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面对日益复杂的勘探对象, D-T2二维核磁共振技术在实际应用中面临无法兼顾扩散系数测量范围和横向弛豫分辨率的困境. 脉冲序列作为D-T2二维核磁共振数据采集的核心技术, 其性能优劣直接影响应用效果, 在综合对比PFG, STE-PFG, BP-PFG、改良式CPMG, 扩散编程, 多回波间隔CPMG脉冲序列性能的基础上, 有效融合脉冲梯度场、恒定梯度场D-T2脉冲序列的优点, 本文提出一种基于脉冲梯度场的双变量、两窗口D-T2脉冲序列改进设计. 针对两个窗口的D-T2二维核磁共振数据反演, 为突破现有反演方法无法兼顾反演精度和解谱效率的瓶颈, 本着第二个窗口回波信号为主、第一个窗口回波信号为辅的原则, 本文提出一种同时使用两个窗口数据参与解谱的联合TSVD反演方法. 气水、油水、稠油、油气水模型不同信噪比条件下的数值模拟结果表明, 本文提供的D-T2改进脉冲序列达到了平衡扩散系数测量范围和横向弛豫分辨率的设计要求, 本文提供的联合TSVD反演方法也有效平衡了反演精度要求和解谱效率. 文中的D-T2改进脉冲序列及联合TSVD反演方法在复杂油气藏流体识别和产能预测中具有广泛的应用前景, 可为促进国内D-T2二维核磁共振岩心分析技术的发展提供有利条件.
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关键词:
- 脉冲序列 /
- 脉冲梯度场 /
- 双变量 /
- 联合TSVD反演方法
In face of the increasingly complicated exploration targets, D-T2 2D NMR technology cannot balance the range of diffusion coefficient and transverse relaxation resolution in practice. As the key technique of D-T2 2D NMR, the property of pulse sequence affects its application. A modified design of bivariate D-T2 pulse sequence based on pulsed field gradient is proposed after summarizing the technical characteristics of PFG, STE-PFG, BP-PFG, modified CPMG, “diffusion editing” and multi echo interval CPMG pulse sequences, which effectively integrates the advantages of D-T2 pulse sequences based on pulsed field gradient and constant field gradient. In order to reduce the difficulties that the existing D-T2 inversion methods cannot balance the inversion efficiency and accuracy, we propose a joint TSVD inversion method which sets the echos from the second window as the main part supplemented by the echos from the first window. Numerical simulation results for gas-water, oil-water, heavy oil and gas-oil-water models in different SNRs indicate that the D-T2 modified pulse sequence can balance the diffusion coefficient measureflent range and transverse relaxation resolution successfully, and the joint TSVD inversion method balances the inversion efficiency and accuracy successfully. Above all, the D-T2 modified pulse sequence and the joint TSVD inversion method have wide applications in the exploration and formation evaluation for unconventional reflervoir, and create favorable conditions for the development of D-T2 2D NMR technology.-
Keywords:
- pulse sequence /
- pulsed field gradient /
- bivariate /
- joint TSVD inversion method
[1] Torrey H C, Korringa J, Seevers D O 1959 Physical Review Letters 3 418
[2] Brown R J S, Gamson B W 1960 Journal of Petroleum Technology 219 201
[3] Morriss C E, Macinnis J, Freedman R, Smaardyk J, Straley C, Kenyon W E, Vinegar H S, Tutunjian P N 1993 The Society of Petrophysicists and Well Log Analysts (SPWLA)’s 37th Annual Logging Symposium Calgary, Alberta, June 13-16, 1993 GGG
[4] Dunn K J, LaTorraca G A, Warner J L, Bergman D J 1994 The Society of Petroleum Engineers (SPE)’s Annual Technical Conference and Exhibition New Orleans, Louisiana, September25-28, 1994 28367
[5] Chang D H, Vinegar H J, Morriss C, Straley C 1994 The Society of Petrophysicists and Well Log Analysts (SPWLA)’s 35th Annual Logging Symposium Tulsa, Oklahoma, June 19-22, 1994 A
