中梯装置双频激电法电阻率数据地形校正研究
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摘要
双频激电法属于频率域激电法,是一种非常有效的地球物理勘探方法,它具有抗干扰能力强、仪器轻便、稳定、观测精度高等优点。该方法能够在地形复杂、环境恶劣的自然条件下开展工作,并在我国的矿产资源勘查中得到了越来越广泛的应用。
长期以来,起伏地形下的地电异常是电法勘探的一个难题,因为这个问题不仅本身复杂,而且目前的科技发展水平也达不到完全解决的地步。近年来经过地球物理专家们的努力,起伏地形下的二维电阻率正演及反演成像问题已经基本解决。本文主要针地形起伏地形下,双频激电中梯装置电阻率数据的地形改正进行研究,希望通过对双频激电采集到的电阻率数据进行地形改正,使改正后的电阻率数据与幅频率Fs一样,也成为判断地下异常的依据。
本文研究了双频激电法电阻率数据点电源边界单元解法以及二、三维起伏地形的地形校正,采用边界单元法在二、三维地形条件下对边界进行剖分,并在前人的工作基础上进行了更加完善的公式推导。编制了二维地形条件下视电阻率地形校正的程序,建立了纯地形模型并对各种不同二维均匀起伏地形进行了研究,总结了规律,建立了非均匀条件下二维起伏地形模型,对低阻直立板状体与高阻水平板状体模型在各种不同地形下的影响进行了分析,验证了本文算法的正确性以及程序的可靠性,为二、三维地形条件下的反演成像研究奠定了基础。
Dual frequency induced polarization method belongs frequency domain IP method, and it is a very effective geophysical method, it has most advantages, such as anti-interference ability, light, stable and high-precision observation, so it can be used in the condition of complex terrain and bad natural condition, and this method has been used more and more widely in mineral exploration.
The research of geoelectric anomaly on the undulate topography has been a difficult problem in the field of electrical prospecting for a long time, it is not only complicated itself, but also the level of technology development cannot be achieved. In recent years, through the efforts of geophysical experts, the problem of 2-D on undulate topography resistivity forward and inverse imaging has been solved. In this paper, we mainly research the terrain correction of resistivity data about dual frequency induced polarization method on undulate topography, and made it becomes another evidence to judge underground media.
This paper researched the boundary element method for resistivity modeling with a point current source of dual frequency induced polarization method and terrain correction in 2D/3D undulate topography, we used BEM to partite the boundary, and carry out a more comprehensive formula derivation on the basis of previous, a suit of 2-D forward algorithm codes is also accomplished, we establish a pure model and research different 2D undulate topography models, and established non-uniform 2D undulating terrain models, analysis low vertical tabular body and high level plate body models, it verified the correct of the algorithm, as well as the reliability of the procedure. These research achievements of DC resistivity has established foundation for further studying2D or 3D resistivity forward modeling and inversion imaging on undulate topography.
长期以来,起伏地形下的地电异常是电法勘探的一个难题,因为这个问题不仅本身复杂,而且目前的科技发展水平也达不到完全解决的地步。近年来经过地球物理专家们的努力,起伏地形下的二维电阻率正演及反演成像问题已经基本解决。本文主要针地形起伏地形下,双频激电中梯装置电阻率数据的地形改正进行研究,希望通过对双频激电采集到的电阻率数据进行地形改正,使改正后的电阻率数据与幅频率Fs一样,也成为判断地下异常的依据。
本文研究了双频激电法电阻率数据点电源边界单元解法以及二、三维起伏地形的地形校正,采用边界单元法在二、三维地形条件下对边界进行剖分,并在前人的工作基础上进行了更加完善的公式推导。编制了二维地形条件下视电阻率地形校正的程序,建立了纯地形模型并对各种不同二维均匀起伏地形进行了研究,总结了规律,建立了非均匀条件下二维起伏地形模型,对低阻直立板状体与高阻水平板状体模型在各种不同地形下的影响进行了分析,验证了本文算法的正确性以及程序的可靠性,为二、三维地形条件下的反演成像研究奠定了基础。
Dual frequency induced polarization method belongs frequency domain IP method, and it is a very effective geophysical method, it has most advantages, such as anti-interference ability, light, stable and high-precision observation, so it can be used in the condition of complex terrain and bad natural condition, and this method has been used more and more widely in mineral exploration.
