有限单元法在直流电阻率法勘探中的研究及应用
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摘要
随着找矿程度的不断深入,浅部易于发现和利用的矿产日趋减少,对寻找深部有色金属矿藏的快速预测定位方法的研究已成为当今整个地质界的最重要研究课题之一。直流电阻率法是矿产资源勘查及水文地质和环境地质调查中,十分有效和应用相当广泛的一种物探方法。
近年来,其应用领域不断拓宽,观测空间从地表发展到地下、水下。直流电阻率法正朝着高密度、高精度方向发展。与此同时,勘探地区地形越来越复杂,对直流电阻率法的资料处理解释也提出了新的要求。
而长期以来,起伏地形条件下的地电异常的处理与解释是电法勘探中的一个难题,这一方面是由于问题本身比较复杂,另一方面是由于同时期的科技发展水平达不到。在数值模拟方法中,有限单元法因具有精度高、解题过程比较规范、能自动满足内部边界条件、适合于复杂地形的物性分布问题等优点而得以应用研究。
本文从二维电性介质点源有限单元模拟出发,介绍了地电二维点源有限单元法原理,有限单元法中边界条件的选取、单元剖分、插值及单元合成,系数矩阵的形成,以及解方程的方法。然后重点对于多种地形(山脊、山谷、山脊与山谷组合)进行了大量的模拟计算,并对计算结果进行了较系统全面的分析和论证,总结出了起伏地形情况下的电阻率法剖面异常分布规律,较好地消除了地形在电阻率法剖面异常中的影响,确保了后期电性资料的地质、地球物理解释效果。
最后借用他人对实际电性资料的应用结果,验证了该方法技术的有效性,说明了用有限单元法研究起伏复杂地形下电阻率剖面异常,对克服起伏地形的影响有一定的实际意义和应用前景。
With the deepening level of prospecting, the shallow mineral easy to find and use has been dwindling, so the study for the methods of quick prediction location to search for deep non-ferrous metal deposits has become one of the most important topics in the entire geological community today. In the mineral exploration and hydro- geological and environmental geology survey, DC resistivity method is an effective and widely applied geophysical method.
In recent years, DC resistivity method has been expanding constantly in the application field, with its observation space from surface to underground and underwater. DC resistivity method has developed in the direction of high-density and high-precision. At the same time, Topography of the area for exploration becomes more and more complex, which also puts forward to new requirements to data processing and interpretation of DC resistivity method.
However, for a long time, the earth resistivity anomaly under the condition of rolling topography is a problem in electrical prospecting, which results from the complicated problem itself for one thing and the backward technological development in the same period for another thing. Among numerical simulation methods, finite element method is applied to research because of these advantages such as high precision, a fairly standard problem-solving process, satisfying the internal boundary conditions automatically, suitable for the physical distribution issues of complex terrain, and so on.
Starting from finite element simulation of two-dimensional electric media for point source, this paper introduces the theory of two-dimensional finite element method for point source in section, selection of boundary conditions, cell triangulation, interpolation and unit synthesis of finite element method, and simulated calculation using high-density measurement on surface and well resistivity measurement to two-dimensional geoelectric model. Besides, data mapping has been done with data analysed qualitatively and quantitatively.
This paper studys futher the resistivity profile anomaly under the undulating terrain, simulates forward resistivity profiles of a variety of typical geoelectric models and analyses the calculated results. And then it is summarized that the regularities of distribution about the resistivity profile anomaly under the undulating terrain, with the false anomaly eliminated successfully.
Finally,the paper shows summarily that it is effective to research the resistivity profile anomaly with finite element method in terms of overcoming the effect of the complicated undulating terrain.
