q.M. Xie, R.H. Xie, W.G. Pan, Chinese J. Geophys. 56, 3943–3952 (2013). (in Chinese)

    Google Scholar 

  7. Y.B. Wu, R.H. Xie, L.Z. Xiao, Adv. Mater. Res. 588, 814–817 (2012)

    Article  Google Scholar 

  8. M. Dentino, J. Mccool, B. Widrow, P IEEE. 66, 1658–1659 (1978)

    Article  Google Scholar 

  9. S. Narayan, A.M. Peterson, M.J. Narasimha, IEEE T. ASSP. 31, 609–615 (1983)

    Article  Google Scholar 

  10. N. Ahmed, T. Natarajan, K.R. Rao, IEEE T. Comput. 100, 90–93 (1974)

    Article  MathSciNet  Google Scholar 

  11. K.R. Rao, N. Ahmed, IEEE Int. Conf. ASSP. 1, 136–140 (1976)

    Google Scholar 

  12. E.R. Ferrara, IEEE T. ASSP. 28, 474–475 (1980)

    Article  Google Scholar 

  13. W. K. Jenkins, J. R. Kreidle, IEEE Int. Symp. Circuits Syst., 875–878 (1986)

  14. S. Hosur, A.H. Tewfik, IEEE Int. Conf. ASSP. 3, 508–510 (1993)

    Google Scholar 

  15. N. Erdol, F. Basbug, IEEE T. Signal Process. 44, 2163–2171 (1996)

    Article  ADS  Google Scholar 

  16. T. Aboulnasr, K. Mayyas, IEEE T. Signal Process. 45, 631–639 (1997)

    Article  ADS  Google Scholar 

  17. S. Hosur, A.H. Tewfik, IEEE T. Signal Process. 45, 617–630 (1997)

    Article  ADS  Google Scholar 

  18. M. V. Wickerhauser, INRIA lectures on wavelet packet algorithms (Lions P-L ed, France, 1991), pp. 31–99

  19. R.R. Coifman, Y. Meyer, V. Wickerhauser, Wavelet analysis and signal processing (Jones and Bartlett, Boston, 1992), pp. 153–178

    Google Scholar 

  20. S.G. Mallat, T. Am. Math. Soc. 315, 69–87 (1989)

    MATH  MathSciNet  Google Scholar 

  21. S.G. Mallat, IEEE T. Pattern Anal. 11, 674–693 (1989)

    Article  MATH  Google Scholar 

  22. S.G. Mallat, IEEE T. ASSP. 37, 2091–2110 (1989)

    Article  Google Scholar 

  23. B. Widrow, M.E. Hoff, Adaptive switching circuits (MIT Press, USA, 1988), pp. 123–134

    Google Scholar 

  24. G.R. Coates, L.Z. Xiao, M.G. Prammer, N.M.R. Logging, Principles and Applications (Gulf Professional Publishing, Texas, 2000), p. 51

    Google Scholar 

Download references

Acknowledgments

This work is supported by the National Natural Science Foundation of China—China National Petroleum Corporation Petrochemical Engineering United Fund (U1262114) and the National Natural Science Foundation of China (41272163).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ranhong Xie.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Meng, X., Xie, R. & Liu, M. NMR Log Data De-noising Method Based on a Variable Order Wavelet Packet Domain Adaptive Filtering. Appl Magn Reson 46, 1265–1282 (2015). https://doi.org/10.1007/s00723-015-0715-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00723-015-0715-y

Keywords

Navigation