The research of geoelectric anomaly on the undulate topography has been a difficult problem in the field of electrical prospecting for a long time, it is not only complicated itself, but also the level of technology development cannot be achieved. In recent years, through the efforts of geophysical experts, the problem of 2-D on undulate topography resistivity forward and inverse imaging has been solved. In this paper, we mainly research the terrain correction of resistivity data about dual frequency induced polarization method on undulate topography, and made it becomes another evidence to judge underground media.
This paper researched the boundary element method for resistivity modeling with a point current source of dual frequency induced polarization method and terrain correction in 2D/3D undulate topography, we used BEM to partite the boundary, and carry out a more comprehensive formula derivation on the basis of previous, a suit of 2-D forward algorithm codes is also accomplished, we establish a pure model and research different 2D undulate topography models, and established non-uniform 2D undulating terrain models, analysis low vertical tabular body and high level plate body models, it verified the correct of the algorithm, as well as the reliability of the procedure. These research achievements of DC resistivity has established foundation for further studying2D or 3D resistivity forward modeling and inversion imaging on undulate topography.
引文
[1]何继善。双频激电法[M]。北京：高等教育出版社,2005；
[2]柳建新,何继善等双频激电法及其在示范区的应用。中国地质。Vol.28(3),2001：32-39；
[3]傅良魁。激发极化法[M].北京：地质出版社,1982；
[4]强建科,何继善。椭球体上双频激电法的正演与反演算法。中南大学学报(自然科学版)Vol.38(6),2007,1199-1205；
[5]罗延钟,张桂青.频率域激电法原理[M]。北京：地质出版社1988；
[6]Wait. J. R. Overvoltage research and geophysical applications. New York: Pergammon Press,1959;
[7]Alfano L. Introduction to the interpretation of resistivity measurements for complicated structural condition [J]. Geophysical Prospecting,1959,7(3):311-366.
[8]Vozoff K. Numerical resistivity interpretation. General in homogeneit [J]. Geophysics,1960,25(6):1184-1194
[9]Kelley G V, and Frischknecht F C. Electrical methods in Geophysical Prospecting [M].Pergamum Press,1966
[10]Dey and Morrison H F. Electromagnetic response of two-dimensional in homogeneities in a dissipative half-space for Turam interpretation prospecting [J]. Geophysical Prospecting,1973,21(2):340-365
[11]Dieter K., et al, IP and resistivity type curves for three-dimensional bodies. Geophysics,1969, Vol.34, No.4.
[12]Hohmann G W. Three-dimensional induced polarization and electromagnetic modeling [J]. Geophysics,1975,40(2):309-324.
[13]Lajoie J J and West G F. Three electromagnetic response of a conductive in homogeneity in a layered earth [J]. Geophysics,1976, 46(6):1133-1156.
[14]Okabe M. Boundary element method for the arbitrary in homogeneitiesin resistivity curves[J]. Geophysical Prospecting,1981,29(1):39-59.
[15]Das. U. C, and Verma S. K. Eletromagnetic response of an arbitrary shaped three-dimensional conductor in a layered earth-numerical results [J]. Geophys. J. R. astr. Soc.1982,68,55-66.
[16]周熙襄,钟本善,严忠琼,江玉乐。电法勘探数值模拟的若干结果,地球物理学报,1983,26(S),479-491；
[17]周熙襄,钟本善,江东玉。点源二维电阻率法有限差分正演计算,物化探电子计算技术,1983.5(3)；
[18]罗延钟,张桂青,电子计算机在电法勘探中的应用,武汉地质学院出版社,1987：
[19]Wild A J, Singh S C. Some unintended features of elastic finite-difference models [J]. Geophysical Prospecting,1998,46:79-101.
