Determining Uncertainty in NMR T2 Distribution Using Frequentist Method
- Authors: Zou Y.1, Xie R.1, Ding Y.1, Arad A.2
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Affiliations:
- State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum
- Shell International Exploration and Production Inc.
- Issue: Vol 47, No 10 (2016)
- Pages: 1081-1094
- Section: Article
- URL: https://journals.rcsi.science/0937-9347/article/view/247551
- DOI: https://doi.org/10.1007/s00723-016-0819-z
- ID: 247551
Cite item
Abstract
Petrophysicists use the T2 distribution from nuclear magnetic resonance (NMR)-logging data inversion to evaluate reservoir. However, low SNR NMR-logging data lead to a great uncertainty of T2 distribution, and therefore, analyzing the uncertainty of T2 distribution has a guiding significance for NMR-logging evaluation. For regularized solution from linear inversion, the mean square error which jointly determined by variance and bias can be used to measure its uncertainty. The variance of regularized T2 distribution can be calculated from the variance of the noise level of measured data. Since the true T2 distribution is unknown, the bias of regularized T2 distribution cannot be accurately calculated. This paper calculated the upper and lower boundaries of the bias of regularized T2 distribution for analyzing the uncertainty of regularized T2 distribution based on the frequentist method, using the NMR echo amplitudes, T2 distribution amplitudes, T2 distribution slopes, and T2 distribution curvatures as prior information to restrict the range of T2 distribution amplitude. The results indicate that as the noise level of measured data increases, the T2 distribution uncertainty increases and the confidence interval of T2 distribution broadens. The confidence interval width of T2 distribution from the norm-smoothing method is narrower than that of from the curvature-smoothing method.
About the authors
Youlong Zou
State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum
Email: xieranhong@cup.edu.cn
China, Beijing, 102249
Ranhong Xie
State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum
Author for correspondence.
Email: xieranhong@cup.edu.cn
China, Beijing, 102249
Yejiao Ding
State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum
Email: xieranhong@cup.edu.cn
China, Beijing, 102249
Alon Arad
Shell International Exploration and Production Inc.
Email: xieranhong@cup.edu.cn
United States, Houston, TX, 77079