核磁共振二维谱反演技术综述

摘要/Abstract

摘要：

二维谱的出现是核磁共振（NMR）检测技术的一次飞跃，从二维谱中可以快速、精确地对不同组分进行区分，因而在测录井和常规实验中被广泛采用. 为了给相关研究提供借鉴和参考，推动二维反演技术的发展，该文对近年来国内外在核磁共振二维谱反演技术领域的研究进展进行了综述. 从实验采集数据中反演出二维谱的过程，比一维反演需要解决更多、更复杂的问题. 通过研究罚函数正则化和子空间正则化两大类方法，分析了不同二维反演算法的优点和不足. 根据对近年来国内外相关文献的深入分析可知，虽说目前已有的二维反演算法都存在一定的局限性，但其仍然具有很大的发展空间.

关键词: 核磁共振（NMR）, 二维反演, , 扩散-横向弛豫, 纵向-横向弛豫

Abstract:

Two-dimensional (2D) NMR parameter maps are widely used in NMR-based well logging and conventional NMR experiments to distinguish different components in mixtures. In recent years, much research efforts were dedicated to develop inversion algorithms that could convert raw experimental data into 2D NMR maps. This paper reviews the recent progresses in this area of research. The methodological complexity of 2D inversion, relative to 1D inversion, was discussed. There are two major approaches for 2D inversion: regularization using penalty terms and regularizing in subspace. The advantages and disadvantages of the approaches were analyzed. It is concluded that all the existing 2D inversion algorithms have limitations such that further development are needed.

Key words: nuclear magnetic resonance, 2D inversion, diffusion, relaxation

中图分类号:

O482. 53

周小龙1，聂生东1*，王远军1，张英力2，杨培强2. 核磁共振二维谱反演技术综述[J]. 波谱学杂志.

ZHOU Xiao-long1, NIE Sheng-dong1*, WANG Yuan-jun1，ZHANG Ying-li2, YANG Pei-qiang2. A Review on the Inversion Methods in 2D NMR[J]. Chinese Journal of Magnetic Resonance.

参考文献

[1] Akkurt R，Bachman H N， Minh C C, et al. New nuclear magnetic resonance comes out of its shell[J]. Oilfield Review，2008，20（4）: 4-23.

[2] Wang Li-li(王丽丽). Low-field pulsed Nuclear Magnetic Resonance transverse relaxation signal deconvolution algorithm(低场脉冲NMR横向弛豫信号解谱算法研究)[D]. A Dissertation Submitted for the Degree of Master at the Graduate School of the Chinese Academy of Sciences(中国科学院研究生院硕士学位论文). 2006.

[3] Meng Xiao-hai(孟小海)，Jiang Zhi-min(姜志敏)，Shi Jing-sheng(史京生)，et al. Two-dimensional NMR spectroscopy for observing rock wettability(二维核磁共振观测岩石润湿性)[J]. Chinese J Magn Reson（波谱学杂志），2012，29(2): 190-199.

[4] Ding Yang(丁阳). NMR T₂ Spectroscopy Inversion Based on Genetic Algorithm(基于遗传算法的核磁共振T₂谱反演)[D]. A Dissertation Submitted for the Degree of Master at Jilin University(吉林大学硕士学位论文)，2010.

[5] Mohnke O, Yaramanci U. Smooth and block inversion of surface NMR amplitudes and decay times using simulated annealing [J]. J Appl Geophys, 2002, 50: 163-177.

[6] Pan Ke-jia(潘克家),Chen Hua(陈华),Tan Yong-ji(谭永基). Multi-exponential inversion of T₂ spectrum in NMR based on differential evolution algorithm(基于差分进化算法的核磁共振T₂谱多指数反演)[J]. Acta Physica Sinica(物理学报)，2008，57（9）：5 956-5 961.

[7] Wang Wei-min(王为民)，Li Pei(李培)，Ye Zhao-hui(叶朝辉). Multi-exponential inversion of NMR relaxation signals(核磁共振弛豫信号的多指数反演)[J]. Science in China(Series A)[中国科学(A辑)]，2001，31(8): 730-736.

[8] Li Peng-ju(李鹏举), Ge Cheng(葛成), Sun Guo-ping(孙国平), et al. Improvement of T₂ spectrum inversion method with singular value decomposition from NMR data(基于奇异值分解的核磁共振测井T₂谱反演方法的改进)[J]. Well Logging Technology(测井技术)，2010，34（3）：215-218.

[9] Jiang Yu-long(江玉龙). Study on Data Interpretation and Experiments of MRIL-Prime Logging(P型核磁测井解释处理方法研究)[D]. A Dissertation Submitted for the Degree of Doctor at Jilin University(吉林大学博士学位论文)，2008.