[6] Coates G R, Marschall D, Mardon D, Galford J 1997 The Society of Petrophysicists and Well Log Analysts (SPWLA)’s 38th Annual Logging Symposium Houston, Texas, June15-18, 1997 QQ
[7] Kleinberg R L, Boyd A 1997 The Society of Petroleum Engineers (SPE)’s Annual Technical Conference and Exhibition San Antonio, Texas, October 5-8, 1997 38737
[8] Wang W M, Guo H K, Ye C H 2001 Acta Petrolei Sinica 22 40 (in Chinese) [王为民, 郭和坤, 叶朝辉2001石油学报 22 40]
[9] Xiao L Z, Liu T Y, Fu R S 2004 Acta Petrolei Sinica 25 38 (in Chinese) [肖立志, 刘堂晏, 傅容珊2004石油学报 25 38]
[10] Zhou B, Wang W M, Guo H K, Huang Y Z, Luo X R 2004 Earth Science (Journal of China University of Geosciences) 29 495 (in Chinese) [周波, 王为民, 郭和坤, 黄延章, 罗晓容2004地球科学(中国地质大学学报) 29 495]
[11] He Y D, Mao Z Q, Xiao L Z, Ren X J 2005 Chinese Journal of Geophysics 48 373 (in Chinese) [何雨丹, 毛志强, 肖立志, 任小军 2005 地球物理学报 48 373]
[12] Xie R H, Xiao L Z, Fu S Q, Liu J J, Liu T D 2007 Journal of China University of Petroleum (Edition of Natural Science) 31 34 (in Chinese) [谢然红, 肖立志, 傅少庆, 刘家军, 刘天定2007中国石油大学学报(自然科学版) 31 34]
[13] Xie R H, Xiao L Z, Fu S Q 2008 Journal of China University of Petroleum (Edition of Natural Science) 32 44 (in Chinese) [谢然红, 肖立志, 傅少庆2008中国石油大学学报(自然科学版) 32 44]
[14] Gao S S, Ye L Y, Xiong W, Guo H K, Hu Z M 2010 Chin. Phys. Lett. 27 128902
[15] Akkurt R, Vinegar H J, Tutunjian P N, Guillory A J 1995 The Society of Petrophysicists and Well Log Analysts (SPWLA)’s 36th Annual Logging Symposium Paris, June 26-29, 1995 N
[16] Akkurt R, Marshall D, Eyvazzadeh R Y, Gardner J S, Mardon D, Dunn K J 1998 The Society of Petroleum Engineers (SPE)’s Annual Technical Conference and Exhibition New Orleans, Louisiana, September 27-30, 1998 49014
[17] Mardon D, Gardner J S, Coates G R, Vinegar H J 1996 The Society of Petrophysicists and Well Log Analysts (SPWLA)’s 37th Annual Logging Symposium New Orleans, Louisiana, June 16-19, 1996 K
[18] Xie R H, Xiao L Z, Liu J J 2011 Chinese Journal of Geophysics 54 2184 (in Chinese) [谢然红, 肖立志, 刘家军 2011 地球物理学报 54 2184]
[19] Li Y, Xiao L Z, Sun H F 2012 Chinese Journal of Magnetic Resonance 29 21 (in Chinese) [李洋, 肖立志, 孙华峰 2012 波谱学杂志 29 21]
[20] Xiao L Z 2007 Well Logging Technology 31 401 (in Chinese) [肖立志2007测井技术 31 401]
[21] Xie R H 2008 Ph. D. Dissertation (Beijing: China University of Petroleum (Beijing)) (in Chinese) [谢然红2008博士学位论文 (北京: 中国石油大学 (北京))]
[22] Sun B Q, Dunn K J 2002 Phy. s Rev. E 65 051309
[23] Sun B Q, Dunn K J 2002 International Symposium of the Society of Core Analysts Monterey, CA, September 22-25, 2002 38
[24] Hrlimann M D, Venkataramanan L 2002 Journal of Magnetic Resonance 157 31
[25] Hrlimann M D, Venkataramanan L, Flaum C, Speier P, Karmonik C, Freedman R, Heaton H 2002 The Society of Petrophysicists and Well Log Analysts (SPWLA)’s 43th Annual Logging Symposium Oiso, Japan, June 2-5, 2002 FFF
[26] Hrlimann M D, Venkataramanan L, Flaum C 2002 Journal of Chemical Physics 117 10223
[27] Song Y Q, Venkataramanan L, Hrlimann M D, Flaum M, Frulla P, Straley C 2002 Journal of Magnetic Resonance 154 261