[20]Lamontagne, Y. and West, G. F., EM response of a rectangular thin plate. Geophysics,1971,36, p26;
[21]Swift, C. M. Jr., Theoretical magnetotelluric and Turam response from two-dimension in homogeneities. Geophysics,1971,36, p1
[22]Jepsen, A. F., Numerical modeling in resistivity prospect ing [J]. Ph.D. these, University of California. Berkeley.1975;
[23]Mufti, J. R., Finite-difference resistivity modeling for arbitrarily shaped two-dimensional structures. Geophysics,1976,41, p62;
[24]Dey, A., Morrison, H. F., Resistivity modeling for arbitrarily shaped three-dimensional structures. Geophysics,1979,44, p753;
[25]Scriba, H., Computation of the electrical potential in three-dimensional structures. Geophysical Prospecting,44, p1;
[26]Zhdanow, M. S. etal, The construction of effective method for electromagnetic modeling. Geophys. J. R. astr. SOC,1982, p68;
[27]Gldman, M. M., Stoyert, C. H., Finite-difference calculations of the transient field of an axially symmetric earth for vertical magnetic dipole excitation. Geophysics,1983,48, p953;
[28]Leppin, M., Electromagnetic modeling of 3-D sources over 2-D in homo-genetics in the time domain:Geophysics,1992,57,994-1003;
[29]Spitzer, K. and Wurmst, B., Speed and Accuracy in 3D resistivity modeling. Geophysics,2001,66;
[30]Spitzer, K. A 3D finite-difference algorithm for DC resistivity modeling using conjugate gradient methods[J]. Geophys. J. Int,1995, 123:903-914.
[31]周熙襄,钟本善,江东玉,点源二维电阻率法有限差分正演计算,物化探电子计算技术,1983,5(3)：1-9
[32]罗延钟,万乐。二维地形不平条件下外电场的有限差分模拟,物化探计算技术,1984,6(4)；
[33]刘树才,周圣武。二维电法数值模拟中的网格剖分方法,物化探计算技术,1995.17；
[34]刘正栋,关洪军,聂永平等。稳定点电流源场三维有限差分正演模拟,解放军理大学学报,2000,1(3)；
[35]吴小平,起伏地形条件下电阻率/激发极化三维正、反演。中国科技大学项目设计,2001；
[36]徐世浙,地球物理中的有限单元法。北京：科学出版社,1994；
[37]杨华,李金铭.起伏地形对近矿围岩充电法影响规律的数值模拟研究。物探与化探,23(3)；
[38]刘海飞,起伏地形电导率连续变化的三维激电数据有限元数值模拟,Manuscript,2008；
[39]徐世浙,地球物理中的边界单元法。北京：科学出版社,1995；
[40]Fox, R. C., Hohmann, G. W., Killpack, T. J., and rijo, L., Topographic effects in resistivity and induced-polarization surveys. Geophysics, 1980,45,p57-93;
[41]Okabe, M., Boundary element method for the arbitrary inhomogeneities in resistivity curves. Geophysical Prospecting,1981,29,39-59;
[42]Nardini, D., and Brebbia, C. A., Transient dynamic analysis by the boundary element method.
[43]Boundary Elements, springer, Verlag,Berlin, Heidelberg, New York;
[44]Xu Shi-zhe and Zhao Sheng-kai, Two-dimensional magnetotelluric modeling by the boundary element method. Journal of Geomagnetism and Geoelectricity,1987,39(11),677-698;
[45]徐世浙,王庆乙等,用边界单元法模拟二维地形对大地电磁场的影响。地球物理学报,1992 35(3),380-388；
[46]Xu Shi-zhe, The effect of two-dimensional terrain with point current source on resistivity surveys. Geophysical research letters,1993,20(10),891-894;
[47]李予国,徐世浙,垂直断面附近二维不均匀体点源电场的边界单元法,物探化探计算技术,1996,18(2)147-151：
[48]黄兰珍,田宪谟等.电阻率法地形改正及其在工程地质勘查中的应用。物探化探计算技术,1997,3；
[49]孙建国,复杂地表条件下地球物理场数值模拟方法评述[J]。世界地质,2007,26(3)：345-361
[50]Dohr G. Applied geophysics [M].Halsted Press, New York,1981.