[10] Li Peng-ju(李鹏举). Study on T₂ Spectrum Inversion and Fluid Identification and Evaluation of NMR(核截共振T₂谱反演及流体识别评价方法研究)[D]. A Dissertation Submitted for the Degree of Doctor at Northeast Petroleum University(东北石油大学博士学位论文)，2010.

[11] Tan Mao-jin(谭茂金), Shi Yao-lin(石耀霖),Xie Guan-bao(谢关宝). NMR T₂ distribution inversion based on genetic algorithm(基于遗传算法的核磁共振T₂分布反演)[J]. Well Logging Technology(测井技术)，2007, 31（5）：413-416.

[12] Luo Li(罗利), Wang Yong-jun(王勇军), Yang Jia(杨嘉), et al. Application of the GeoReveal MRIL-P T₂ spectrum inversion method to the evaluation of low porosity & permeability reservoirs (GeoReveal MRIL-P核磁解谱技术在低孔渗储层评价中的应用)[J]. Natural Gas Industry(天然气工业), 2011, 31(2): 59-62.

[13] Li Peng-ju(李鹏举), Shi Shang-ming(施尚明), Song Yan-jie(宋延杰). Method of T₂ spectrum inversion with conjugate gradient algorithm from NMR data(核磁共振T₂谱最优化反演方法)\[J\]. Nuclear Electronics & Detection Technology(核电子学与探测技术), 2010, 30(5): 712-716.

[14] Yao Xu-gang(姚绪刚), Wang Zhong-dong(王忠东). A new inversion algorithm for NMR relaxation distribution(一种新的核磁共振弛豫谱反演算法)[J]. Well Logging Technology(测井技术), 2003, 27(5): 373-376.

[15] Jiang Rui-zhong(姜瑞忠), Yao Yan-ping(姚彦平), Miao Sheng(苗盛), et al. Improved algorithm for singular value decomposition inversion of T₂ spectrum in nuclear magnetic resonance(核磁共振T₂谱奇异值分解反演改进算法)[J]. Acta Petrolei Sinica(石油学报), 2005, 26(6): 57-59.

[16] Chen Hua(陈华), Pan Ke-jia(潘克家), Tan Yong-ji(谭永基). A new method for multi- exponential Inversion of NMR relaxation signal(核磁共振弛豫信号多指数反演新方法)[J]. Well Logging Technology(测井技术), 2009, 33(1): 37-40.

[17] Venkataramanan L, Song Y Q, Hurlimann M D. Solving fredholm integrals of the first kind with tensor product structure in 2 and 2.5 dimensions[J]. IEEE T Signal Proces, 2002, 50(5): 1 017-1 026.

[18] Song Y Q, Venkataramanan L, Hurlimann M D, et al. T₁T₂ correlation spectra obtained using a fast two-dimensional laplace inversion[J]. J Magn Reson, 2002, (154): 261-268.

[19] Sun B Q, Dunn K J. Methods of Decoupling Diffusion Effects from Relaxation times to Determine Properties of Porous Media Containing Fluids: US, Patent 6833698B2[P], 200411-21.

[20] Sun B Q, Dunn K J. Method for Obtaining MultiDimensional Proton Density Distributions from a System of Nuclear Spins: US, Patent 6937014B2[P], 2005-08-30.

[21] Honerkamp J, Weese J. Tikhonovs regularization method for ill-posed problems: A comparison of different methods for the determination of the regularization parameter[J]. Continuum Mech Therm, 1990, 2: 17-30.

[22] Kazufumi Ito, Bangti Jin. A new approach to nonlinear constrained Tikhonov regularization[J]. Inverse Probl, 2011, 27: 105 005-105 027

[23] Provencher S W. A constrained regularization method for inverting data represented by linear algebraic or integral equations[J]. Comput Phys Commun, 1982, 27: 213-227.

[24] Provencher S W. CONTIN: A general purpose constrained regularization program for inverting noisy linear algebraic and integral equations[J]. Comput Phys Commun, 1982, 27: 229-242. 

[25] Richard C A，Brian B, Clifford H T. Parameter Estimation and Inverse Problems(Second Edition)[M]. US: Academic Press, 2012.

[26] Iain J D. On the inversion of diffusion NMR data: Tikhonov regularization and optimal choice of the regularization parameter[J]. J Magn Reson, 2011, 211: 178-185.

[27] Chouzenoux , Moussaoui S, Idier J, et al. Optimization of a maximum entropy criterion for 2d nuclear magnetic resonance reconstruction[J]. ICASSP, 2010, 4 154-4 157.

[28] Chouzenoux , Moussaoui S, Idier J, et al. Efficient maximum entropy reconstruction of nuclear magnetic resonance T₁T₂ spectra[J]. IEEE T Signal Process, 2010, 58(12): 6 040-6 051.

