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Two-Step Inversion Method for NMR Relaxometry Data Using Norm Smoothing and Artificial Fish Swarm Algorithm

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Abstract

The inversion of nuclear magnetic resonance (NMR) relaxometry data based on the first kind of Fredholm equation is an ill-posed problem. The accurate transverse relaxation time (T2) distribution is of great significance to improve the application of NMR. The T2 distribution from the norm smoothing method for low signal-to-noise ratio (SNR) data is inaccurate owing to a large penalty term of the objective function. It is therefore important to improve the inaccuracy of the regularized solution. A two-step inversion method for NMR relaxometry data using norm smoothing and artificial fish swarm algorithm (AFSA) is proposed to improve the accuracy of inversion results. First, the raw NMR echo data are compressed using a simplified singular value decomposition method to reduce the inversion time. The regularized inversion solution from the norm smoothing method is taken as the initial values of the AFSA. Through the uncertainty analysis of the regularized inversion solution, the boundary of the fish swarm is determined. A more accurate solution is obtained by the iteration of the AFSA. The results show that the AFSA-optimized T2 distribution is closer to the T2 distribution of model than the regularized inversion solution in terms of the relaxation time and intensity of signal, and thus calculating the formation porosity more accurately. The proposed method shows good performance for processing NMR core data.

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Acknowledgements

The authors gratefully thank the financial supports from the National Natural Science Foundation of China (41674126).

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Authors and Affiliations

  1. State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum (Beijing), Beijing, 102249, China

    Mingxuan Gu, Ranhong Xie & Lizhi Xiao

  2. Key Laboratory of Earth Prospecting and Information Technology, China University of Petroleum (Beijing), Beijing, 102249, China

    Mingxuan Gu, Ranhong Xie & Lizhi Xiao

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  1. Mingxuan Gu
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  2. Ranhong Xie
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  3. Lizhi Xiao
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Correspondence to Ranhong Xie.

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Gu, M., Xie, R. & Xiao, L. Two-Step Inversion Method for NMR Relaxometry Data Using Norm Smoothing and Artificial Fish Swarm Algorithm. Appl Magn Reson 52, 1615–1634 (2021). https://doi.org/10.1007/s00723-021-01403-5

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