三维地质体的地下电磁响应
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摘要
本文介绍了频率域电磁法的基本原理,用积分方程法计算了三维异常体的地下电磁响应,研究了层状大地水平谐变电偶极子三维异常体的地下电磁响应特性。该研究结果为地下坑道内做频率域电磁法勘探实践进行了有益的探索。
本文正演计算从麦克斯韦方程组出发,研究了均匀大地谐变电偶极子地表一次电场,推导了层状大地水平谐变电偶极子在地下一次电场,结合数字滤波的方法原理,编写了层状大地水平谐变电偶极子在地下电磁场的正演模拟程序。在计算地下三维倾斜异常体内产生的异常电场时,为了进行数值计算,首先把三维倾斜异常体剖分为N个边长为?的立方体单元,且假设电场在每个单元内为常数,计算出各剖分单元中心一次场,利用积分方程和并矢格林函数理论将麦克斯韦方程转化为矩阵方程,求解该矩阵方程便得到各剖分单元中心点的异常电场。利用导出的层状大地三维异常体产生的地下异常电磁场表达式和在异常体上的一次电场表达式来计算异常体在地下产生的二次场。最后,利用层状大地水平谐变电偶极子地下电磁场正演程序计算出地下一次场,与三维异常体在地下处产生的二次场相加,求得地下的总电场。地下电磁响应的正演计算与地表不同,本文推导了地下波区视电阻率表达式。
本文通过设计不同的地球物理异常体模型,做了大量的正演计算,研究了层状大地水平谐变电偶极子三维异常体的地下电磁响应特性。根据频率电磁测深法视电阻率拟断面图分布特征,主要做了以下几项研究:(1)研究了均匀大地中三维异常体地下异常规律。(2)研究了两层大地中三维异常体随倾角变化的地下异常变化规律。(3)研究了两层大地中三维异常体随埋深变化的地下异常变化规律。
This paper briefly introduced the basic principle of the E.M frequency sounding. On calculating the underground electromagnetic field in three-dimensional inclined anomalous body by the integral equation .The findings have carried on the beneficial exploration for underground E.M field of the horizontal harmonious electric dipole in the layered earth.
This paper derived the expression of underground E.M field of the horizontal harmonious electric dipole in the layered earth ,the field survey method as well as the principle of digital filtering, at the same time the forward modeling programs for the E.M field in the upper and underground earth of the level harmonious electric dipole in the layered earth using the digital filtering method are coded. On calculating the electric field in three-dimensional inclined anomalous body, in order to do numerical calculation, At first, the three-dimensional inclined anomalous body is divided into N cubic element with the side length ?and supposed that the electric field in each element is constant. After obtaining the primary field value on the central point of each anomalous element, then transfer the Maxwell’s equations into a matrix equation by using the integral equation and dyadic Green’s function theory, and the anomalous field value has been obtained on the central point of each anomalous element by resolving the matrix equation. According to the reciprocity principle, on calculating the secondary field on the underground measuring point corresponding to the central point of each anomalous element, the E.M field expression is used on the earth’s surface of the level harmonious electric dipole in the layered-earth. Finally, the primary field value was been work out on the underground measuring point by using the forward modeling programs of the horizontal harmonious electric dipole in the layered earth, then add it to the secondary field value produced by the anomalous electrical field on the underground measuring point corresponding to the central point of each anomalous element that to obtain the total field value of the level harmonious electric dipole.
In this paper, the author investigated the E.M response property of the horizontal harmonious electric dipole on the underground of layered earth for three-dimensional inclined anomalous body by doing plenty of forward modeling calculation. According to the distribution characteristic of the underground apparent resistivity pseudo-section map of the frequency domain E.M sounding, the author mainly did the following research:1) On calculating the E.M response of three-dimensional inclined anomalous body in homogeneous half-space by using the integral equation forward modeling programs, the author investigated underground spatial distribution laws of anomalous. 2) The author investigated change law of the anomalous E.M field for three-dimensional inclined good conductor along with the buried depth of the top of the anomalous body, and estimated the underground detection capacity to three-dimensional inclined anomalous body of certain bulk. 3) The author investigated change law of the anomalous E.M field along with the dip angle of three-dimensional inclined good conductor by changing the dip angle of three-dimensional inclined good conductor in two-layer earth.