[28] Dunn K J 2010 Nuclear Magnetic Resonance Logging Theory and Application (Shandong: China University of Petroleum Press) p133-146 (in Chinese) [邓克俊 2010 核磁共振测井理论及应用(山东:中国石油大学出版社) 第133-146页]
[29] Hrlimann M D, Flaum M, Venkataramanan L, Flaum C, Freedman R, Hirasaki G J 2003 Magnetic Resonance Imaging 21 305
[30] Flaum M, Chen J, Hirasaki G J 2004 The Society of Petrophysicists and Well Log Analysts (SPWLA)’s 45th Annual Logging Symposium Noordwijk, Holland, June 6-9, 2004 JJ
[31] Sun B Q, Dunn K J, Bilodeau B J, Dalen S C V, Stonard S W, Rushaid A 2004 The Society of Petrophysicists and Well Log Analysts (SPWLA)’s 45th Annual Logging Symposium Noordwijk, Netherlands, June 6-9, 2004 KK
[32] Sun B Q, Dunn K J 2004 Magnetic Resonance Imaging 23 259
[33] Sun B Q, Oloson M, Baranowski J, Chen S, Li W, Georgi D 2006 The Society of Petrophysicists and Well Log Analysts (SPWLA)’s 47th Annual Logging Symposium Veracruz, Mexico, June 4-7, 2006 EE
[34] Xie R H, Xiao L Z 2009 Chinese Journal of Geophysics 52 2410 (in Chinese) [谢然红, 肖立志 2009 地球物理学报 52 2410]
[35] Shi Y J, Liu T D 2009 Well Logging Technology 33 584 (in Chinese) [石玉江, 刘天定 2009 测井技术 33 584]
[36] Tan M J, Zou Y L, Liu B K, Yang X 2011 Well Logging Technology 35 130 (in Chinese) [谭茂金, 邹友龙, 刘兵开, 杨萱 2011 测井技术 35 130]
[37] Tan M J, Zou Y L 2012 Chinese Journal of Geophysics 55 683 (in Chinese) [谭茂金, 邹友龙 2012 地球物理学报 55 683]
[38] Hu F L, Zhou C C, Li C L, Xu H J, Zhou F M, Si Z W 2012 Petroleum Exploration & Development 39 552 (in Chinese) [胡法龙, 周灿灿, 李潮流, 徐红军, 周凤鸣, 司兆伟 2012 石油勘探与开发 39 552]
[39] Stejskal E O, Tanner J E 1965 The Journal of Chemical Physics 42 288
[40] Stejskal E O 1965 The Journal of Chemical Physics 43 3597
[41] Tanner J E 1970 The Journal of Chemical Physics 52 2523
[42] Karlicek J R F, Lowe I J 1980 Journal of Magnetic Resonance 37 75
[43] Cotts R M, Hoch M J R, Sun T, Markert J T 1989 Journal of Magnetic Resonance 83 252
[44] Latour L L, Li L, Sotak C H 1993 Journal of Magnetic Resonance 101 72
[45] Vandusschoten D 1995 Journal of Magnetic Resonance 112 237
[46] Mair R W, Cory D G, Peled S, Tseng C H, Patz S, Walsworth R L 1998 Journal of Magnetic Resonance 135 478
[47] Zhang X, Li C H, Ye C H, Liu M L 2001 Analytical Chemistry 73 3528
[48] Albina R M, Vladimir D S 2007 Journal of Magnetic Resonance 188 122
[49] Hunter M W, Jackson A N, Callaghan P T 2010 Journal of Magnetic Resonance 204 11
[50] Qu Y T, Jiang Z M, Shi J S, Zhu T T, Meng X H, Wang W M 2012 Chinese Journal of Magnetic Resonance 29 51 (in Chinese) [曲岩涛, 姜志敏, 史京生, 朱涛涛, 孟小海, 王为民 2012 波谱学杂志 29 51]
[51] Li X J, Nie S D, Wang Y J, Yang P Q 2013 Chinese Journal of Magnetic Resonance 30 322 (in Chinese) [李新军, 聂生东, 王远军, 杨培强 2013 波谱学杂志 30 322]
[52] Wang W M, Li P, Ye C H 2001 Science in China （Series A） 31 730 (in Chinese) [王为民, 李培, 叶朝辉 2001 中国科学 31 730]
[53] Venkataramanan L, Song Y Q, Hrlimann M D 2002 IEEE Transactions on Signal Processing 50 1017
[54] Wang Z D, Xiao L Z, Liu T Y 2003 Science in China （Series G） 33 323 (in Chinese) [王忠东, 肖立志, 刘堂宴 2003 中国科学 33 323]
