地面核磁共振找水正反演研究
|
摘要
随着我国经济的迅速发展以及人民生活水平的不断提高,工农业及生活用水需求量逐年增加,这给我国,特别是北方地区的大中城市水资源供需形势带来更大的压力,水资源已成为影响当地经济发展的一个主要制约因素。地下水资源在我国水资源中占有举足轻重的地位,由于其分布广、水质好、不易被污染、调蓄能力强、供水保证程度高,正被越来越广泛地开发利用。
核磁共振是近些年来发展很快的一个物理学分支,它最早使用于医学透视,近十几年来,被地球物理学家们所关注并应用于地球物理探测,地面核磁共振找水作为目前唯一能直接探测地下水的地球物理学方法,以其低廉的野外施工成本和良好的找水效果,被越来越广泛的应用于世界上无水或者缺水地区的地下水资源勘察。
目前,以Legchenko,A.,Yaramanci,u.,Weichman,P.B.等为代表的西方许多科学家正在积极开展研究和开发工作,并取得了相当的成果,核磁共振一维正、反演理论经过近几年的研究创新已经发展的较为成熟,反演理论也由当初的纯粹的利用核磁共振初始振幅反演含水率参数发展到结合并利用核磁共振信号相位同步反演地下电阻率信息的新阶段,一改过去必须借用其他电磁测深法预先勘察地下电阻率分布的思路。
国内目前这一领域的研究大多都集中在该方法野外试验有效性的讨论上,除了吉林大学翁爱华老师先后发表的数篇代表国内现阶段核磁共振理论最新动态的文章外,真正涉及正、反演等相关方法理论的研究并不多,在国内,正演相对反演较为成熟,核磁共振反演理论尚处在尝试阶段,距离我们期待的严格符合实际情况的核磁共振正、反演软件国产化目标还有一定距离。
本文分六个章节来总结硕士论文的研究工作。
第一章为绪论。论述了本论文选题的目的和意义;核磁共振正反问题的国内外研究现状和存在的问题;论文的研究目标、内容和解决的关键问题;研究过程中采取的方法和技术路线以及研究过程中的几点创新。
第二章简单介绍了核磁共振的基本原理。其中主要包括拉摩尔进动、在交变磁场作用下M的运动以及核磁共振找水方法野外测量参数和反演得到的水文地质参数介绍。
第三章详细推导、数值模拟并研究了核磁共振地下垂直激发场。其中主要包括:核磁共振地下激发场非齐次边值关系的形成;地面导线环在地下形成的电场、磁场、垂直激发场的公式推导;利用经典的Chave算法对含有贝塞儿函数的积分核进行积分运算;探讨了地磁倾角、磁偏角和地下介质导电性对垂直场强度和相位的影响。
第四章为核磁共振正演理论研究。详细推导和阐述了核磁共振正演理论、计算方法;数值模拟了核磁共振扳倒角、三维核函数、一维核函数,并研究探讨了其与激发脉冲矩、地下介质导电性、具体深度等参数之间的关系;分别利用常规方法和简约模型计算了核磁共振初始响应;探讨了影响核磁共振初始振幅的各因素。
第五章为核磁共振反演理论研究。在介质不导电的情况下,利用奇异值分解法对不同的含水层模型的理论观测数据和添加高斯随机噪声后的观测数据进行了反演研究;改进了模拟退火算法,把模拟退火算法和“区域思想”进行了有机的结合;利用改进的模拟退火算法对一般条件下的含水层模型理论观测数据和添加高斯随机噪声后的观测数据进行了反演试验,验证了改进的模拟退火算法反演地面核磁共振含水率分布的可行性。
第六章归纳全文,同时对该方法存在的问题、后续研究任务、未来发展及其将来的应用进行展望与评述。
核磁共振找水方法是一种年轻的全新的地球物理方法,研究开发的空间还很广阔,同时由于它属于较尖端且较前缘的具有一定学科交叉性的探测技术,整个学科发展还受到物理学、工程水文地质、岩石物理学、测控技术、软件技术等相关学科的影响,要想使核磁共振找水方法更好的为我们服务,就必须提高与之相关学科的建设,这也决定了它以后的发展道路将是漫长而曲折的,但笔者坚信,随着核磁共振找水研究工作的不断深入和发展,核磁共振找水相关理论将日臻完善,会越来越显示出强大的生命力,为当今地球科学的发展做出自己的贡献。
With the rapid development of China's economy and the continuous improvement of people's living standards, industrial and agricultural water demand has increased year by year, water supply and demand situation brings our country greater pressure, especially in the large and medium-sized cities in north of China, water resources becomes a major constraint of local economic development. Groundwater resources occupy a pivotal position in our country's water resources, for its wide distribution, good quality, be contaminated difficultly, and a high degree of assurance of water supply, it being used and developed more and more widely.