本文正演计算从麦克斯韦方程组出发,研究了均匀大地谐变电偶极子地表一次电场,推导了层状大地水平谐变电偶极子在地下一次电场,结合数字滤波的方法原理,编写了层状大地水平谐变电偶极子在地下电磁场的正演模拟程序。在计算地下三维倾斜异常体内产生的异常电场时,为了进行数值计算,首先把三维倾斜异常体剖分为N个边长为?的立方体单元,且假设电场在每个单元内为常数,计算出各剖分单元中心一次场,利用积分方程和并矢格林函数理论将麦克斯韦方程转化为矩阵方程,求解该矩阵方程便得到各剖分单元中心点的异常电场。利用导出的层状大地三维异常体产生的地下异常电磁场表达式和在异常体上的一次电场表达式来计算异常体在地下产生的二次场。最后,利用层状大地水平谐变电偶极子地下电磁场正演程序计算出地下一次场,与三维异常体在地下处产生的二次场相加,求得地下的总电场。地下电磁响应的正演计算与地表不同,本文推导了地下波区视电阻率表达式。
本文通过设计不同的地球物理异常体模型,做了大量的正演计算,研究了层状大地水平谐变电偶极子三维异常体的地下电磁响应特性。根据频率电磁测深法视电阻率拟断面图分布特征,主要做了以下几项研究:(1)研究了均匀大地中三维异常体地下异常规律。(2)研究了两层大地中三维异常体随倾角变化的地下异常变化规律。(3)研究了两层大地中三维异常体随埋深变化的地下异常变化规律。
This paper briefly introduced the basic principle of the E.M frequency sounding. On calculating the underground electromagnetic field in three-dimensional inclined anomalous body by the integral equation .The findings have carried on the beneficial exploration for underground E.M field of the horizontal harmonious electric dipole in the layered earth.
This paper derived the expression of underground E.M field of the horizontal harmonious electric dipole in the layered earth ,the field survey method as well as the principle of digital filtering, at the same time the forward modeling programs for the E.M field in the upper and underground earth of the level harmonious electric dipole in the layered earth using the digital filtering method are coded. On calculating the electric field in three-dimensional inclined anomalous body, in order to do numerical calculation, At first, the three-dimensional inclined anomalous body is divided into N cubic element with the side length ?and supposed that the electric field in each element is constant. After obtaining the primary field value on the central point of each anomalous element, then transfer the Maxwell’s equations into a matrix equation by using the integral equation and dyadic Green’s function theory, and the anomalous field value has been obtained on the central point of each anomalous element by resolving the matrix equation. According to the reciprocity principle, on calculating the secondary field on the underground measuring point corresponding to the central point of each anomalous element, the E.M field expression is used on the earth’s surface of the level harmonious electric dipole in the layered-earth. Finally, the primary field value was been work out on the underground measuring point by using the forward modeling programs of the horizontal harmonious electric dipole in the layered earth, then add it to the secondary field value produced by the anomalous electrical field on the underground measuring point corresponding to the central point of each anomalous element that to obtain the total field value of the level harmonious electric dipole.
In this paper, the author investigated the E.M response property of the horizontal harmonious electric dipole on the underground of layered earth for three-dimensional inclined anomalous body by doing plenty of forward modeling calculation. According to the distribution characteristic of the underground apparent resistivity pseudo-section map of the frequency domain E.M sounding, the author mainly did the following research:1) On calculating the E.M response of three-dimensional inclined anomalous body in homogeneous half-space by using the integral equation forward modeling programs, the author investigated underground spatial distribution laws of anomalous. 2) The author investigated change law of the anomalous E.M field for three-dimensional inclined good conductor along with the buried depth of the top of the anomalous body, and estimated the underground detection capacity to three-dimensional inclined anomalous body of certain bulk. 3) The author investigated change law of the anomalous E.M field along with the dip angle of three-dimensional inclined good conductor by changing the dip angle of three-dimensional inclined good conductor in two-layer earth.