[55] Jiang R Z, Yao Y P, Miao S Zhang C S 2005 Acta Petrolei Sinica 26 57 (in Chinese) [姜瑞忠, 姚彦平, 苗盛, 张春生 2005 石油学报 26 57]
[56] Pan K J, Chen H, Tan Y J 2008 Acta Physica Sinica 57 5956 (in Chinese) [潘克家, 陈华, 谭永基 2008 物理学报 57 5956]
[57] Lin F, Wang Z W, Li J Y, Zhang X A, Jiang Y L 2011 Applied Geophysics 8 233
[58] Ito K, Jin B T 2011 Inverse Problems 27 5005
[59] Gao Y, Xiao L Z, Xie Q M 2014 Journal of China University of Petroleum )Edition of Natural Science) (自然科学版) 38 50 (in Chinese) [高阳, 肖立志, 谢庆明 2014 中国石油大学学报 38 50]
[60] Sun B Q, Dunn K J 2005 Journal of Magnetic Resonance 172 152
[61] Tonning E, Polder D, Callaghan P T, Engelsen S B 2007 Journal of Magnetic Resonance 188 10
[62] Xie R H, Xiao L Z, Liu J J, Dunn K J 2009 Chinese Journal of Geophysics 52 2913 (in Chinese) [谢然红, 肖立志, 刘家军, 邓克俊 2009 地球物理学报 52 2913]
[63] Tan M J, Zou Y L, Zhou C C 2013 Computers & Geosciences 51 366
[64] Zhou X L, Nie S D, Wang Y J, Zhang Y L, Yang P Q 2013 Chinese Journal of Magnetic Resonance 30 541 (in Chinese) [周小龙, 聂生东, 王远军, 张英力, 杨培强 2013 波谱学杂志 30 541]
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[1] Torrey H C, Korringa J, Seevers D O 1959 Physical Review Letters 3 418
[2] Brown R J S, Gamson B W 1960 Journal of Petroleum Technology 219 201
[3] Morriss C E, Macinnis J, Freedman R, Smaardyk J, Straley C, Kenyon W E, Vinegar H S, Tutunjian P N 1993 The Society of Petrophysicists and Well Log Analysts (SPWLA)’s 37th Annual Logging Symposium Calgary, Alberta, June 13-16, 1993 GGG
[4] Dunn K J, LaTorraca G A, Warner J L, Bergman D J 1994 The Society of Petroleum Engineers (SPE)’s Annual Technical Conference and Exhibition New Orleans, Louisiana, September25-28, 1994 28367
[5] Chang D H, Vinegar H J, Morriss C, Straley C 1994 The Society of Petrophysicists and Well Log Analysts (SPWLA)’s 35th Annual Logging Symposium Tulsa, Oklahoma, June 19-22, 1994 A
[6] Coates G R, Marschall D, Mardon D, Galford J 1997 The Society of Petrophysicists and Well Log Analysts (SPWLA)’s 38th Annual Logging Symposium Houston, Texas, June15-18, 1997 QQ
[7] Kleinberg R L, Boyd A 1997 The Society of Petroleum Engineers (SPE)’s Annual Technical Conference and Exhibition San Antonio, Texas, October 5-8, 1997 38737
[8] Wang W M, Guo H K, Ye C H 2001 Acta Petrolei Sinica 22 40 (in Chinese) [王为民, 郭和坤, 叶朝辉2001石油学报 22 40]
[9] Xiao L Z, Liu T Y, Fu R S 2004 Acta Petrolei Sinica 25 38 (in Chinese) [肖立志, 刘堂晏, 傅容珊2004石油学报 25 38]
[10] Zhou B, Wang W M, Guo H K, Huang Y Z, Luo X R 2004 Earth Science (Journal of China University of Geosciences) 29 495 (in Chinese) [周波, 王为民, 郭和坤, 黄延章, 罗晓容2004地球科学(中国地质大学学报) 29 495]
[11] He Y D, Mao Z Q, Xiao L Z, Ren X J 2005 Chinese Journal of Geophysics 48 373 (in Chinese) [何雨丹, 毛志强, 肖立志, 任小军 2005 地球物理学报 48 373]
[12] Xie R H, Xiao L Z, Fu S Q, Liu J J, Liu T D 2007 Journal of China University of Petroleum (Edition of Natural Science) 31 34 (in Chinese) [谢然红, 肖立志, 傅少庆, 刘家军, 刘天定2007中国石油大学学报(自然科学版) 31 34]