近年来,其应用领域不断拓宽,观测空间从地表发展到地下、水下。直流电阻率法正朝着高密度、高精度方向发展。与此同时,勘探地区地形越来越复杂,对直流电阻率法的资料处理解释也提出了新的要求。
而长期以来,起伏地形条件下的地电异常的处理与解释是电法勘探中的一个难题,这一方面是由于问题本身比较复杂,另一方面是由于同时期的科技发展水平达不到。在数值模拟方法中,有限单元法因具有精度高、解题过程比较规范、能自动满足内部边界条件、适合于复杂地形的物性分布问题等优点而得以应用研究。
本文从二维电性介质点源有限单元模拟出发,介绍了地电二维点源有限单元法原理,有限单元法中边界条件的选取、单元剖分、插值及单元合成,系数矩阵的形成,以及解方程的方法。然后重点对于多种地形(山脊、山谷、山脊与山谷组合)进行了大量的模拟计算,并对计算结果进行了较系统全面的分析和论证,总结出了起伏地形情况下的电阻率法剖面异常分布规律,较好地消除了地形在电阻率法剖面异常中的影响,确保了后期电性资料的地质、地球物理解释效果。
最后借用他人对实际电性资料的应用结果,验证了该方法技术的有效性,说明了用有限单元法研究起伏复杂地形下电阻率剖面异常,对克服起伏地形的影响有一定的实际意义和应用前景。
With the deepening level of prospecting, the shallow mineral easy to find and use has been dwindling, so the study for the methods of quick prediction location to search for deep non-ferrous metal deposits has become one of the most important topics in the entire geological community today. In the mineral exploration and hydro- geological and environmental geology survey, DC resistivity method is an effective and widely applied geophysical method.
In recent years, DC resistivity method has been expanding constantly in the application field, with its observation space from surface to underground and underwater. DC resistivity method has developed in the direction of high-density and high-precision. At the same time, Topography of the area for exploration becomes more and more complex, which also puts forward to new requirements to data processing and interpretation of DC resistivity method.
However, for a long time, the earth resistivity anomaly under the condition of rolling topography is a problem in electrical prospecting, which results from the complicated problem itself for one thing and the backward technological development in the same period for another thing. Among numerical simulation methods, finite element method is applied to research because of these advantages such as high precision, a fairly standard problem-solving process, satisfying the internal boundary conditions automatically, suitable for the physical distribution issues of complex terrain, and so on.
Starting from finite element simulation of two-dimensional electric media for point source, this paper introduces the theory of two-dimensional finite element method for point source in section, selection of boundary conditions, cell triangulation, interpolation and unit synthesis of finite element method, and simulated calculation using high-density measurement on surface and well resistivity measurement to two-dimensional geoelectric model. Besides, data mapping has been done with data analysed qualitatively and quantitatively.
This paper studys futher the resistivity profile anomaly under the undulating terrain, simulates forward resistivity profiles of a variety of typical geoelectric models and analyses the calculated results. And then it is summarized that the regularities of distribution about the resistivity profile anomaly under the undulating terrain, with the false anomaly eliminated successfully.
Finally,the paper shows summarily that it is effective to research the resistivity profile anomaly with finite element method in terms of overcoming the effect of the complicated undulating terrain.
引文
[1]Lamontagne,Y. and West,G.F., EM response of a rectangular thin plate.Geophysics, 1971,36,p26;
[2]Swift,C.M.Jr., Theoretical magnetotelluric and Turam response from two-dimension inhomogeneities. Geophysics, 1971,36,p1
[3]Mufti,J.R., Finite-difference resistivity modeling for arbitrarily shaped two-dimensionalstructures. Geophysics, 1976,41,p62;
[5]Mufti,J.R., A practical approach to finite-difference modelin. Geophysics, 1978,43,p5;
[6]Spitzer, K. and Wurmstich, B., Speed and Accuracy in 3D resistivity modeling. Geophysics,2001,66;
[7]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);
[8]罗延钟,万乐,维地形不平条件h外电场的有限差分模拟[J].物化探计算技术,1984, 6 (4);
[9]罗延钟,万乐,用数值模拟方法构组保角变换坐标网[J].物化探计算技术,1986 8 (1);
[10]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);
[11]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) ;
[12]宋维琪,周红,频率域电磁场偏移成像[J]石油地球物理勘探,1997 32 (4);
[13]林树海,伶文琪,多频电磁波测井的数值模拟[J].长春科技大学学报,1998 28(4);
[14]田宪漠,黄兰珍.电法勘探边界单元法[M].北京地质出版社,1990
[15]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.