[51]特尔福德WM,吉尔达特LP,谢里夫RE, etal.应用地球物理[M]。吴荣祥译。北京：地质出版社,1982.
[52]Sheriff RE. Encyclopedic dictionary of exploration geophysics [M]. 2"d Edition. Tulsa:SEG,1984, p233
[53]Telford WM, Geldaed L P, Sheriff RE. Applied geophysics[M]. Cambridge: Cambridge University press,1990
[54]Tessmer E, Kosloff D, Behle A. Elastic wave propagation simulation in the presence of surface topography[J]. Geophysics J Int,1992,108: 621-632.
[55]Hestholm S, Ruud B.3-D finite-difference elastic wave modeling including surface topography[J]. Geophysics,63(2):613-622.
[56]Hestholm S. Elastic wave modeling with free surface stability of long simulation [J]. Geophysics,2003,68(1):314-321.
[57]Tessmer E, Kosloff D.3-D elastic modeling with surface topography by a Chebychev spectral method[J]. Geophysical,1994,59(3):464-473.
[58]Hesthlom S, Ruud B.2D finite-difference elastic wave modeling including surface topography [J]. Geophysical Prospecting,1994, 42,371-390.
[59]Ruud B, Hestholm S.2D surface topography boundary conditions in seismic wave model ing [J]. Geophysical Prospecting,2001,49,445-460.
[60]肖怀宇.带地形的瞬变电磁法三维数值模拟[D].北京：中国地质大学,2006.
[61]陈伯舫,侯作中,范国华.有限差分法计算三维地形影响的电磁感应[J]。地震学报,1998,20(5)：541-544.
[62]王秀明,张海澜.用于具有不规则起伏自由表面的介质中弹性波模拟的有限差分算法[J]。中国科学G辑,2004,34(5)：481-493.
[63]介玉新,揭冠周,李广信.用适体坐标变换方法求解渗流[J]。岩土工程学报,2004,26(1)：52-56
[64]魏文礼,王玲玲等.曲线网格生成技术研究[J]。河海大学学报,1998,26(3)：93-96.
[65]赵景霞,张叔伦等.曲网络伪谱法二维声波模拟[J]。石油物探,2003,42(1)：1-5.
[66]刘鲁波,陈晓非,王彦宾.切比雪夫伪谱法模拟地震波场[J]。西北地震学报,2007,29(1)：18-25.
[67]揭冠周,介玉新,李广信.模拟自由面渗流的适体坐标变换方法[J]。清华大学学报(自然科学版),2003,43(2)：273-284.
[68]Fox R. C, Hohmann G W, Killpack T J, and Rijo L. Topographic effects in resistivity and induced-polarization surveys [J]. Geophysics,1980, 45,57-93.
[69]Chouteau,M. and Bouchard, K., Two-dimensional terrain correction in magneto telluric surveys. Geophysics,1988,53,854-862;
[70]Xu shi-zhe, Gao Zucheng, and Zhao Sheng-kai,, An intergral formulation for three-dimensional terrain modeling for resistivity surveys. Geophysics,1988,53,546-552;
[71]Xu S-Z. The Boundary element method for solving 2.5-D electrical field under relief terrain [J]. Guilin College of Geology (in Chinese), 1984,4:119-133;
[72]Lun-Tao Tong, Chieh-Hou Yang. Incorporation of topography into two-dimensional resistivity inversion. Geophysics,1990,55(3):354-361;
[73]阮百尧,村上裕,徐世浙。电阻率/激发极化数据的2D反演程序[J].物探化探计算技术,1999,21(2)；
[74]吴小平。非平坦地形条件下电阻率三维反演。地球物理学报,2005,Vol.48(4),932-936
[75]吕玉增,阮百尧。复杂地形条件下四面体剖分电阻率三维有限元数值模拟。地球物理学进展,2006,Vol.21(4),1302-1308。
[76]刘海飞,起伏地形电导率连续变化的三维激电数据有限元数值模拟,地球物理学报,2008；
[77]强健科.起伏地形三维电阻率数据正演模拟与反演成像研究[D]。北京：中国地质大学,2006.