引文
[1]李金铭,地电场与电法勘探.地质出版社.2005
[2] G.W.Hohmann.Three-dimentional induced polarization and electromagnetic modeling Geophysics,VOL.40,P.309-324,1975
[3]Dieter K.,et al.IP and resistivity type curyes for three-dimentional bodies. Geophysics,VOL.34,No.4
[4]徐世浙.点源二维地点剖面的边界元解法.桂林冶金地质学院学报, Vol.4. P.119-337,1984
[5]徐世浙.地球物理中的边界单元法.科学出版社1999
[6] Wannamaker P.E. Advances in three-dimentional magnetotellyric modeling Using Integral equations.Geophisics,1991,56(11):1716-1728
[7] Pridmore D F.three-dimentional modeling of electric and electromagnetic Data using the FEM.[ph.D.thesis],Utah:univ of Utah,1978
[8] Lee K.H.,Pridmore D.F. and Morrison H.F. Hybrid three-dimentional EM modeling scheme.Geophisics,Vol.46,No.5,1981
[9] Dey A. and Morrision H.F. Resistivity modeling for Arbitrarily Shaped 3-D Structure.Geophisics,Vol.44(4),P.753-780,1979
[10]徐世浙,赵生凯,楼云菊.水平地形三维电场的边界单元解法.物化探计算技术,VOL.6,NO.3
[11]周熙襄,钟本善.三维任意形体电法数值模拟的积分方程法.物化探计算技术,VOL.7,NO.22
[12]李晓波,朴化荣.两层大地中三维体的激发极化与电阻率响应的积分方程模拟.地球物理学报,VOL.31,NO.3,P.342-352,1988
[13]朴化荣,殷长春.频率测深水平磁场的正演计算及应用.物探化探计算技术,VOL.11,NO.3,P.204-213,1989
[14]殷长春.赤道向频率域电磁测深三维电磁模拟技术研究.石油地球物理学报,VOL.29,NO.6,P.746-753,757,1994
[15]殷长春,刘斌.瞬变电磁法三维问题正演及激电效应特征研究.地球物理学报,第37卷,增刊,1994
[16]戴光明,罗延钟.用边界元法求积分方程数值.物探化探计算技术,1995年第4期
[17]张碧星,鲁来玉等.电张量格林并矢与三维电磁模拟.中南工业大学学报,第30卷第6期,1999
[18]孙紫英,胡玉平,鲍光淑.非均匀半空间三维边界积分方程数值模拟.物探与化探,VOL.24,NO.6,2000
[19]底青云,王妙月.积分方程法三维电阻率成像.地球物理学报,2001年第6期
[20]考夫曼A.A.,凯勒G.V.频率域和时间域电磁测深.地质出版社,1987
[21]程志平.电法勘探教程.冶金工业出版社,2007
[22]朴化荣,殷长春.频率测深正演问题滤波算法及人机联作反演.物化探计算技术,VOL.19,NO.2,P.137-147,1987
[23]汤洪志,黄辉明等.频率测深正演滤波算法及算例.华东地质学院学报,VOL.24,NO.2,P.114-118,2001
[24] Anderson W.L.,1979,Computer Program.Numerical integration of related Hankel transforms of orders 0 and 1 by adaptive digital filtering, Geophisics 44,1287-1305
[25] Tai Chen-To.Dyadic Green’s function in electromagnetic theory.International Text Book Co.,1971
[26] Cavalcance,G.P.S.,Rogers,D.A.and Giarola,A.J.,Analysis of electromagnetic wave propagation in multilayercd media using dyadic Green's functions, Radio Science. 19,503-508,1982
[27]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
[28]汤洪志,黄辉明等.频率测深正演滤波算法及算例.华东地质学院学报,VOL.24,NO.2,P.114-118,2001
[29]何继善编译,可控源音频大地地磁法.中南工业大学出版社. 1990
[30]石昆法,可控源音频大地地磁法理论与应用.科学出版社.1999
[31]罗延钟,张桂青,频率域激电法原理.地质出版社.1988
[32]张辉,李桐林,董瑞霞.体积分方程法模拟电偶源三维电磁响应.地球物理学进展,Vol.21,No.2,2006
[33]何长文,邵敏,何展翔.三维电磁技术研究与应用新进展.石油地球物理勘探,第39卷,增刊,2004
[34]陈明生,阎述,陶冬琴.电偶源频率电磁测深中的Ex分量.COAL GEOLOGY &EXPLORATION,第26期,P.60-66,1998
[35]陈小斌,赵国泽,马霄.大地电磁三维模型的一维二维反演近似问题研究.工程地球物理学报,Vol.3,No.1,2006
[36]石应骏等.大地电磁测深法教程.地震出版社1985.
