摘要
起伏地表问题一直是三维电阻率法勘探中一项重要的研究课题,对其进行数值模拟研究关键问题有两点:其一、三维起伏地形及其它边界条件的精确描述;其二、三维复杂地电模型的精确描述。本文通过网格映射方案将起伏地表转换成水平地表解决第一问题;通过网格类算法的代表——有限差分法解决第二问题。根据网格映射原理,推导出坐标变换后稳定电流场的基本方程和边界条件,在变换后空间采用有限差分法数值模拟,最后将计算结果回归到原空间,实现了起伏地表条件下三维电阻率法正演问题。未知节点电位的求取最终归结到线性方程组Au = f的求解上,由于三维问题网格节点众多,如何节约存储空间和提高计算速度是其关键。在此,系数矩阵采用一维压缩存储方案,在线性方程组求解上比较了常规的共轭梯度法(CG)和基于LU分解的乔勒斯基共轭梯度法(ICCG),计算结果表明:后者计算速度比常规共轭梯度法快一倍,可以处理网格精细剖分的三维电阻率法数值模拟问题。通过编制程序,系统地研究了不同地形形态、不同地电条件、不同装置条件下的直流电场响应,得到了具有参考价值的结论;探讨了三维电阻率法在探测断层、接触带等常见地质单元时受地形影响的规律;对复杂地表条件,即起伏地形和浅部不均匀体组合存在时视电阻率异常特征进行分析,同时总结了消除二者影响后异常的分布规律。通过上述若干问题研究,为起伏地表三维电阻率法实际勘探工作提供理论依据。
Resistivity method is a group of exploration methods based on different stone conductivities between rocks (mining),solving a group of geological problems through the observation and research by the distribution of the artificial electric field underground. With the improving of the body awareness level and the complex of the exploration objectives, the development of resistivity method has also encountered some problems, such as complex terrain, abnormal response of multiple objects, the cognition of three-dimensional observation methods and so on. We also encounter some problems in practical production, the reserves of temporary mines is limited in our nation and nearly to bankrupt. So we need to explore more unconscious mines especially in northwest and southwest China. The topography in these areas is so complicated that it will be influenced by the topography if we develop resistivity method to detect mines in these places. However, due to the development of computer technology and mathematic theory, we gain a better use of numerical simulation. So it’s suitable to use numerical simulation method to study the 3-D resistivity method on the basis of irregular topography.
The character of the simulated medium and boundary shape both causes impacts on the DC field and both of the impacts are essential. With the level of calculating technology and the development of the hardware, there is no problem on complicate medium simulating in DC field. This paper using the finite difference method, using the cube subdivision method when discrete grids, if the grids are subdivided slimly enough, we can also implement the simulation of the complicate medium; On the contrary, it’s hard to implement the numerical simulation of the irregular surface. The key of this problem is the boundary condition that depends on the normal and tangential directions of the boundary .Therefore, numerical simulation program must be precise to identify all nodes of normal and tangential direction. This paper uses a strategy of“grid mapping”to implement it. Tessmer and some other people have raised a method called the indirect method or methods of“grid mapping”to solve the irregular terrain problem, Hestholm transformed the“grid mapping”method and combined with the finite difference method, studying the numerical simulation of visco-elastic medium model in the condition of irregular surface. In this paper, we use the“Tessmer mapping”method dealing with the irregular problems and bring the terrain function into the control equation directly, cast light upon the control function that in the physical domain coordinate, deduce the current field control equation with terrain in orthogonal domain, when simulating the stability of current field. Combine with the finite difference method in computational domain so as to realize the forward calculation of three-dimensional resistivity method.
Every processing method on the condition of irregular topography cannot characterize the boundary conditions completely, grid mapping method cannot either. The calculating of this method refers to the first and second partial directional derivative of topography. The extra differential coefficient results in the complicated formation of the basic functions. In spite that we can use this method to process any complicated topography, and can combine the method with any complicated medium models, it stills results in the instability in the process of mapping when the curvature of the topography is big or the curvature changes dramatically. So this method is suitable to process the terrain with small curvature and smooth surface such as hills or the terrain with small changed curvature and continuous curvature such as valleys.