[29] Hansen P C, O'Leary D P. The use of the L-curve in the regularization of discrete ill-posed problems[J]. SIAM J Sci Comput, 1993, 14: 1 487-1 503.

[30] Feng Li-xin(冯立新). The Computational Methods and Applications of Inverse Problems(反问题的计算方法及应用)[M]. Haebin(哈尔滨)：HIT Press（哈尔滨工业大学出版社），2011.

[31] Butler J P, Reeds J A, Dawson S V. Estimating solutions of the first kind integral equations with nonnegative constraints and optimal smoothing[J]. SIAM J Numer Anal, 1981, 18(3): 381-397.

[32] Venkataramanan L, Song Y Q, Hurlimann M D. Nuclear Magnetic Resonance measurements and methods of analyzing Nuclear Magnetic Resonance data: US, 6462542 B1[P]. 2002-10-08.

[33] Fordham E J, Sezginer A, Hall L D. Imaging multi-exponential relaxation in the (y; logT) plane, with application to clay filtration inrock cores[J]. J Magn Reson A, 1995, 113: 139-150.

[34] Borgia G C, Brown R J S, Fantazzini P. Uniform-penalty inversion of multi-exponential decay data[J]. J Magn Reson, 1988, 132: 65-77.

[35] Borgia G C, Brown R J S, Fantazzini P. Examples of uniform-penalty inversion of multi-exponential relaxation data[J]. Magn Reson Imaging, 1998, 16: 549-552.

[36] Borgia G C, Brown R J S, Fantazzini P. Uniform-penalty inversion of multi-exponential decay data: II. data spacing, T₂ data, systematic data errors, and diagnostics[J]. Magn Reson Imaging, 2000, 147: 273-285.

[37] Haber E. Numerical strategies for the solution of inverse problem[D]. A Dissertation Submitted for the Degree of Master at University of British Columbia, 1997. 

[38] Gu Zhao-bin(顾兆斌), Liu Wei(刘卫). The inversion of two-dimensional NMR map(核磁共振二维谱反演)[J]. Chinese J Magn Reson(波谱学杂志), 2007, 24(3): 311-319.

[39] Tan Mao-jin(谭茂金), Zou You-long(邹友龙), Liu Bing-kai(刘兵开), et al. Inversion simulation of (T₂, D) 2D NMR logging and analysis of observation parameters effects in gaswater model(气水模型(T₂, D)二维核磁共振测井数值模拟及参数影响分析)[J]. Well Logging Technology(测井技术)，2011，35(2): 130-136.

[40] Xie Ran-hong(谢然红), Xiao Li-zhi(肖立志), Dunn keh-jim(邓克俊), et al. Two-dimensional NMR Logging(二维核磁共振测井)[J]. Well Logging Technology(测井技术), 2005, 29(5): 430-433.

[41] Xie Ran-hong(谢然红), Xiao Li-zhi(肖立志), Lu Da-wei(陆大卫). (T₂, T₁) two-dimensional NMR method for fluid typing(识别储层流体的(T₂, T₁)二维核磁共振方法)[J]. Well Logging Technology(测井技术), 2009, 33(01): 26-31.

[42] Xie Ran-hong(谢然红), Xiao Li-zhi(肖立志). The (T₂, D) NMR logging method for fluids characterization((T₂, D)二维核磁共振测井识别储层流体的方法)[J]. Chinese J Geophysics(地球物理学报), 2009, 52(9): 2 410-2 418.

[43] Lin F, Wang Z W, Li J Y, et al. Study on algorithms of low SNR inversion of T₂ spectrum in NMR[J]. Appl Geophysics, 2011, 8(3): 233-238.

[44] Sandgren N, Stoica P, Selen Y. Frequency-selective SVD-based magnetic resonance spectroscopy with prior knowledge[J]. Signals, Systems and Computers, 2004, 2: 1 605-1 608.

[45] Tan M J, Zou Y L, Zhou C C. A new inversion method for (T₂, D) 2D NMR logging and fluid typing, Computers & Geosciences[J]. Computers & Geosciences, 2013, 51: 366-380

[46] Sun Bo-qin(孙伯勤), Dunn Kehjim(邓克俊). Fast NMR CPMG data inversion using fluid component decompositions(核磁共振回波串的液体分量分解快速反演法)[J]. Chinese J Magn Reson(波谱学杂志), 2010, 27(3): 298-309.

[47] Sun B Q, Dunn K J. A global inversion method for multi-dimensional NMR logging[J]. J Magn Reson, 2005, 172: 152-160.

[48] smund U, Geir H S, Eddy W H, et al. ANAHESS, A new second order sum of exponentials fit algorithm, compared to the tikhonov regularization approach, with NMR applications[J]. International Journal of Research and Reviews in Applied Sciences, 2010, 2(3): 195-210.