[78]Shi-Zhe Xu, Shengkai Zhao, and YiNi. Aboundary element method for 2-D dc resistivity modeling with a point current source. Geophysics, 1998,63(2):399-403
[79]徐世浙。电源二维地电剖面的边界单元解法。桂林冶金地质学院学报,1984,12,4(4)：119-134.
[80]徐世浙,赵生凯。三维地形上点电源电场的边界单元解法。桂林冶金地质 学院学报,1985,6,5(2)：163-168.
[81]刘继东。用异常电位边界单元法做电测深资料地形改正。煤田地质与勘探,1998,7,26(3)：45-65
[82]徐世浙。点电源二维电场问题中傅氏反变换的k的选择。物探化探计算技术,1988,8,10(3)：236-239
[2]柳建新,何继善等双频激电法及其在示范区的应用。中国地质。Vol.28(3),2001：32-39；
[3]傅良魁。激发极化法[M].北京：地质出版社,1982；
[4]强建科,何继善。椭球体上双频激电法的正演与反演算法。中南大学学报(自然科学版)Vol.38(6),2007,1199-1205；
[5]罗延钟,张桂青.频率域激电法原理[M]。北京：地质出版社1988；
[6]Wait. J. R. Overvoltage research and geophysical applications. New York: Pergammon Press,1959;
[7]Alfano L. Introduction to the interpretation of resistivity measurements for complicated structural condition [J]. Geophysical Prospecting,1959,7(3):311-366.
[8]Vozoff K. Numerical resistivity interpretation. General in homogeneit [J]. Geophysics,1960,25(6):1184-1194
[9]Kelley G V, and Frischknecht F C. Electrical methods in Geophysical Prospecting [M].Pergamum Press,1966
[10]Dey and Morrison H F. Electromagnetic response of two-dimensional in homogeneities in a dissipative half-space for Turam interpretation prospecting [J]. Geophysical Prospecting,1973,21(2):340-365
[11]Dieter K., et al, IP and resistivity type curves for three-dimensional bodies. Geophysics,1969, Vol.34, No.4.
[12]Hohmann G W. Three-dimensional induced polarization and electromagnetic modeling [J]. Geophysics,1975,40(2):309-324.
[13]Lajoie J J and West G F. Three electromagnetic response of a conductive in homogeneity in a layered earth [J]. Geophysics,1976, 46(6):1133-1156.
[14]Okabe M. Boundary element method for the arbitrary in homogeneitiesin resistivity curves[J]. Geophysical Prospecting,1981,29(1):39-59.
[15]Das. U. C, and Verma S. K. Eletromagnetic response of an arbitrary shaped three-dimensional conductor in a layered earth-numerical results [J]. Geophys. J. R. astr. Soc.1982,68,55-66.
[16]周熙襄,钟本善,严忠琼,江玉乐。电法勘探数值模拟的若干结果,地球物理学报,1983,26(S),479-491；
[17]周熙襄,钟本善,江东玉。点源二维电阻率法有限差分正演计算,物化探电子计算技术,1983.5(3)；
[18]罗延钟,张桂青,电子计算机在电法勘探中的应用,武汉地质学院出版社,1987：
[19]Wild A J, Singh S C. Some unintended features of elastic finite-difference models [J]. Geophysical Prospecting,1998,46:79-101.
[20]Lamontagne, Y. and West, G. F., EM response of a rectangular thin plate. Geophysics,1971,36, p26;
[21]Swift, C. M. Jr., Theoretical magnetotelluric and Turam response from two-dimension in homogeneities. Geophysics,1971,36, p1
[22]Jepsen, A. F., Numerical modeling in resistivity prospect ing [J]. Ph.D. these, University of California. Berkeley.1975;
[23]Mufti, J. R., Finite-difference resistivity modeling for arbitrarily shaped two-dimensional structures. Geophysics,1976,41, p62;
[24]Dey, A., Morrison, H. F., Resistivity modeling for arbitrarily shaped three-dimensional structures. Geophysics,1979,44, p753;
[25]Scriba, H., Computation of the electrical potential in three-dimensional structures. Geophysical Prospecting,44, p1;
[26]Zhdanow, M. S. etal, The construction of effective method for electromagnetic modeling. Geophys. J. R. astr. SOC,1982, p68;
[27]Gldman, M. M., Stoyert, C. H., Finite-difference calculations of the transient field of an axially symmetric earth for vertical magnetic dipole excitation. Geophysics,1983,48, p953;
[28]Leppin, M., Electromagnetic modeling of 3-D sources over 2-D in homo-genetics in the time domain:Geophysics,1992,57,994-1003;
[29]Spitzer, K. and Wurmst, B., Speed and Accuracy in 3D resistivity modeling. Geophysics,2001,66;
[30]Spitzer, K. A 3D finite-difference algorithm for DC resistivity modeling using conjugate gradient methods[J]. Geophys. J. Int,1995, 123:903-914.
