An improved TSVD algorithm to inverse NMR relaxation time
Gao Yang1, Xiao Lizhi2
1. College of Science, China University of Petroleum (Beijing), Beijing 102249, China;
2. College of Geophysics and Information Engineering, China University of Petroleum (Beijing), Beijing 102249, China
Abstract：Truncated singular value decomposition (TSVD) algorithm is widely used for nuclear magnetic resonance (NMR) relaxation (T2) inversion. Truncated singular value and non-negative restriction are critical to this algorithm. In this article, we propose a new method to determine the truncated singular value, and use simultaneous iterative reconstruction technique (SIRT) algorithm to non-negative restriction. Thus, the improved TSVD algorithm suits to low SNR echo trains. In this new algorithm, we just decompose the singular value once. So the algorithm is faster than the old one, and keeps the T2 spectrum continuity. Digital simulations show that the inversions by the proposed algorithm match very well with the model, and better than the inversions by other algorithms when SNR=5. The inversion of real core data shows that the proposed algorithm works very well for shale reservoir NMR core analysis and NMR logging.
Coates G R,Xiao L Z,Prammer M G. NMR Logging Principles and Applications. Texas:Gulf Publishing Company,1999.
[2]
肖立志. 核磁共振成像测井与岩石核磁共振及其应用. 北京:科学出版社,1998.
[3]
Dunn K J,Latorraca G A,Warner J L. On the calculation and interpretation of NMR relaxation time distribution. SPE28367,69th Annual SPE Technical Conference and Exhibition,New Orleans,1994,45-54.
Wang Caizhi,Shang Weizhong. Application of singular value decomposition ( SVD) in solution of T2 relaxation spectra from nuclear magnetic resonance(NMR) log data. OGP,2003,38(1):91-94.
[5]
肖立志,张恒荣,廖广志等.基于Backus-Gilbert理论的孔隙介质核磁共振弛豫反演.地球物理学报,2012,55(11):3821-3828.Xiao Lizhi,Zhang Hengrong,Liao Guangzhi et al. Inversion of NMR relaxation in porous media based on Backus-Gilbert theory. Chinese J Geophys,2012,55(11):3821-3828.
[6]
张恒荣. 基于BG理论的多孔介质核磁共振弛豫反演方法研究[硕士学位论文]. 北京:中国石油大学(北京),2010. Zhang Hengrong. Research on Inversion Method of NMR Relaxation in Porous Media Based on BG Theory[M]. Beijing:China University of Petroleum (Beijing),2010.
[7]
Backus G E,Gilbert J F. The resolving power of gross earth data. Geophysical Journal,1968,16(2):169-205.
[8]
Backus G E,Gilbert J F. Uniqueness in the inversion of inaccurate gross earth data. Philosophical Transactions,1970, 266(1173):123-192.
Jiang Ruizhong,Yao Yanping. Improved algorithm for singular value decomposition inversion of T2 spectrum in nuclear magnetic resonance. Acta Petrol Sinica,2005,26(6):57-59.
Liao Guangzhi,Xiao Lizhi,Xie Ranhong et al. Influence factors of multi-exponential inversion of NMR relaxation measurement in porous media. Chinese J Geophys,2007,50(3):932-938.
[12]
Dunn K J,Bergman D J,Latorraca G A. Nuclear Magnetic Resonance:Petrophysical and Logging Applications. Pergamon:Elsevier Science,2002.