Nuclear magnetic resonance is developed very rapidly in recent years, it was earliest used in medical perspective, in the past 10 years, geophysicists pay attention to it, and then it was applied in geophysical exploration. As the only directly detecting groundwater geophysical method, for its low cost and good effect in detecting water, it was more and more widely used in groundwater resources detecting in the worlds that no water or water-deficient area's.
At present, Legchenko, A., Yaramanci, U., Weichan, P.B., as the representative of Hesperian scientists, are actively carrying out research and development work in this field, And they have achieved considerable results. one-dimensional nuclear magnetic resonance forward and inversion have been more and more mature after the past few years research and innovation. They developed the inverse method from inverse the initial water content purely using amplitude to extract underground resistivity join with nuclear magnetic resonance phase, it changed the idea that we must detect the underground resistivity before we use surface nuclear magnetic resonance prospect for water in the past.
Inland research in the field is main focus at the discussions of the validity of this method. Except Weng Aihua of jilin university has published several articles in the field, there is no expert that dedicating in theoretical study. Surface nuclear magnetic resonance inverse theory is still in the stage of attempt, there is a definite distance between present level and the goal that hold homemade forward and inverse software we look forward.
This paper consists mainly of six chapters.
Chapter one is the exordium. It includes: intention and significance of this course of study; current progress and problems in forward and inversion at home and abroad; research target, research content and key problems solved; technical ways and means; several originalities in the research process.
Chapter two simply introduced the basic principles of nuclear magnetic resonance. It mainly includes lamoer precession、the movement of M in the alternating magnetic field and measurement parameters and inverse parameters of surface nuclear magnetic resonance.
Chapter three deduced in detail and discussed the vertical excitation field. It mainly includes excitation electromagnetic field underground that produced by large loop source; using Chave algorithm in integrating function contains bessel function; discussed the influence of geomagnetic obliquity angle、geomagnetic declination angle、conductivity of the medium underground to vertical excitation field intensity and phase.
Chapter four is the surface nuclear magnetic resonance forward theoretical research. Presents in detail surface nuclear magnetic resonance forward theory、calculation methods; numerical simulated nuclear magnetic resonance toppled angle、3D kernel function、1D kernel function, discussed the relationship between them and excitation pulse, underground medium conductivity, depth and so on; we calculated the initial amplitude separately by conventional methods and simple model; discussed the factors that influenced nuclear magnetic resonance initial amplitude.
Chapter five is the surface nuclear magnetic resonance inversion theoretical research. In the circumstances that the media conductivity is bad, we separately made inversion research of theoretical observational data and the theoretical observation data added Gaussian random noise using singular value decomposition method; improved simulated annealing algorithm, combined Regional idea to simulated annealing algorithm; we separately made inverse experimentation of theoretical observational data and the theoretical observation data added Gaussian random noise using improved simulated annealing algorithm, validated the feasibility of inverse surface nuclear magnetic resonance aquifer parameters using improved simulated annealing algorithm.
Chapter six arrives at some conclusions. Meanwhile, the remaining problems of this method and researches to be done had been discussed, as well as prospects for future development and application.
Surface nuclear magnetic resonance is a young geophysical methods, research and development space is broad. Because it is a foreland with interdisciplinary intercross exploration technology, the development of this technology is influenced by physical Science、engineering hydrogeology、rock physics、measurement and control technology、software technology、and so on. In order to make surface nuclear magnetic resonance serving us better, we must improve the associated disciplines which also decides that its future development road will be long and tortuous. But we firmly believe that surface nuclear magnetic resonance theory is improving daily with the surface nuclear magnetic resonance study continuous development, and it will increasingly demonstrate its strong vitality and make its own contribution to the development of today's earth science.