[31]周熙襄,钟本善,江东玉,点源二维电阻率法有限差分正演计算,物化探电子计算技术,1983,5(3)：1-9
[32]罗延钟,万乐。二维地形不平条件下外电场的有限差分模拟,物化探计算技术,1984,6(4)；
[33]刘树才,周圣武。二维电法数值模拟中的网格剖分方法,物化探计算技术,1995.17；
[34]刘正栋,关洪军,聂永平等。稳定点电流源场三维有限差分正演模拟,解放军理大学学报,2000,1(3)；
[35]吴小平,起伏地形条件下电阻率/激发极化三维正、反演。中国科技大学项目设计,2001；
[36]徐世浙,地球物理中的有限单元法。北京：科学出版社,1994；
[37]杨华,李金铭.起伏地形对近矿围岩充电法影响规律的数值模拟研究。物探与化探,23(3)；
[38]刘海飞,起伏地形电导率连续变化的三维激电数据有限元数值模拟,Manuscript,2008；
[39]徐世浙,地球物理中的边界单元法。北京：科学出版社,1995；
[40]Fox, R. C., Hohmann, G. W., Killpack, T. J., and rijo, L., Topographic effects in resistivity and induced-polarization surveys. Geophysics, 1980,45,p57-93;
[41]Okabe, M., Boundary element method for the arbitrary inhomogeneities in resistivity curves. Geophysical Prospecting,1981,29,39-59;
[42]Nardini, D., and Brebbia, C. A., Transient dynamic analysis by the boundary element method.
[43]Boundary Elements, springer, Verlag,Berlin, Heidelberg, New York;
[44]Xu Shi-zhe and Zhao Sheng-kai, Two-dimensional magnetotelluric modeling by the boundary element method. Journal of Geomagnetism and Geoelectricity,1987,39(11),677-698;
[45]徐世浙,王庆乙等,用边界单元法模拟二维地形对大地电磁场的影响。地球物理学报,1992 35(3),380-388；
[46]Xu Shi-zhe, The effect of two-dimensional terrain with point current source on resistivity surveys. Geophysical research letters,1993,20(10),891-894;
[47]李予国,徐世浙,垂直断面附近二维不均匀体点源电场的边界单元法,物探化探计算技术,1996,18(2)147-151：
[48]黄兰珍,田宪谟等.电阻率法地形改正及其在工程地质勘查中的应用。物探化探计算技术,1997,3；
[49]孙建国,复杂地表条件下地球物理场数值模拟方法评述[J]。世界地质,2007,26(3)：345-361
[50]Dohr G. Applied geophysics [M].Halsted Press, New York,1981.
[51]特尔福德WM,吉尔达特LP,谢里夫RE, etal.应用地球物理[M]。吴荣祥译。北京：地质出版社,1982.
[52]Sheriff RE. Encyclopedic dictionary of exploration geophysics [M]. 2"d Edition. Tulsa:SEG,1984, p233
[53]Telford WM, Geldaed L P, Sheriff RE. Applied geophysics[M]. Cambridge: Cambridge University press,1990
[54]Tessmer E, Kosloff D, Behle A. Elastic wave propagation simulation in the presence of surface topography[J]. Geophysics J Int,1992,108: 621-632.
[55]Hestholm S, Ruud B.3-D finite-difference elastic wave modeling including surface topography[J]. Geophysics,63(2):613-622.