[13] Xie R H, Xiao L Z, Fu S Q 2008 Journal of China University of Petroleum (Edition of Natural Science) 32 44 (in Chinese) [谢然红, 肖立志, 傅少庆2008中国石油大学学报(自然科学版) 32 44]
[14] Gao S S, Ye L Y, Xiong W, Guo H K, Hu Z M 2010 Chin. Phys. Lett. 27 128902
[15] Akkurt R, Vinegar H J, Tutunjian P N, Guillory A J 1995 The Society of Petrophysicists and Well Log Analysts (SPWLA)’s 36th Annual Logging Symposium Paris, June 26-29, 1995 N
[16] Akkurt R, Marshall D, Eyvazzadeh R Y, Gardner J S, Mardon D, Dunn K J 1998 The Society of Petroleum Engineers (SPE)’s Annual Technical Conference and Exhibition New Orleans, Louisiana, September 27-30, 1998 49014
[17] Mardon D, Gardner J S, Coates G R, Vinegar H J 1996 The Society of Petrophysicists and Well Log Analysts (SPWLA)’s 37th Annual Logging Symposium New Orleans, Louisiana, June 16-19, 1996 K
[18] Xie R H, Xiao L Z, Liu J J 2011 Chinese Journal of Geophysics 54 2184 (in Chinese) [谢然红, 肖立志, 刘家军 2011 地球物理学报 54 2184]
[19] Li Y, Xiao L Z, Sun H F 2012 Chinese Journal of Magnetic Resonance 29 21 (in Chinese) [李洋, 肖立志, 孙华峰 2012 波谱学杂志 29 21]
[20] Xiao L Z 2007 Well Logging Technology 31 401 (in Chinese) [肖立志2007测井技术 31 401]
[21] Xie R H 2008 Ph. D. Dissertation (Beijing: China University of Petroleum (Beijing)) (in Chinese) [谢然红2008博士学位论文 (北京: 中国石油大学 (北京))]
[22] Sun B Q, Dunn K J 2002 Phy. s Rev. E 65 051309
[23] Sun B Q, Dunn K J 2002 International Symposium of the Society of Core Analysts Monterey, CA, September 22-25, 2002 38
[24] Hrlimann M D, Venkataramanan L 2002 Journal of Magnetic Resonance 157 31
[25] Hrlimann M D, Venkataramanan L, Flaum C, Speier P, Karmonik C, Freedman R, Heaton H 2002 The Society of Petrophysicists and Well Log Analysts (SPWLA)’s 43th Annual Logging Symposium Oiso, Japan, June 2-5, 2002 FFF
[26] Hrlimann M D, Venkataramanan L, Flaum C 2002 Journal of Chemical Physics 117 10223
[27] Song Y Q, Venkataramanan L, Hrlimann M D, Flaum M, Frulla P, Straley C 2002 Journal of Magnetic Resonance 154 261
[28] Dunn K J 2010 Nuclear Magnetic Resonance Logging Theory and Application (Shandong: China University of Petroleum Press) p133-146 (in Chinese) [邓克俊 2010 核磁共振测井理论及应用(山东:中国石油大学出版社) 第133-146页]
[29] Hrlimann M D, Flaum M, Venkataramanan L, Flaum C, Freedman R, Hirasaki G J 2003 Magnetic Resonance Imaging 21 305
[30] Flaum M, Chen J, Hirasaki G J 2004 The Society of Petrophysicists and Well Log Analysts (SPWLA)’s 45th Annual Logging Symposium Noordwijk, Holland, June 6-9, 2004 JJ
[31] Sun B Q, Dunn K J, Bilodeau B J, Dalen S C V, Stonard S W, Rushaid A 2004 The Society of Petrophysicists and Well Log Analysts (SPWLA)’s 45th Annual Logging Symposium Noordwijk, Netherlands, June 6-9, 2004 KK
[32] Sun B Q, Dunn K J 2004 Magnetic Resonance Imaging 23 259
[33] Sun B Q, Oloson M, Baranowski J, Chen S, Li W, Georgi D 2006 The Society of Petrophysicists and Well Log Analysts (SPWLA)’s 47th Annual Logging Symposium Veracruz, Mexico, June 4-7, 2006 EE
[34] Xie R H, Xiao L Z 2009 Chinese Journal of Geophysics 52 2410 (in Chinese) [谢然红, 肖立志 2009 地球物理学报 52 2410]