核磁共振是近些年来发展很快的一个物理学分支,它最早使用于医学透视,近十几年来,被地球物理学家们所关注并应用于地球物理探测,地面核磁共振找水作为目前唯一能直接探测地下水的地球物理学方法,以其低廉的野外施工成本和良好的找水效果,被越来越广泛的应用于世界上无水或者缺水地区的地下水资源勘察。
目前,以Legchenko,A.,Yaramanci,u.,Weichman,P.B.等为代表的西方许多科学家正在积极开展研究和开发工作,并取得了相当的成果,核磁共振一维正、反演理论经过近几年的研究创新已经发展的较为成熟,反演理论也由当初的纯粹的利用核磁共振初始振幅反演含水率参数发展到结合并利用核磁共振信号相位同步反演地下电阻率信息的新阶段,一改过去必须借用其他电磁测深法预先勘察地下电阻率分布的思路。
国内目前这一领域的研究大多都集中在该方法野外试验有效性的讨论上,除了吉林大学翁爱华老师先后发表的数篇代表国内现阶段核磁共振理论最新动态的文章外,真正涉及正、反演等相关方法理论的研究并不多,在国内,正演相对反演较为成熟,核磁共振反演理论尚处在尝试阶段,距离我们期待的严格符合实际情况的核磁共振正、反演软件国产化目标还有一定距离。
本文分六个章节来总结硕士论文的研究工作。
第一章为绪论。论述了本论文选题的目的和意义;核磁共振正反问题的国内外研究现状和存在的问题;论文的研究目标、内容和解决的关键问题;研究过程中采取的方法和技术路线以及研究过程中的几点创新。
第二章简单介绍了核磁共振的基本原理。其中主要包括拉摩尔进动、在交变磁场作用下M的运动以及核磁共振找水方法野外测量参数和反演得到的水文地质参数介绍。
第三章详细推导、数值模拟并研究了核磁共振地下垂直激发场。其中主要包括:核磁共振地下激发场非齐次边值关系的形成;地面导线环在地下形成的电场、磁场、垂直激发场的公式推导;利用经典的Chave算法对含有贝塞儿函数的积分核进行积分运算;探讨了地磁倾角、磁偏角和地下介质导电性对垂直场强度和相位的影响。
第四章为核磁共振正演理论研究。详细推导和阐述了核磁共振正演理论、计算方法;数值模拟了核磁共振扳倒角、三维核函数、一维核函数,并研究探讨了其与激发脉冲矩、地下介质导电性、具体深度等参数之间的关系;分别利用常规方法和简约模型计算了核磁共振初始响应;探讨了影响核磁共振初始振幅的各因素。
第五章为核磁共振反演理论研究。在介质不导电的情况下,利用奇异值分解法对不同的含水层模型的理论观测数据和添加高斯随机噪声后的观测数据进行了反演研究;改进了模拟退火算法,把模拟退火算法和“区域思想”进行了有机的结合;利用改进的模拟退火算法对一般条件下的含水层模型理论观测数据和添加高斯随机噪声后的观测数据进行了反演试验,验证了改进的模拟退火算法反演地面核磁共振含水率分布的可行性。
第六章归纳全文,同时对该方法存在的问题、后续研究任务、未来发展及其将来的应用进行展望与评述。
核磁共振找水方法是一种年轻的全新的地球物理方法,研究开发的空间还很广阔,同时由于它属于较尖端且较前缘的具有一定学科交叉性的探测技术,整个学科发展还受到物理学、工程水文地质、岩石物理学、测控技术、软件技术等相关学科的影响,要想使核磁共振找水方法更好的为我们服务,就必须提高与之相关学科的建设,这也决定了它以后的发展道路将是漫长而曲折的,但笔者坚信,随着核磁共振找水研究工作的不断深入和发展,核磁共振找水相关理论将日臻完善,会越来越显示出强大的生命力,为当今地球科学的发展做出自己的贡献。
With the rapid development of China's economy and the continuous improvement of people's living standards, industrial and agricultural water demand has increased year by year, water supply and demand situation brings our country greater pressure, especially in the large and medium-sized cities in north of China, water resources becomes a major constraint of local economic development. Groundwater resources occupy a pivotal position in our country's water resources, for its wide distribution, good quality, be contaminated difficultly, and a high degree of assurance of water supply, it being used and developed more and more widely.