[56]Hestholm S. Elastic wave modeling with free surface stability of long simulation [J]. Geophysics,2003,68(1):314-321.
[57]Tessmer E, Kosloff D.3-D elastic modeling with surface topography by a Chebychev spectral method[J]. Geophysical,1994,59(3):464-473.
[58]Hesthlom S, Ruud B.2D finite-difference elastic wave modeling including surface topography [J]. Geophysical Prospecting,1994, 42,371-390.
[59]Ruud B, Hestholm S.2D surface topography boundary conditions in seismic wave model ing [J]. Geophysical Prospecting,2001,49,445-460.
[60]肖怀宇.带地形的瞬变电磁法三维数值模拟[D].北京：中国地质大学,2006.
[61]陈伯舫,侯作中,范国华.有限差分法计算三维地形影响的电磁感应[J]。地震学报,1998,20(5)：541-544.
[62]王秀明,张海澜.用于具有不规则起伏自由表面的介质中弹性波模拟的有限差分算法[J]。中国科学G辑,2004,34(5)：481-493.
[63]介玉新,揭冠周,李广信.用适体坐标变换方法求解渗流[J]。岩土工程学报,2004,26(1)：52-56
[64]魏文礼,王玲玲等.曲线网格生成技术研究[J]。河海大学学报,1998,26(3)：93-96.
[65]赵景霞,张叔伦等.曲网络伪谱法二维声波模拟[J]。石油物探,2003,42(1)：1-5.
[66]刘鲁波,陈晓非,王彦宾.切比雪夫伪谱法模拟地震波场[J]。西北地震学报,2007,29(1)：18-25.
[67]揭冠周,介玉新,李广信.模拟自由面渗流的适体坐标变换方法[J]。清华大学学报(自然科学版),2003,43(2)：273-284.
[68]Fox R. C, Hohmann G W, Killpack T J, and Rijo L. Topographic effects in resistivity and induced-polarization surveys [J]. Geophysics,1980, 45,57-93.
[69]Chouteau,M. and Bouchard, K., Two-dimensional terrain correction in magneto telluric surveys. Geophysics,1988,53,854-862;
[70]Xu shi-zhe, Gao Zucheng, and Zhao Sheng-kai,, An intergral formulation for three-dimensional terrain modeling for resistivity surveys. Geophysics,1988,53,546-552;
[71]Xu S-Z. The Boundary element method for solving 2.5-D electrical field under relief terrain [J]. Guilin College of Geology (in Chinese), 1984,4:119-133;
[72]Lun-Tao Tong, Chieh-Hou Yang. Incorporation of topography into two-dimensional resistivity inversion. Geophysics,1990,55(3):354-361;
[73]阮百尧,村上裕,徐世浙。电阻率/激发极化数据的2D反演程序[J].物探化探计算技术,1999,21(2)；
[74]吴小平。非平坦地形条件下电阻率三维反演。地球物理学报,2005,Vol.48(4),932-936
[75]吕玉增,阮百尧。复杂地形条件下四面体剖分电阻率三维有限元数值模拟。地球物理学进展,2006,Vol.21(4),1302-1308。
[76]刘海飞,起伏地形电导率连续变化的三维激电数据有限元数值模拟,地球物理学报,2008；
[77]强健科.起伏地形三维电阻率数据正演模拟与反演成像研究[D]。北京：中国地质大学,2006.
[78]Shi-Zhe Xu, Shengkai Zhao, and YiNi. Aboundary element method for 2-D dc resistivity modeling with a point current source. Geophysics, 1998,63(2):399-403
[79]徐世浙。电源二维地电剖面的边界单元解法。桂林冶金地质学院学报,1984,12,4(4)：119-134.
[80]徐世浙,赵生凯。三维地形上点电源电场的边界单元解法。桂林冶金地质 学院学报,1985,6,5(2)：163-168.
[81]刘继东。用异常电位边界单元法做电测深资料地形改正。煤田地质与勘探,1998,7,26(3)：45-65
[82]徐世浙。点电源二维电场问题中傅氏反变换的k的选择。物探化探计算技术,1988,8,10(3)：236-239
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