[16]徐世浙,地球物理中的有限单元法,北京,科学出版社[M],1994。
[17]底青云,王妙月,稳定电流场有限元模拟研究,地球物理学报[J]2,252.1998。
[18]Coggon.J.H ,Electromagnetic and electrical modelling by the finite element method,Geophysics,197l(36),l 32-l 55
[19]Dey A.and Monrrison,H.F.,Resistivity modelling for arbitrarily shaped two—dimensional structures,Geophysical Prospecting。1979,27,106-l 36
[20]周熙襄、钟本善、严忠琼、江玉乐,电法勘探正演数值模拟的若干结果[J].地球物理学报479-491 l983。
[21]罗延钟、盂永良,关于用有限单元法对二维构造做电阻率法模拟的几个问题地球物理学报[J].29,613-621,1986。
[22]徐世浙、赵生凯.二维各向异性地电断面大地电磁场的有限元法解法[J].地震学报78O-9O 1985。
[23]陈明生、严义生,二维水平电偶极变频测深阻抗视电阻率的有限元正演计算[J].地球物理学报30,201-208 1987.
[24]刘国兴,点源二维有限元法在三电位电极系正演模拟中的应用[J].长春地质学院学报,2l 103—110 1991。
[25]阮爱国赵和云,地电台址构造条件的三维有限元数值模拟[J].西北地震学报13 22—28·1991
[26]赵和云阮爱国,地电台址大范围介质条件的数值模拟研究[J].西北地震学报14,64一70·1992.
[27]陈伯舫、范国华、冯硪云.导体边缘附近虚感应矢量性质的数值模拟研地球物理学报[J].34 82—88 1991。
[28]徐世浙等,水平地形三维电场的边界元解法[J].物化探计算技6(3)·1984.
[29]徐世浙,三维地形均匀各向异性岩石点电源场的边界单元解[M].山东海洋学院院报,15(2) 1985.
[30]田宪谟,电源场电阻率法三维地形改正的边界元[J].成都地质学院学报.13(3) 1986。
[31]田宪、黄兰珍,围岩充电法充电场的边界元法数值计算[J].成都地震学院学报18(2),1991。
[32]傅良魁、陈福集,电法勘探中有覆盖层的点源三维边界元法正演[J].现代地质,4(3) 89-100 1990。
[33]马钦忠、钱家拣,二维层状介质点电源边界单元解,西北地震学报[J].13(2),5一7 1991。
[34]钱家栋、马钦忠,点电源二维起伏界面三层介质边界元法[J].西北地震学报14(2) 3—12 1992。
[35]徐世浙,应用有限元法进行二维磁场计算向上廷和换算[J].地球物理学报26.增刊842-855.1983。
[36]陈乐寿,有限元法在大地电磁场正演计算中的应用及改进[J],地质科学2.241-260 1981。
[37]段本春,朱永盛,电法二维有限元正演计算的若干新结果[J].物化探计算技术,第16卷,第1期,1994年2月。
[38]周熙襄,钟本善等.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.
[39]徐世浙,点电源二维电场问题中付氏反变换的波数K的选择[J].物化探计算技术,第10卷,第3期,1988年8月。
[40]刘杰,起伏地形电阻率剖面异常研究[D].中南大学长沙,2008.
[41]曹书锦,直流率法边坡勘探地形影响问题的三维有限元数值模拟[D].吉林,2009
[42]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,(3345-361)。
[43]韩江涛,起伏地表三维电阻率法数值模拟与分析[D],武汉,2009
[44]屈超纯,张静,宋守根,点源场计算方法,云南科技出版社[J],1999:76-85,197
[45]强健科,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
[46]屈超纯,张静,宋守根.点源场计算方法[M].昆明:云南科技出版社,1999.
[2]Swift,C.M.Jr., Theoretical magnetotelluric and Turam response from two-dimension inhomogeneities. Geophysics, 1971,36,p1
[3]Mufti,J.R., Finite-difference resistivity modeling for arbitrarily shaped two-dimensionalstructures. Geophysics, 1976,41,p62;
[5]Mufti,J.R., A practical approach to finite-difference modelin. Geophysics, 1978,43,p5;
[6]Spitzer, K. and Wurmstich, B., Speed and Accuracy in 3D resistivity modeling. Geophysics,2001,66;
[7]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);
[8]罗延钟,万乐,维地形不平条件h外电场的有限差分模拟[J].物化探计算技术,1984, 6 (4);
[9]罗延钟,万乐,用数值模拟方法构组保角变换坐标网[J].物化探计算技术,1986 8 (1);
[10]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);
[11]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) ;
[12]宋维琪,周红,频率域电磁场偏移成像[J]石油地球物理勘探,1997 32 (4);
[13]林树海,伶文琪,多频电磁波测井的数值模拟[J].长春科技大学学报,1998 28(4);
[14]田宪漠,黄兰珍.电法勘探边界单元法[M].北京地质出版社,1990
[15]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.
