Skip to main content
SpringerLink
Log in

A Rapid NMR T2 Inversion Method Based on Norm Smoothing

  • Original Paper
  • Published:
Applied Magnetic Resonance Aims and scope Submit manuscript

Abstract

Norm smoothing is commonly used in nuclear magnetic resonance (NMR) T2 inversion and the choice of a suitable regularization parameter is a key step for obtaining a satisfactory inversion result, which is usually achieved by repeating T2 inversion multiple times. However, a greater number of inversions result in a slower speed for the inversion process. In this paper, we propose a rapid norm smoothing T2 inversion method achieved using a new selection method for the regularization parameter. First, the singular value decomposition (SVD) method is used to calculate singular values of the kernel matrix to compress the echo train data. Subsequently, a suitable regularization parameter is calculated based on the signal-to-noise ratio (SNR) of the echo train and the maximum singular value of the kernel matrix, which avoids the repetitions of the T2 inversion. Finally, a rapid T2 inversion is obtained using the Butler–Reeds–Dawson (BRD) method. Numerical simulation and logging data inversion results show that the new method can rapidly provide reasonable T2 spectra for data with different SNRs and is insensitive to the amount of the compressed data.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

References

  1. K.J. Dunn, D.J. Bergman, G.A. LaTorraca, Nuclear Magnetic Resonance: Petrophysical and Logging Applications (Pergamon, New York, 2002)

    Google Scholar 

  2. G.R. Coates, R.C.A. Peveraro, A. Hardwick, D. Roberts, in SPE Annual Technical Conference and Exhibition (Dallas, Texas, 6–9 October 1991), p. 627

  3. R. Sigal, Petrophysics 43(1), 38–46 (2002)

    MathSciNet  Google Scholar 

  4. A. Timur, J. Petrol. Technol. 21(06), 775–786 (1969)

    Article  Google Scholar 

  5. G.R. Coates, J. Galford, D. Mardon, D. Marschall, Log Anal. 39(1), 51–63 (1998)

    Google Scholar 

  6. R. Freedman, S. Lo, M. Flaum, G.J. Hirasaki, A. Matteson, A. Sezginer, SPE J. SPE-75325-PA (2001)

  7. K.J. Dunn, G.A. LaTorraca, J. Magn. Reson. 140(1), 153–161 (1999)

    Article  ADS  Google Scholar 

  8. A. Sezginer, Determining bound and unbound fluid volumes using nuclear magnetic resonance pulse sequences. US, Patent 5,363,041, 1994

  9. R. Freedman, Method and apparatus for compressing data produced from a well tool in a wellbore prior to transmitting the compressed data uphole to a surface apparatus. US, Patent 5,381,092, 1995

  10. Y.L. Zou, R.H. Xie, Comput. Geosci. 19(2), 389–401 (2015)

    Article  Google Scholar 

  11. M.G. Prammer, in SPE Annual Technical Conference and Exhibition (New Orleans, Louisiana, 25–28 September 1994), p. 55

  12. J.P. Butler, J.A. Reeds, S.V. Dawson, SIAM J. Numer. Anal. 18(3), 381–397 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  13. K.J. Dunn, G.A. LaTorraca, J.L. Warner, D.J. Bergman, in SPE Annual Technical Conference and Exhibition (New Orleans, Louisiana, 25–28 September 1994), p. 45

  14. S. Chen, W. Shao, G. Hursan, B. Sun, in SPWLA 50th Annual Logging Symposium (The Woodlands, Texas, 21–24 June 2009), SPWLA-2009-31589

  15. E. Chouzenoux, S. Moussaoui, J. Idier, F. Mariette, IEEE Trans. Signal Process. 58(12), 6040–6051 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  16. Y. Zou, R. Xie, Y. Ding, A. Arad, Geophysics 81(1), D1–D8 (2016)

    Article  Google Scholar 

  17. V.A. Morozov, Soviet Math. Dokl. 7(1), 414–417 (1966)

    MathSciNet  Google Scholar 

  18. G.H. Golub, M. Heath, G. Wahba, Technometrics 21(2), 215–223 (1979)

    Article  MathSciNet  Google Scholar 

  19. P.C. Hansen, SIAM Rev. 34(4), 561–580 (1992)

    Article  MathSciNet  Google Scholar 

  20. P.C. Hansen, T.K. Jensen, G. Rodriguez, J. Comput. Appl. Math. 198(2), 483–492 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  21. Y.Q. Song, L. Venkataramanan, M.D. Hürlimann, M. Flaum, P. Frulla, C. Straley, J. Magn. Reson. 154(2), 261–268 (2002)

    Article  ADS  Google Scholar 

  22. Y.L. Zou, R.H. Xie, A. Arad, Pet. Sci. 13(2), 237–246 (2016)

    Article  Google Scholar 

Download references

Acknowledgements

We thank the editors and reviewers for their constructive comments and suggestions on this manuscript. This work was funded by the National Science and Technology Major Project of the Ministry of Science and Technology of China (2016ZX05033-003-001).

Author information

Authors and Affiliations

  1. SINOPEC Exploration and Production Research Institute, Beijing, 100083, China

    Youlong Zou, Jun Li, Junlei Su & Aiqin Zhang

Authors
  1. Youlong Zou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Junlei Su
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Aiqin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Youlong Zou.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zou, Y., Li, J., Su, J. et al. A Rapid NMR T2 Inversion Method Based on Norm Smoothing. Appl Magn Reson 48, 1043–1053 (2017). https://doi.org/10.1007/s00723-017-0928-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00723-017-0928-3

Search

Navigation