In the process of the numerical simulation to form the linear differential equations, it involves the storage of the coefficient and the calculate of the large-scale linear equations inevitably .In case of the node character of the discrete coefficient matrix is sparse matrix, this paper adopts one-dimensional compression storage program proposed by Wu Xiaoping, this program saves much storage space. In the comparison of the common conjugate gradient method and the conjugate gradient method based on LU decomposition on the stage of solving linear equations, the latter calculation has a double speed. A computer with a CPU which basic frequency is 1.9GHz, can calculate a supple point within about 10 seconds using a 3-D model with the size of 45×23×17.
Analysis the influenced laws that caused by terrains qualitatively and quantitatively when using the 3-D resistivity method through the numerical simulation of some typical terrain models. The abnormal resistivity surveyed by medium gradient method is enantiomorphous to terrain; While pole-pole method is opposite because it’s abnormal resistivity is coherent with terrain; The abnormal resistivity surveyed by tri-electrodes method is coherent with terrain when the polar distance is small, abnormal resistivity is enantiomorphous to terrain when the polar distance is bigger. The symmetry four-electrode method is similar to the tri-electrodes method, the difference is that it has a lower influence compared to the tri-electrodes method, the pure terrain abnormity mainly distributes in the portrait; The abnormity surveyed by dipole-dipole method is coherent with terrain, and dipole-dipole method is greatly influenced by terrain, the pure terrain abnormity mainly distributes in the horizon. Analysis the influence quantitatively, here is an example of a valley which span is D in horizon: the pole-pole method has an low influence, when the polar distance AM=D/2,the influence is the biggest, when AM=D the influence is getting weak; As to tri-electrodes, when surveying at right below the valley that AO=2D,the influence is at it’s peak value, when surveying at the two foot sides that AO=D, the terrain has a biggest influence, if the polar distance is AB=D ,the terrain also has a biggest influence, it getting to weak when AB=2D;As to symmetry four-electrode method ,when surveying at right below the valley that AB=2D, terrain has a serious influence, when measuring at the foot sides of the valley AB=D, the terrain has a biggest influence, when AB=2D the influence becomes to incline; As to dipole-dipole method, when the polar distance is OO′=D, terrain has a serious influence, when OO′=2D, the influence becomes to incline; when there is a combination of few kinds of terrain, the influence law from pure terrain is similar to a single terrain, but the abnormity is much confused because of the inter influence between different terrains. So we have to pay more attention in the interpretation of the practical data.
By numerical simulation analysis to some geology tectonics of some special models, such as slip fault with low resistivity, perpendicular contact, abnormal body near surface and so on, conclude some aberrance law of apparent resistivity abnormity in the condition of irregular terrain.(1)We can adopt a reasonable exploration device to gain a big abnormal response if the slip faults in the area has a low resistivity, have to point out that transverse section method has a better abnormal resistivity response compared to portrait section method. The transverse section method requires a low polar distance, if we can choose a right polar distance, we could gain a good surveying result.(2)Terrain effects can change the abnormity apparent resistivity laws if survey in the perpendicular contact, the areas that are influenced seriously are the foot sides of valleys or hills. The superimposes of different terrains destroy the original abnormity laws in the perpendicular contact. The influences on hills are bigger than valleys when both of the two terrains have the same angels.(3)We can eliminate the influence caused by complicated terrain (combination of irregular terrain and abnormal body) in a big degree using a correcting function, while due to the ignore of influence and the high-order term in the function, the correct results cannot coherent with the value of background completely. The abnormity laws form corrected data have a direct relationship with the surveying devices, the position of inflexion and the position of inhomogeneous body.
Using the numerical simulation analysis above, we can provide theories and references to the practical survey when using 3-D resistivity method in the irregular topography.
引文
[1]韩江涛,刘国兴,刘伟.由激电异常进行异常体快速定位的方法[J].吉林大学学报(地球科学版),2008,38(2):324-329.
[2] Abdelrahman E M, EI-Araby H M, Hassaneen A G,et al.New methods for shape and depth determinations from SP data [J].Geophysics, 2003, 68(4):1202-1210.
[3] Abdelrahman E M, Ammar A A B, Hassanein H I, et al.Derivative analysis of SP anomalies [J]. Geophysics,1998,63(3):890-897.
[4] Wild A J, Singh S C.Some unintended features of elastic finite-differnce models[J]. Geophysical Prospecting, 1998, 46(1): 79-101.
[5] Lamontagne Y, West G F. EM response of a rectangular thin plate[J].Geophysics, 1971,36(6):1204-1222.