Nuclear magnetic resonance is developed very rapidly in recent years, it was earliest used in medical perspective, in the past 10 years, geophysicists pay attention to it, and then it was applied in geophysical exploration. As the only directly detecting groundwater geophysical method, for its low cost and good effect in detecting water, it was more and more widely used in groundwater resources detecting in the worlds that no water or water-deficient area's.
At present, Legchenko, A., Yaramanci, U., Weichan, P.B., as the representative of Hesperian scientists, are actively carrying out research and development work in this field, And they have achieved considerable results. one-dimensional nuclear magnetic resonance forward and inversion have been more and more mature after the past few years research and innovation. They developed the inverse method from inverse the initial water content purely using amplitude to extract underground resistivity join with nuclear magnetic resonance phase, it changed the idea that we must detect the underground resistivity before we use surface nuclear magnetic resonance prospect for water in the past.
Inland research in the field is main focus at the discussions of the validity of this method. Except Weng Aihua of jilin university has published several articles in the field, there is no expert that dedicating in theoretical study. Surface nuclear magnetic resonance inverse theory is still in the stage of attempt, there is a definite distance between present level and the goal that hold homemade forward and inverse software we look forward.
This paper consists mainly of six chapters.
Chapter one is the exordium. It includes: intention and significance of this course of study; current progress and problems in forward and inversion at home and abroad; research target, research content and key problems solved; technical ways and means; several originalities in the research process.
Chapter two simply introduced the basic principles of nuclear magnetic resonance. It mainly includes lamoer precession、the movement of M in the alternating magnetic field and measurement parameters and inverse parameters of surface nuclear magnetic resonance.
Chapter three deduced in detail and discussed the vertical excitation field. It mainly includes excitation electromagnetic field underground that produced by large loop source; using Chave algorithm in integrating function contains bessel function; discussed the influence of geomagnetic obliquity angle、geomagnetic declination angle、conductivity of the medium underground to vertical excitation field intensity and phase.
Chapter four is the surface nuclear magnetic resonance forward theoretical research. Presents in detail surface nuclear magnetic resonance forward theory、calculation methods; numerical simulated nuclear magnetic resonance toppled angle、3D kernel function、1D kernel function, discussed the relationship between them and excitation pulse, underground medium conductivity, depth and so on; we calculated the initial amplitude separately by conventional methods and simple model; discussed the factors that influenced nuclear magnetic resonance initial amplitude.
Chapter five is the surface nuclear magnetic resonance inversion theoretical research. In the circumstances that the media conductivity is bad, we separately made inversion research of theoretical observational data and the theoretical observation data added Gaussian random noise using singular value decomposition method; improved simulated annealing algorithm, combined Regional idea to simulated annealing algorithm; we separately made inverse experimentation of theoretical observational data and the theoretical observation data added Gaussian random noise using improved simulated annealing algorithm, validated the feasibility of inverse surface nuclear magnetic resonance aquifer parameters using improved simulated annealing algorithm.
Chapter six arrives at some conclusions. Meanwhile, the remaining problems of this method and researches to be done had been discussed, as well as prospects for future development and application.
Surface nuclear magnetic resonance is a young geophysical methods, research and development space is broad. Because it is a foreland with interdisciplinary intercross exploration technology, the development of this technology is influenced by physical Science、engineering hydrogeology、rock physics、measurement and control technology、software technology、and so on. In order to make surface nuclear magnetic resonance serving us better, we must improve the associated disciplines which also decides that its future development road will be long and tortuous. But we firmly believe that surface nuclear magnetic resonance theory is improving daily with the surface nuclear magnetic resonance study continuous development, and it will increasingly demonstrate its strong vitality and make its own contribution to the development of today's earth science.
