• OpenAccess
  • Study on Multi-Exponential Inversion Method for NMR Relaxation Signals with Tikhonov Segularization  [iCBBE 2013]
  • DOI: 10.4236/eng.2013.510B007   PP.32 - 37
  • Author(s)
  • Shanshan Chen, Hongzhi Wang, Xuelong Zhang
  • The analysis of NMR data in terms of inversion of relaxation distribution is hampered by the ill-posed nature of the required solution about the Fredholm integral equation. Naive approaches such as multi-exponential fitting or standard least-squares algorithms are numerically unstable and often failed. This paper updates the application of Tikhonov regularization to stabilize this numerical inversion problem and demonstrates the method for automatically choosing the optimal value of the regularization parameter. The approach is computationally efficient and easy to implement using standard matrix algebra techniques, which is based on mathematical ware MATLAB. Example analyses arepresented using both synthetic data and experimental results of NMR studies on the liquid samples like as oils and yoghurt.

  • NMR; Relaxometry; Inversion Relaxation; MATLAB
  • References
  • [1]
    L. z. Xiao, “The Principle and Application of NMR Imaging Logging and Rock NMR,” Science Press, Beijing, 1998.
    G. X. Xiong and L. B. Li, “The Principle of Magnetic Resonance Imaging,” Science Press, Beijing, 2007.
    H. Z. Wang and X. L. Zhan, “Experimentation of Magnetic Resonance Imaging,” Science Press, Beijing, 2008.
    L. Z. Xiao, Z. D. Wang and T. Y. Liu, “Application of Multi-Exponential Inversion Method to NMR Measurements,” Petroleum Science, Vol. 1, No. 1, 2004, pp. 20-22.
    H. Wang and G. Y. Li, “Combination of Inversion and Fitting as an Effective Method for the Analysis of NMR Relaxation Data,” Acta Physica Sinica, Vol. 54, No. 3, 2005, pp. 1431-1436.
    A. H. Weng and Z. B. Li, “On High Rresolution Inversion of NMR Logging Data,” Well Logging Technology, Vol. 26, No. 6, 2002, pp. 455-459.
    W. M. Wang, P. Li and C. H. Ye, “Multi-Exponential Inversion of NMR Relaxation Signal,” Science of China (A), Vol. 38, No. 8, 2001, pp. 730-736.
    R. D. Jiang, Y. P. Yao and S. Miao, “Improved Algorithm for Singular Alue Decomposition Inversion of T2 Spectrum in Nuclear Magnetic Resonance,” Acta Petrolei Sinica, Vol. 26, No. 6, 2005, pp. 57-59.
    K. P. Whittall and A. L. MacKay, “Quantitative Interpretation of NMR Relaxation Data,” Journal of Magnetic Resonance, Vol. 84, 1989, pp. 134-152.
    G. C. Borgia, R. J. S. Brown and P. Fantazzini, “Uniform Penalty Invertion of Multi-Exponential Decay Data (II),” Journal of Magnetic Resonance, Vol. 147, 2000, pp. 273-285.
    Y. Q. Song and L. P. Robert, “Assigning Uncertainties in the Inversion of NMR Relaxation Data,” Journal of Magnetic Resonance, Vol. 174, 2005, pp. 314-324.
    S. Ghodh, M. K Kenvin and Y. Pan, “A Simulation Based Method to Assess Inversion Algorithms for Transverse Relaxation Data,” Journal of Magnetic Resonance, Vol. 191, 2008, pp. 226-230.
    F. Lin, Z. W. Wang and J. Y. Li, “Study on Algorithms of Low SNR Inversion of T2 Spectrum in NMR,” Applied Geophysics, Vol. 3, 2011, pp. 233-238.

Engineering Information Institute is the member of/source content provider to