[16]徐世浙,地球物理中的有限单元法,北京,科学出版社[M],1994。
[17]底青云,王妙月,稳定电流场有限元模拟研究,地球物理学报[J]2,252.1998。
[18]Coggon.J.H ,Electromagnetic and electrical modelling by the finite element method,Geophysics,197l(36),l 32-l 55
[19]Dey A.and Monrrison,H.F.,Resistivity modelling for arbitrarily shaped two—dimensional structures,Geophysical Prospecting。1979,27,106-l 36
[20]周熙襄、钟本善、严忠琼、江玉乐,电法勘探正演数值模拟的若干结果[J].地球物理学报479-491 l983。
[21]罗延钟、盂永良,关于用有限单元法对二维构造做电阻率法模拟的几个问题地球物理学报[J].29,613-621,1986。
[22]徐世浙、赵生凯.二维各向异性地电断面大地电磁场的有限元法解法[J].地震学报78O-9O 1985。
[23]陈明生、严义生,二维水平电偶极变频测深阻抗视电阻率的有限元正演计算[J].地球物理学报30,201-208 1987.
[24]刘国兴,点源二维有限元法在三电位电极系正演模拟中的应用[J].长春地质学院学报,2l 103—110 1991。
[25]阮爱国赵和云,地电台址构造条件的三维有限元数值模拟[J].西北地震学报13 22—28·1991
[26]赵和云阮爱国,地电台址大范围介质条件的数值模拟研究[J].西北地震学报14,64一70·1992.
[27]陈伯舫、范国华、冯硪云.导体边缘附近虚感应矢量性质的数值模拟研地球物理学报[J].34 82—88 1991。
[28]徐世浙等,水平地形三维电场的边界元解法[J].物化探计算技6(3)·1984.
[29]徐世浙,三维地形均匀各向异性岩石点电源场的边界单元解[M].山东海洋学院院报,15(2) 1985.
[30]田宪谟,电源场电阻率法三维地形改正的边界元[J].成都地质学院学报.13(3) 1986。
[31]田宪、黄兰珍,围岩充电法充电场的边界元法数值计算[J].成都地震学院学报18(2),1991。
[32]傅良魁、陈福集,电法勘探中有覆盖层的点源三维边界元法正演[J].现代地质,4(3) 89-100 1990。
[33]马钦忠、钱家拣,二维层状介质点电源边界单元解,西北地震学报[J].13(2),5一7 1991。
[34]钱家栋、马钦忠,点电源二维起伏界面三层介质边界元法[J].西北地震学报14(2) 3—12 1992。
[35]徐世浙,应用有限元法进行二维磁场计算向上廷和换算[J].地球物理学报26.增刊842-855.1983。
[36]陈乐寿,有限元法在大地电磁场正演计算中的应用及改进[J],地质科学2.241-260 1981。
[37]段本春,朱永盛,电法二维有限元正演计算的若干新结果[J].物化探计算技术,第16卷,第1期,1994年2月。
[38]周熙襄,钟本善等.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.
[39]徐世浙,点电源二维电场问题中付氏反变换的波数K的选择[J].物化探计算技术,第10卷,第3期,1988年8月。
[40]刘杰,起伏地形电阻率剖面异常研究[D].中南大学长沙,2008.
[41]曹书锦,直流率法边坡勘探地形影响问题的三维有限元数值模拟[D].吉林,2009
[42]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,(3345-361)。
[43]韩江涛,起伏地表三维电阻率法数值模拟与分析[D],武汉,2009
[44]屈超纯,张静,宋守根,点源场计算方法,云南科技出版社[J],1999:76-85,197
[45]强健科,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
[46]屈超纯,张静,宋守根.点源场计算方法[M].昆明:云南科技出版社,1999.
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