引文
[1]潘玉玲,张昌达等.地面核磁共振找水理论和方法.中国地质大学出版社,2000:45-47
[2]李振宇,李俊丽等.地面核磁共振找水方法综述.勘探地球物理进展,2002(25):55-58
[3]冯蕴深.磁共振原理,高等教育出版社,1992:20-35
[4]张荣,胡祥云,杨迪琨等.地面核磁共振技术述评.地球物理学进展,2006(21):284-289
[5]Legchenko,A.,Baltassat,J.M.,Beauce,A.,et al.Nuclear magnetic resonance as a geophysical tool for hydrogeologists.Journal of Applied Geophysics 2002(50):21-46
[6]Yaramanci,U.,Hertrich,M..Magnetic resonance sounding(MRS)for geophysical groundwater investigation.Proceedings of the 2~(nd)international conference on Environmental and Engineering Geophysics,2006,228-234
[7]Legchenko,A.V.,Shushakov,O.A..Inversion of surface NMR data.Geophysics,1998,16:75-84
[8]Weichman,P.B.,Lun,D.R.,et al.Study of surface nuclear magnetic resonce inverse problems.Journal of applied Geophysics,2002(50),129-147
[9]Mohnke,O.,Yaramanci,U..Smooth and block inversion of surface NMR amplitudes and decay times using simulated annealing.Journal of applied Geophysics,2002(50),163-177
[10]Guillen,A.,Legchenko,A..Inversion of surface nuclear magnetic resonance data by an adapted Monte Carlo method applied to water resource characterization.Journal of applied Geophysics,2002(50),193-205
[11]Braun,M.,Yaramanci,U..Study on complex inversion of magnetic resonance sounding signals.Near Surface Geophysics,2005(3):155-163
[12]Braun,M.,Yaramanci,U..Inversions of Surface-NMR signals using complex kernels.Proceedings of the 9~(th)EEGS conference,Prague/Czech Republic.2003
[13]Braun,M.,Yaramanci,U..Inversion of resistivity in Magnetic Resonance Sounding.Journal of applied Geophysics,2008(X),1-14
[14]Hertrich,M.,Yaramanci,U..Joint inversion of Surface Nuclear Magnetic Resonance and Vertical Electrical Sounding.Journal of applied Geophysics,2002(50),179-191
[15]张文权,翁爱华.地面核磁共振正则化反演方法研究.吉林大学学报,2007(37):809-813
[16]翁爱华,王雪秋,刘国兴等.导电性影响的地面核磁共振反演.地球物理学报,2007(50):890-896
[17]Warsa,W.,Mohnke,O.,Yaramanci,U..3-D modeling and assessment of 2-D inversion of surface NMR.MRS-2~(ND)international workshop,2003:19-21
[18]王鹏.均匀地电条件下地面核磁共振三维正演.中国地质大学(武汉)硕士论文,2007
[19]Chave,A.D..Numerical integration of related Hankel transforms by quadrature and continued fraction expansion.Geophysics,1983(48):1671-1685
[20]华军,蒋延生,汪文秉.双重贝塞尔函数积分的数值计算.煤田地质与勘探.2001(29):58-61
[21]李振宇,唐辉明,潘玉玲.地面核磁共振方法在地质工程中的应用.中国地质大学出版社,2006:26-30
[22]曹昌祺.地面导线环的辐射电阻.地球物理学报,1978(21):77-87
[23]朴化荣.电磁测深法原理.地质出版社,1990:30-45
[24]汤井田,何继善.可控源音频大地电磁法及其应用.中南大学出版社.2005:25-35
[25]Anderson,W.L..Computation of Green's tensor integrals for three-dimensional electromagnetic problems using fast hankel transforms[J].Geophysics,1984(49):1754-1759
[26]Anderson,W.L..A hybrid fast Hankel transformation algorithm for electro-magnetic modeling.Geophysics,1989(54):263-266
[27]Johansen,H.K..Fast Hankel transform[J].Geophys Prosp,1979(27):877-901
[28]莫平华.一阶贝塞尔函数广义积分的数值计算.数学理论与应用,2007(27):65-67
[29]熊彬.大回线瞬变电磁2.5维正演算法及其资料解释方法中若干关键技术研究.中国地质大学(武汉)博士论文,2004
[30]Anderson,W.L..Computer Program Numerical integration of related Hankel transforms of orders 0 and 1 by adaptive digital filtering.Geophysics,1979(44):1287-1305
[31]翁爱华,王雪秋.利用数值积分提高一维模型电偶源电磁测深响应计算精度.西北地震学报,2003(25):193-197
[32]张辉,李桐林,董瑞霞,徐凯军.利用高斯求积和连分式展开计算电磁张量格林函数积分.地球物理学进展,2005(20):667-670
[33]皮新明.一类积分方程的近似解.武汉水利电力大学学报,1997(30):82-85
[34]卢健.瞬变电磁法矩形线框一维正演及电磁信号去噪的研究[J].大连理工大学硕士学位论文,2004.