[6] Swift C M.Theoretical magnetotelluric and turam response from two-dimension inhomo-geneities[J]. Geophysics, 1971, 36(1):38-52.
[7] Jepsen A R. Numerical modeling in resistivity prospecting[M].Berkeley: Ph.D. University of California,1975.
[8] Mufti I R.Finite-difference resistivity modeling for arbitrarily shaped two- dimensional structures[J]. Geophysics,1976,41(1):62-78.
[9] Dey A,Motrison H F.Resistivity modeling for arbitrarily shaped three-dimensional structures[J].Geophysics, 1979,44(1):753-780.
[10] Scriba H.Computation of the electrical potential in thee-dimensional structures[J]. Geophysical Prospecting,1981, 29(5):669-824.
[11] Zhdanow M S,Golubev N G,Spichak V V, et al.The construction of effective method for electromagnetic modeling[J].Geophys.J.R.astr.SOC,1982,68(3): 589-607.
[12] Gldman M M, Stoyert C H. Finite-diffeence calculations of the transient field of anaxially symmetric earth for vertical magnetic dipole excitation[J].Geophysics, 1983,48(7): 953-963.
[13] Leppin M. Electromagnetic modeling of 3-D sources over 2-D inhomo-geneties inthe time domain [J]. Geophysics, 1992, 57(8):994-1003.
[14] Spitzer K. A 3D finite-difference algorithm for DC resistivity modeling using conjugate gradient methods[J]. Geopyhs.J.Int,1995,123(3):903-914.
[15] Spitzer K, Wurmstich B. Speed and accuracy in 3D resistivity modeling[J]. Society of Exploration Geophysicists, 1999,7:161-176.
[16]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[J].物化探电子计算技术,1983,5(3):1-9.
[17]罗延钟,万乐.二维地形不平条件下均匀外电场的有限差分模拟[J].物探化探计算技术,1984,6(4):15-26.
[18]刘树才,周圣武.二维电法数值模拟中的网格剖分方法[J].物化探计算技术, 1995,17(1):49-51.
[19]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[J].解放军理工大学学报,2000,1(3):45-50.
[20]刘正栋,关洪军,聂永平,等.稳定地电场三维有限差分正演模拟[J].石油物探,2001,40(1):107-114.
[21]刘树才,刘志新,姜志海,等.矿井直流电法三维正演计算的若干问题[J].物探与化探,2004,28(2):170-176.
[22]吴小平,徐果明,李时灿.利用不完全Cholesky共轭梯度法求解点源三维电场[J].地球物理学报,1998,41(6):848-854.
[23]刘志新,许新刚,岳建华.矿井电法三维有限元正演模拟—直流电透视方法技术研究[J].物探化探计算技术,2003,25(4):302-307.
[24]齐基威茨O C,邱Y K.结构和连续力学中的有限单元法[M].北京:国防工业出版社,1967.
[25] Coggon J H.Electromagnetic and electrical modeling by the finite element method[J].Geophysics,1971,36(2):132-151.
[26] Rodi W L. A technique for improving the accuracy of finite-element solutions for magnetotelluric data,Geophys. J. R. Astr. SOC,1976,44(2): 483-506.
[27] Rijo L.Modeling of electric and electromagnetic data[M]. Ph.D. dessertation, Univ. of Utan, 1977.
[28] Kaikkonen P.Numerical VLF modeling[J].Geophysical Prospecting,1979,27,106-136.
[29] Jone T K,Cho D H.Transient time-domain electromagnetic[J].Geophysics,1980, 45(2):271-291.
[30] Pridmore D F,Hohmann Q W, Ward S H, et al.An investigation of finite-element modeling for electrical and electromagnetic data in three dimensions[J]. Geophysics,1981,46(7):1009-1024.
[31] Wannamaker P E, Stodt J A, Rijo L.Two-dimensional topographic response in magnetotellurics modeled using finite element[J].Geophysics,1986,51(11): 2131- 2144.
[32] Unsworth M J, Travis B J,Chave A D.Electromagnetic induction by a finite electric dipole source over a 2-D earth[J].Geophysics, 1993, 58(2):198-214.
[33]朱伯芳.有限单元法原理与应用[M].北京:水利出版社,1979.
[34]李大潜.有限元素法在电法测井中的应用[M].北京:石油工业出版社,1980.
[35]周熙襄,钟本善,严忠琼,等.有限单元法在直流电法勘探正问题中的应用[J].物探化探计算技术,1980,2(3):57-67.