[37]傅良魁.应用地球物理教程.地质出版社,1991
[38]傅良魁.电法勘探教程.地质出版社,1983
[39]陈乐寿,王光锷,大地电磁测深放.地质出版社,1990
[40]罗延钟,万乐,可控源音频大地电磁法.地质出版社.1996
[41]黄俊革,鲍光淑,阮百尧.坑道直流电阻率测深异常研究[J] .地球物理学报,48(1): P.222～228. 2005
[42]黄俊革,阮百尧,王家林.坑道直流电阻率法超前探测的快速反演.地球物理学报.3:620～624. 2007
[43]高致宏,闫述,王秀臣,张卜文.巷道超前(电法)探测的应用现状与存在问题[J] .煤炭技术,25(5) :120～121. 2006
[44]闫高翔.分辨率直流电法探测在隧道施工超前地质预报中的应用[J] .铁道勘查, (1) :42～44,2007
[45]李玉宝.矿井电法超前探测技术[J] .煤炭科学技术,30(2) : 1～3. 2002
[46]刘天放,李志聃.矿井地球物理勘探[M] .北京:煤炭工业出版社,1993.
[47]青雯井.下电法超前探测方法及其应用[J] .煤田地质与勘探,29(5):60～62.2001
[48]程久龙,王玉和等.巷道掘进中电阻率法超前探测原理与应用[J] .煤田地质与勘探, 28(4): 60～62. 2000
[49]岳建华,李志聃.矿井直流电法勘探中的巷道影响[J].煤炭学报,24(1):7～10,1999
[2] G.W.Hohmann.Three-dimentional induced polarization and electromagnetic modeling Geophysics,VOL.40,P.309-324,1975
[3]Dieter K.,et al.IP and resistivity type curyes for three-dimentional bodies. Geophysics,VOL.34,No.4
[4]徐世浙.点源二维地点剖面的边界元解法.桂林冶金地质学院学报, Vol.4. P.119-337,1984
[5]徐世浙.地球物理中的边界单元法.科学出版社1999
[6] Wannamaker P.E. Advances in three-dimentional magnetotellyric modeling Using Integral equations.Geophisics,1991,56(11):1716-1728
[7] Pridmore D F.three-dimentional modeling of electric and electromagnetic Data using the FEM.[ph.D.thesis],Utah:univ of Utah,1978
[8] Lee K.H.,Pridmore D.F. and Morrison H.F. Hybrid three-dimentional EM modeling scheme.Geophisics,Vol.46,No.5,1981
[9] Dey A. and Morrision H.F. Resistivity modeling for Arbitrarily Shaped 3-D Structure.Geophisics,Vol.44(4),P.753-780,1979
[10]徐世浙,赵生凯,楼云菊.水平地形三维电场的边界单元解法.物化探计算技术,VOL.6,NO.3
[11]周熙襄,钟本善.三维任意形体电法数值模拟的积分方程法.物化探计算技术,VOL.7,NO.22
[12]李晓波,朴化荣.两层大地中三维体的激发极化与电阻率响应的积分方程模拟.地球物理学报,VOL.31,NO.3,P.342-352,1988
[13]朴化荣,殷长春.频率测深水平磁场的正演计算及应用.物探化探计算技术,VOL.11,NO.3,P.204-213,1989
[14]殷长春.赤道向频率域电磁测深三维电磁模拟技术研究.石油地球物理学报,VOL.29,NO.6,P.746-753,757,1994