[35]翁爱华,李舟波,王雪秋.地表大回线源在任意层状介质中产生磁场的计算.物探化探计算技术,2000(22):245-249
[36]刘继东,方文藻.用线性数字滤波法计算大回线源在地下形成的瞬变电磁场,物探化探计算技术,1996(18):231-237
[37]Legchenko,A.,Valla,P..A review of the basic principles for proton magnetic resonance sounding measurements.Journal of Applied Geophysics,2002(50):3-19
[38]Weichman,P.B.,Lavely,E.M.,Ritzwoller,M.H..Surface nuclear magnetic resonance imaging of large systems.Physics Review Letters,1999,82:4102-4105.
[39]Weichman,P.B.,Lavely,E.M.,Ritzwoller,M.H.,Theory of surface nuclear magnetic resonance with applications to geophysical imaging problems.Physics Review letters,2000,62:1290-1312
[40]翁爱华,李舟波,王雪秋.地表大回线源在任意层状介质中产生磁场的计算.物探化探计算技术,2000(22):245-249
[41]翁爱华,王雪秋.高精度地面核磁共振数据正演计算.吉林大学学报,2007(37):620-623
[42]Yaramanci,U.,Lange,G.,Knodel,K..Surface NMR within a geophysical study of an aquifer at Haldensleben(Germany).Geophysical Prospecting,1999(47):923-943
[43]Schirov,M.D.,Rojkowski,A.D..On the accuracy of parameters determination from SNMR measurements.Journal of applied Geophysics,2002(50),207-216
[44]Valla,P.,Legchenko,A..One-dimensional modelling for proton magnetic resonance sounding measurements over an electrically conductive medium.Journal of applied Geophysics,2002(50),217-229
[45]Muller-petke,M.,Yaramanci,U..Resolution studies for Magnetic Resonance Sounding using the singular value decomposition.Journal of applied Geophysics 2008(X),1-11
[46]Trushkin,D.V.,Shushakov,O.A.,Legchenko,A.V..Surface NMR applied to an electroconductive medium.Geophysical Prospecting,1995(43):623-633
[47]黄小为,吴传生,朱华平.基于奇异值分解建立的一种新的正则化方法.数学物理学报,2005(25A):331-336
[48]徐张明,沈荣瀛,华宏星.奇异值分解和正则化方法.上海交通大学学报,2002(36):834-838
[49]梁栋,韦穗,吴福朝,杨尚俊.一种基于奇异值分解的分层重构算法.中国科学技术大学学报,2001(31):571-576
[50]张文飞,李晓江.多参数反演的分步正则化法.石油地球物理勘探,1997(32):338-344
[51]师学明,王家映.一维层状介质大地电磁模拟退火反演.地球科学,1998(23):542-545
[52]翁爱华,李舟波,王雪秋.层状导电介质中地面核磁共振响应特征理论研究.地球物理学报,2004(47):156-163
[53]Tsallis,C..Possible generalization of Bolizmann-Gibbs statistics.Journal of Statistical Physics,1988,52:479-487
[54]Kirkpatrick,S.,Gelatt,C.D.,Yecchi,M.p..Optimization by simulated annealing.Science,1983,220:671-680
[55]Basu,A.,Frazer,L..Rapid determination of the critical temperature in simulated annealing inversion.Science,1990,249:1409-1412
[56]张霖斌,姚振兴,纪晨,张中杰.快速模拟退火算法及应用.石油地球物理勘探,1997,32:654-659
[57]Ingber,I..Very fast simulated re-annealing.Math compute Modeling,1989,12:967-973
[58]顾汉明,江涛,王家映.改进快速模拟退火方法进行AVO岩性参数反演.地球科学,1999,24:418-421
[59]姜彦南,阮帅,王绪本,高永才.核磁共振地下水勘查的模拟退火反演.物探化探计算技术,2005,27:124-126
[60]Legchenko,A.,Valla,P..Processing of surface proton magnetic resonance signals using non-linear fitting.Journal of applied Geophysics,1998(39),77-83
[2]李振宇,李俊丽等.地面核磁共振找水方法综述.勘探地球物理进展,2002(25):55-58
[3]冯蕴深.磁共振原理,高等教育出版社,1992:20-35
[4]张荣,胡祥云,杨迪琨等.地面核磁共振技术述评.地球物理学进展,2006(21):284-289
[5]Legchenko,A.,Baltassat,J.M.,Beauce,A.,et al.Nuclear magnetic resonance as a geophysical tool for hydrogeologists.Journal of Applied Geophysics 2002(50):21-46