[36]周熙襄.电法勘探数值模拟技术[M].成都:四川科学技术出版社,1986.
[37]罗延钟,张桂青.电子计算机在电法勘探中的应用[M].武汉:武汉地质学院出版社,1987.
[38]徐世浙.有限元法及其在物探中的应用简介[J].物探化探计算技术,1982, 4(2):86-103.
[39]徐世浙.二维分块均匀物体重力异常的计算[J].中国科技大学学报,1984, 14(1):126-132.
[40]徐世浙,赵生凯.三维地形上点电源电场的边界单元解法[J].桂林冶金地质学院学报,1985,5(2):163-168.
[41]徐世浙,赵生凯.二维各向异性地电剖面的大地电磁场的有限单元解法[J].地震学报,1985,7(7):80-90.
[42]徐世浙,赵生凯.地形对大地电磁勘探的影响[J].西北地震学报,1985,7(4): 69-78.
[43]徐世浙.电导率分层线性变化的水平层的点电源电场的数值解[J].地球物理学报,1986,29(1):84-90.
[44]徐世浙.点源二维各向异性地电断面直流电场的有限元解法[J].山东海洋学院学报,1988,18(1):81-90.
[45]徐世浙.点源二维电场问题中傅氏反变换的波数的选择[J].物探化探计算技术,1988,10(3):235-239.
[46]徐世浙.地球物理中的有限单元法[M].北京:科学出版社,1994.
[47]阮百尧,熊彬,徐世浙.三维地电断面电阻率测深有限元数值模拟[J].地球科学,2001,26(1):73-77.
[48]阮百尧,熊彬.电导率连续变化的三维电阻率测深有限元数值模拟[J].地球物理学报,2002,45(1):131-138.
[49]熊彬,阮百尧,罗延钟.复杂地形条件下直流电阻率异常三维数值模拟研究[J].地质与勘探,2003,39(4):60-64.
[50]黄俊革,阮百尧,鲍光淑.三维地电断面激发极化法有限元数值模拟[J].地球科学—中国地质大学学报,2003,28(3):323-326.
[51]黄俊革.三维电阻率/极化率有限元正演模拟与反演成像[D].湖南:中南大学,2003.
[52]强健科.起伏地形三维电阻率正演模拟与反演成像研究[D].北京:中国地质大学,2006.
[53] Alfano L.Introduction to the interpretation of resistivity measurements for complicated structural condition[J].Geophysical Prospecting,1959,7(3):311- 366.
[54] Vozoff K. Numerical resistivity interpretation.General inhomogeneity[J]. Geophysics,1960, 25(6): 1184-1194.
[55] Kelley G V, Frischknecht F C. Electrical methods in geophysical prospecting[M]. Pergamon Press,1966.
[56] Dieter K,Paterson N R,Grant F S. IP and resistivity type curves for three- dimensional bodies[J].Geophysics,1969,34(4):615-632.
[57] Dey A, 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.
[58] Hohmann G W.Three-dimensional induced polarization and electromagnetic modeling[J].Geophysics ,1975,40(2):309-324.
[59] Lajoie J J,West G F. The electromagnetic reponse of a conductive inhomoge- neity in alayered earth[J].Geophysics ,1976, 46(6):1133-1156.
[60] Okabe M.Boundary element method for the arbitrary inhomogeneities in resistivity curves[J].Geoohvsical Prosnecting,1981,29(1):39-59.
[61] Das U C, Verma S K. Eletromagnetic response of an arbitrarily shaped three- dimensional conductor in alayered earth-numerical results[J]. Geophysical Journal International, 1982, 69(1):55-66.
[62]周熙襄,钟本善,严忠琼,等.电法勘探数值模拟的若干结果[J].地球物理学报, 1983,26(5):479-491.
[63]傅良魁.电法勘探教程[M].北京:地质出版社,1983.
[64]王家映.地球物理反演理论[M].北京:中国地质大学出版社,1998.
[65]李棋.物探数值方法导论[M].北京:地质出版社,1991.
[66]庄浩.三维电阻率层析成像研究[D].长沙:中南工业大学,1998.
[67]戴振铎,鲁述.电磁理论中的并矢格林函数[M].武汉:武汉大学出版社,1995.
[68]周平,朱汉清.有限元一边界元祸合法计算任意截面形状二维介质柱雷达散射截面[J].淮阴师范学院学报(自然科学版),2004,3(4):281-284.