[15]殷长春,刘斌.瞬变电磁法三维问题正演及激电效应特征研究.地球物理学报,第37卷,增刊,1994
[16]戴光明,罗延钟.用边界元法求积分方程数值.物探化探计算技术,1995年第4期
[17]张碧星,鲁来玉等.电张量格林并矢与三维电磁模拟.中南工业大学学报,第30卷第6期,1999
[18]孙紫英,胡玉平,鲍光淑.非均匀半空间三维边界积分方程数值模拟.物探与化探,VOL.24,NO.6,2000
[19]底青云,王妙月.积分方程法三维电阻率成像.地球物理学报,2001年第6期
[20]考夫曼A.A.,凯勒G.V.频率域和时间域电磁测深.地质出版社,1987
[21]程志平.电法勘探教程.冶金工业出版社,2007
[22]朴化荣,殷长春.频率测深正演问题滤波算法及人机联作反演.物化探计算技术,VOL.19,NO.2,P.137-147,1987
[23]汤洪志,黄辉明等.频率测深正演滤波算法及算例.华东地质学院学报,VOL.24,NO.2,P.114-118,2001
[24] Anderson W.L.,1979,Computer Program.Numerical integration of related Hankel transforms of orders 0 and 1 by adaptive digital filtering, Geophisics 44,1287-1305
[25] Tai Chen-To.Dyadic Green’s function in electromagnetic theory.International Text Book Co.,1971
[26] Cavalcance,G.P.S.,Rogers,D.A.and Giarola,A.J.,Analysis of electromagnetic wave propagation in multilayercd media using dyadic Green's functions, Radio Science. 19,503-508,1982
[27]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
[28]汤洪志,黄辉明等.频率测深正演滤波算法及算例.华东地质学院学报,VOL.24,NO.2,P.114-118,2001
[29]何继善编译,可控源音频大地地磁法.中南工业大学出版社. 1990
[30]石昆法,可控源音频大地地磁法理论与应用.科学出版社.1999
[31]罗延钟,张桂青,频率域激电法原理.地质出版社.1988
[32]张辉,李桐林,董瑞霞.体积分方程法模拟电偶源三维电磁响应.地球物理学进展,Vol.21,No.2,2006
[33]何长文,邵敏,何展翔.三维电磁技术研究与应用新进展.石油地球物理勘探,第39卷,增刊,2004
[34]陈明生,阎述,陶冬琴.电偶源频率电磁测深中的Ex分量.COAL GEOLOGY &EXPLORATION,第26期,P.60-66,1998
[35]陈小斌,赵国泽,马霄.大地电磁三维模型的一维二维反演近似问题研究.工程地球物理学报,Vol.3,No.1,2006
[36]石应骏等.大地电磁测深法教程.地震出版社1985.
[37]傅良魁.应用地球物理教程.地质出版社,1991
[38]傅良魁.电法勘探教程.地质出版社,1983
[39]陈乐寿,王光锷,大地电磁测深放.地质出版社,1990
[40]罗延钟,万乐,可控源音频大地电磁法.地质出版社.1996
[41]黄俊革,鲍光淑,阮百尧.坑道直流电阻率测深异常研究[J] .地球物理学报,48(1): P.222～228. 2005
[42]黄俊革,阮百尧,王家林.坑道直流电阻率法超前探测的快速反演.地球物理学报.3:620～624. 2007
[43]高致宏,闫述,王秀臣,张卜文.巷道超前(电法)探测的应用现状与存在问题[J] .煤炭技术,25(5) :120～121. 2006
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