[6]Yaramanci,U.,Hertrich,M..Magnetic resonance sounding(MRS)for geophysical groundwater investigation.Proceedings of the 2~(nd)international conference on Environmental and Engineering Geophysics,2006,228-234
[7]Legchenko,A.V.,Shushakov,O.A..Inversion of surface NMR data.Geophysics,1998,16:75-84
[8]Weichman,P.B.,Lun,D.R.,et al.Study of surface nuclear magnetic resonce inverse problems.Journal of applied Geophysics,2002(50),129-147
[9]Mohnke,O.,Yaramanci,U..Smooth and block inversion of surface NMR amplitudes and decay times using simulated annealing.Journal of applied Geophysics,2002(50),163-177
[10]Guillen,A.,Legchenko,A..Inversion of surface nuclear magnetic resonance data by an adapted Monte Carlo method applied to water resource characterization.Journal of applied Geophysics,2002(50),193-205
[11]Braun,M.,Yaramanci,U..Study on complex inversion of magnetic resonance sounding signals.Near Surface Geophysics,2005(3):155-163
[12]Braun,M.,Yaramanci,U..Inversions of Surface-NMR signals using complex kernels.Proceedings of the 9~(th)EEGS conference,Prague/Czech Republic.2003
[13]Braun,M.,Yaramanci,U..Inversion of resistivity in Magnetic Resonance Sounding.Journal of applied Geophysics,2008(X),1-14
[14]Hertrich,M.,Yaramanci,U..Joint inversion of Surface Nuclear Magnetic Resonance and Vertical Electrical Sounding.Journal of applied Geophysics,2002(50),179-191
[15]张文权,翁爱华.地面核磁共振正则化反演方法研究.吉林大学学报,2007(37):809-813
[16]翁爱华,王雪秋,刘国兴等.导电性影响的地面核磁共振反演.地球物理学报,2007(50):890-896
[17]Warsa,W.,Mohnke,O.,Yaramanci,U..3-D modeling and assessment of 2-D inversion of surface NMR.MRS-2~(ND)international workshop,2003:19-21
[18]王鹏.均匀地电条件下地面核磁共振三维正演.中国地质大学(武汉)硕士论文,2007
[19]Chave,A.D..Numerical integration of related Hankel transforms by quadrature and continued fraction expansion.Geophysics,1983(48):1671-1685
[20]华军,蒋延生,汪文秉.双重贝塞尔函数积分的数值计算.煤田地质与勘探.2001(29):58-61
[21]李振宇,唐辉明,潘玉玲.地面核磁共振方法在地质工程中的应用.中国地质大学出版社,2006:26-30
[22]曹昌祺.地面导线环的辐射电阻.地球物理学报,1978(21):77-87
[23]朴化荣.电磁测深法原理.地质出版社,1990:30-45
[24]汤井田,何继善.可控源音频大地电磁法及其应用.中南大学出版社.2005:25-35
[25]Anderson,W.L..Computation of Green's tensor integrals for three-dimensional electromagnetic problems using fast hankel transforms[J].Geophysics,1984(49):1754-1759
[26]Anderson,W.L..A hybrid fast Hankel transformation algorithm for electro-magnetic modeling.Geophysics,1989(54):263-266
[27]Johansen,H.K..Fast Hankel transform[J].Geophys Prosp,1979(27):877-901
[28]莫平华.一阶贝塞尔函数广义积分的数值计算.数学理论与应用,2007(27):65-67
[29]熊彬.大回线瞬变电磁2.5维正演算法及其资料解释方法中若干关键技术研究.中国地质大学(武汉)博士论文,2004
[30]Anderson,W.L..Computer Program Numerical integration of related Hankel transforms of orders 0 and 1 by adaptive digital filtering.Geophysics,1979(44):1287-1305
[31]翁爱华,王雪秋.利用数值积分提高一维模型电偶源电磁测深响应计算精度.西北地震学报,2003(25):193-197
[32]张辉,李桐林,董瑞霞,徐凯军.利用高斯求积和连分式展开计算电磁张量格林函数积分.地球物理学进展,2005(20):667-670
[33]皮新明.一类积分方程的近似解.武汉水利电力大学学报,1997(30):82-85
[34]卢健.瞬变电磁法矩形线框一维正演及电磁信号去噪的研究[J].大连理工大学硕士学位论文,2004.