[69]谢靖.物探数据处理的数学方法[M].北京:地质出版社,1981.
[70]李忠元.电磁场边界元素法[M].北京:北京工业学院出版社,1987.
[71]田宪漠,黄兰珍.电法勘探用边界单元法[M].北京:地质出版社,1990.
[72]徐世浙,汪晓东.多域地电断面均匀电场边界单元法正演[J].物探化探计算技术,1990,10(2):106-112.
[73]徐世浙,王庆乙.用边界单元法模拟二维地形对大地电磁场的影响[J].地球物理学报,1992,35(3):380-388.
[74] Xu Shi-zhe, Zhao Sheng-kai.Two-dimensional magnetotelluric modeling by the boundary element method[J].Journal of Geomagnetism and Geoelectricity,1987, 39(11):677-698.
[75] Xu Shi-zhe.The effect of two-dimensional terrain with point current source on resistivity surveys[J]. Geophysical Research Ietters, 1993,20(10):891-894.
[76] Torres V C, Habashy T M. Rapid 2.5-D forward modeling and inversion via a new nonlinear scattering approximation[J].Radio Science,1994,29(4):1051- 1079.
[77]毛先进,鲍光淑,宋守根.半空间中多个二维体电阻率响应的边界积分方程模拟[J].地球物理学报,1996,39(6):823-834.
[78]毛先进,鲍光淑.2.5维问题电阻率正演的新方法[J].中南工业大学学报,1997, 28(4):307-310.
[79]毛先进,鲍光淑.边界积分方程法二维电阻率层析成像[J].物探化探计算技术, 1998,20(3):226-229.
[80] Hohmann G W. Three-dimensional induced polarization and electromagnetic modeling[J].Geophysics,1975,40(2):309-324.
[81]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.
[82] Dohr G. Applied geophysics[M].Halsted Press,New York,1981.
[83]特尔福德W M ,吉尔达特L P,谢里夫R E,et al.应用地球物理学[M].吴荣祥译.北京:地质出版社,1982.
[84] Sheriff R E. Encyclopedic dictionary of exploration geophysics[M]. 2nd Edition. Tulsa:SEG ,1984.
[85] Telford W M , Geldard L P, Sheriff R E. Applied geophysics [M]. Cambridge: Cambridge University Press,1990.
[86] Tessmer E, Kosloff D,Behle A.Elastic wave propagation simulation in the presence of surface topography[J]. Geophysics J Int ,1992,108(2): 621-632.
[87] Hestholm S, Ruud B.3-D finite-difference elastic wave modeling including surface topography[J]. Geophysics ,1998,63(2):613-622.
[88] Hestholm S.Elastic wave modeling with free surfaces:stability of long sinulations[J].Geophysics,2003,68 (1):314-321.
[89] Tessmer E,Kosloff D.3-D elastic modeling with surface topography by a Chebychev spectral method [J] .Geophysics,1994,59 (3):464-473.
[90] Hesthlom S,Ruud B.2D finite-difference elastic wave modeling including surface topography[J].Geophysical Prospecting,1994,42(5):371-390.
[91] Ruud B,Hestholm S.2D surface topography boundary conditions in seismic wave modeling[J].Geophysical Prospecting, 2001,49(4):445-460.
[92]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.
[93]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.
[94]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.
[95]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.
[96]魏文礼,王玲玲,金忠青.曲线网格生成技术研究[J].河海大学学报,1998,26(3): 93-96.
[97]赵景霞,张叔伦,孙沛勇.曲网络伪谱法二维声波模拟[J].石油物探,2003, 42(1): 1-5.
[98]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.
[99]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.
[100] Fox R C, Hohmann G W, Killpack T J, et al. Topographic effects in resistivity and induced-polarization surveys[J].Geophysics,1980,45(1):57-93.
[101] Chouteau M, Bouchard K. Two-dimensional terrain correction in agnetotelluric surveys[J].Geophysics,1988,53(6):854-862.
[102] Tong L T, Yang C H. Two-dimensional resistivity inversion[J].Incorporation of Topography into Geophysics,1990,55(3):354-361.
[103]阮百尧,村上裕,徐世浙.电阻率激发极化数据的二维反演程序[J].物探化探计算技术,1999,21(2):116-125.
[104]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[J].地球物理学进展,2006,21(4):1302-1308.