[35] Shi Y J, Liu T D 2009 Well Logging Technology 33 584 (in Chinese) [石玉江, 刘天定 2009 测井技术 33 584]
[36] Tan M J, Zou Y L, Liu B K, Yang X 2011 Well Logging Technology 35 130 (in Chinese) [谭茂金, 邹友龙, 刘兵开, 杨萱 2011 测井技术 35 130]
[37] Tan M J, Zou Y L 2012 Chinese Journal of Geophysics 55 683 (in Chinese) [谭茂金, 邹友龙 2012 地球物理学报 55 683]
[38] Hu F L, Zhou C C, Li C L, Xu H J, Zhou F M, Si Z W 2012 Petroleum Exploration & Development 39 552 (in Chinese) [胡法龙, 周灿灿, 李潮流, 徐红军, 周凤鸣, 司兆伟 2012 石油勘探与开发 39 552]
[39] Stejskal E O, Tanner J E 1965 The Journal of Chemical Physics 42 288
[40] Stejskal E O 1965 The Journal of Chemical Physics 43 3597
[41] Tanner J E 1970 The Journal of Chemical Physics 52 2523
[42] Karlicek J R F, Lowe I J 1980 Journal of Magnetic Resonance 37 75
[43] Cotts R M, Hoch M J R, Sun T, Markert J T 1989 Journal of Magnetic Resonance 83 252
[44] Latour L L, Li L, Sotak C H 1993 Journal of Magnetic Resonance 101 72
[45] Vandusschoten D 1995 Journal of Magnetic Resonance 112 237
[46] Mair R W, Cory D G, Peled S, Tseng C H, Patz S, Walsworth R L 1998 Journal of Magnetic Resonance 135 478
[47] Zhang X, Li C H, Ye C H, Liu M L 2001 Analytical Chemistry 73 3528
[48] Albina R M, Vladimir D S 2007 Journal of Magnetic Resonance 188 122
[49] Hunter M W, Jackson A N, Callaghan P T 2010 Journal of Magnetic Resonance 204 11
[50] Qu Y T, Jiang Z M, Shi J S, Zhu T T, Meng X H, Wang W M 2012 Chinese Journal of Magnetic Resonance 29 51 (in Chinese) [曲岩涛, 姜志敏, 史京生, 朱涛涛, 孟小海, 王为民 2012 波谱学杂志 29 51]
[51] Li X J, Nie S D, Wang Y J, Yang P Q 2013 Chinese Journal of Magnetic Resonance 30 322 (in Chinese) [李新军, 聂生东, 王远军, 杨培强 2013 波谱学杂志 30 322]
[52] Wang W M, Li P, Ye C H 2001 Science in China （Series A） 31 730 (in Chinese) [王为民, 李培, 叶朝辉 2001 中国科学 31 730]
[53] Venkataramanan L, Song Y Q, Hrlimann M D 2002 IEEE Transactions on Signal Processing 50 1017
[54] Wang Z D, Xiao L Z, Liu T Y 2003 Science in China （Series G） 33 323 (in Chinese) [王忠东, 肖立志, 刘堂宴 2003 中国科学 33 323]
[55] Jiang R Z, Yao Y P, Miao S Zhang C S 2005 Acta Petrolei Sinica 26 57 (in Chinese) [姜瑞忠, 姚彦平, 苗盛, 张春生 2005 石油学报 26 57]
[56] Pan K J, Chen H, Tan Y J 2008 Acta Physica Sinica 57 5956 (in Chinese) [潘克家, 陈华, 谭永基 2008 物理学报 57 5956]
[57] Lin F, Wang Z W, Li J Y, Zhang X A, Jiang Y L 2011 Applied Geophysics 8 233
[58] Ito K, Jin B T 2011 Inverse Problems 27 5005
[59] Gao Y, Xiao L Z, Xie Q M 2014 Journal of China University of Petroleum )Edition of Natural Science) (自然科学版) 38 50 (in Chinese) [高阳, 肖立志, 谢庆明 2014 中国石油大学学报 38 50]
[60] Sun B Q, Dunn K J 2005 Journal of Magnetic Resonance 172 152
[61] Tonning E, Polder D, Callaghan P T, Engelsen S B 2007 Journal of Magnetic Resonance 188 10
[62] Xie R H, Xiao L Z, Liu J J, Dunn K J 2009 Chinese Journal of Geophysics 52 2913 (in Chinese) [谢然红, 肖立志, 刘家军, 邓克俊 2009 地球物理学报 52 2913]
[63] Tan M J, Zou Y L, Zhou C C 2013 Computers & Geosciences 51 366
[64] Zhou X L, Nie S D, Wang Y J, Zhang Y L, Yang P Q 2013 Chinese Journal of Magnetic Resonance 30 541 (in Chinese) [周小龙, 聂生东, 王远军, 张英力, 杨培强 2013 波谱学杂志 30 541]
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