[35]翁爱华,李舟波,王雪秋.地表大回线源在任意层状介质中产生磁场的计算.物探化探计算技术,2000(22):245-249
[36]刘继东,方文藻.用线性数字滤波法计算大回线源在地下形成的瞬变电磁场,物探化探计算技术,1996(18):231-237
[37]Legchenko,A.,Valla,P..A review of the basic principles for proton magnetic resonance sounding measurements.Journal of Applied Geophysics,2002(50):3-19
[38]Weichman,P.B.,Lavely,E.M.,Ritzwoller,M.H..Surface nuclear magnetic resonance imaging of large systems.Physics Review Letters,1999,82:4102-4105.
[39]Weichman,P.B.,Lavely,E.M.,Ritzwoller,M.H.,Theory of surface nuclear magnetic resonance with applications to geophysical imaging problems.Physics Review letters,2000,62:1290-1312
[40]翁爱华,李舟波,王雪秋.地表大回线源在任意层状介质中产生磁场的计算.物探化探计算技术,2000(22):245-249
[41]翁爱华,王雪秋.高精度地面核磁共振数据正演计算.吉林大学学报,2007(37):620-623
[42]Yaramanci,U.,Lange,G.,Knodel,K..Surface NMR within a geophysical study of an aquifer at Haldensleben(Germany).Geophysical Prospecting,1999(47):923-943
[43]Schirov,M.D.,Rojkowski,A.D..On the accuracy of parameters determination from SNMR measurements.Journal of applied Geophysics,2002(50),207-216
[44]Valla,P.,Legchenko,A..One-dimensional modelling for proton magnetic resonance sounding measurements over an electrically conductive medium.Journal of applied Geophysics,2002(50),217-229
[45]Muller-petke,M.,Yaramanci,U..Resolution studies for Magnetic Resonance Sounding using the singular value decomposition.Journal of applied Geophysics 2008(X),1-11
[46]Trushkin,D.V.,Shushakov,O.A.,Legchenko,A.V..Surface NMR applied to an electroconductive medium.Geophysical Prospecting,1995(43):623-633
[47]黄小为,吴传生,朱华平.基于奇异值分解建立的一种新的正则化方法.数学物理学报,2005(25A):331-336
[48]徐张明,沈荣瀛,华宏星.奇异值分解和正则化方法.上海交通大学学报,2002(36):834-838
[49]梁栋,韦穗,吴福朝,杨尚俊.一种基于奇异值分解的分层重构算法.中国科学技术大学学报,2001(31):571-576
[50]张文飞,李晓江.多参数反演的分步正则化法.石油地球物理勘探,1997(32):338-344
[51]师学明,王家映.一维层状介质大地电磁模拟退火反演.地球科学,1998(23):542-545
[52]翁爱华,李舟波,王雪秋.层状导电介质中地面核磁共振响应特征理论研究.地球物理学报,2004(47):156-163
[53]Tsallis,C..Possible generalization of Bolizmann-Gibbs statistics.Journal of Statistical Physics,1988,52:479-487
[54]Kirkpatrick,S.,Gelatt,C.D.,Yecchi,M.p..Optimization by simulated annealing.Science,1983,220:671-680
[55]Basu,A.,Frazer,L..Rapid determination of the critical temperature in simulated annealing inversion.Science,1990,249:1409-1412
[56]张霖斌,姚振兴,纪晨,张中杰.快速模拟退火算法及应用.石油地球物理勘探,1997,32:654-659
[57]Ingber,I..Very fast simulated re-annealing.Math compute Modeling,1989,12:967-973
[58]顾汉明,江涛,王家映.改进快速模拟退火方法进行AVO岩性参数反演.地球科学,1999,24:418-421
[59]姜彦南,阮帅,王绪本,高永才.核磁共振地下水勘查的模拟退火反演.物探化探计算技术,2005,27:124-126
[60]Legchenko,A.,Valla,P..Processing of surface proton magnetic resonance signals using non-linear fitting.Journal of applied Geophysics,1998(39),77-83