[105]吴小平.起伏地形条件下电阻率/激发激化三维正反演[D].安徽:中国科技大学项目设计,2001.
[106]强建科,罗延钟.三维地形直流电阻率有限元法模拟[J].地球物理学报,2007, 50(5): 1606-1613.
[107]王祥春,刘学伟.起伏地表二维声波方程地震波场模拟与分析[J].石油地球物理勘探,2007,42(3):268-276.
[108] Wang X C, Liu X W.3-D acoustic wave equation forward modeling with topography[J].Applied Geophysics,2007,4(1):8-14.
[109]吴小平,徐果明,李时灿.解大型稀疏方程组ICCG方法及其计算机实现[J]. 1999,27(6):54-55.
[110]吴小平,徐果明.利用ICCG迭代技术加快电阻率三维正演计算[J].煤田与地质勘探,1999,27(3):62-66.
[111]吴小平,汪彤彤.利用共轭梯度算法的电阻率三维有限元正演[J].地球物理学报,2003,46(3):428-432.
[112]宛新林.基于LANCZOS迭代技术的电阻率三维正反演研究[D].安徽:中国科学技术大学,2004.
[113]宛新林,席道瑛,高尔根.LANCZOS迭代算法及其在三维地电场数值模拟计算中的应用研究[J].物探化探计算技术,2004,26(1):47-52.
[114]宛新林,席道瑛,高尔根.三维电阻率正演计算中的Lanczos迭代算法[J].岩土力学,2003,24(supp):108-111.
[115]熊俊,刘建,黄小兰,等.渗流计算中的一维压缩存储及PCG程序设计[J].矿业研究于开发,2006,26(1):67-70.
[116]刘国兴.电法勘探原理与方法[M].北京:地质出版社,2005.
[117]邓起东,徐锡伟,张先康,等.城市活动断裂的探测方法和技术[J].地学前缘, 2003, 10(1):93-104.
[118]陈峰,廖春庭,安金珍.剪切和摩擦滑动大模型的视电阻率变化幅度和各向异性[J].地球物理学报,2003,46(5):667-675.
[119]郝锦绮,冯锐,周建国,等.岩石破裂过程中电阻率变化机理的探讨[J].地球物理学报,2002,45(2):426-433.
[120]陈峰,安金珍,廖椿庭.原始电阻率各向异性岩石电阻率变化的方向性[J].地球物理学报,2003,46(2):271-278.
[121]陈峰,修济刚,安金珍,等.岩石电阻率变化各向异性与微裂隙扩展方位实验研究[J].地震学报,2000,22(3):310-318.
[122]毛桐恩,胥广银,范思源,等.地电阻率各向异性度的动态演化图象与地震孕育过程[J].地震学报,1999,21(2):180-186.
[123]陈大元,修济刚,安金珍,等.单轴压力下有补给水岩石电阻率变化各向异性研究[J].中国地球物理学会年刊,1994.
[124]吴子泉,谭捍东,王成虎.电阻率横向剖面法在倾斜断层精确探测中的应用研究[J].地球物理学报,2007,50(2):625-631.
[125]吴子泉,尹成.电阻率横向剖面法及其在隐伏断层探测中的应用研究[J]地球物理学进展,2006,21(4):1296-1301.
[126]余君鹏,秦松贤.湘南姑婆山岩体北西侧侵入接触带构造控矿研究[J].地质科技情报,2007,26(2):25-29.
[127]易顺华,李珍.侵入接触构造的地质力学研究[J].地质力学学报,1997, 3(2):61- 65.
[128]张献民.电阻率法地形校正公式的应用条件[J].地质与勘探,1991,27(1): 36-40.
[129]张天伦.消除直流电阻率三极梯度法中各种干扰的实验与研究[J].石油地球物理勘探,1995,30(1):100-110.
[130]邓晓红.浅部不均匀体导致视电阻率拟断面畸变[J].地质与勘探,2003, 39 (supp):129-134.
[131]邓晓红,方慧,奚家鉴,等.剔除高密度电阻率法三极装置浅部不均匀体效应影响的方法及效果[J].物探与化探,2004,28(4):314-316.
[132]强建科,阮百尧.不同电阻率测深方法对旁侧不均匀体的反映[J].物探与化探, 2003,27(5):379-382.
[133]强建科,阮百尧,熊彬.浅部不均匀体对目标体电阻率异常影响的研究[J].地球物理学报,2004,47(3):542-548.