一种改进的阻抗张量分解方法及其应用
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摘要
由于近地表电性结构的非均匀性,会导致大地电磁阻抗张量产生畸变,为了描述地质体真实的电性结构特征,往往对大地电磁阻抗张量数据进行畸变分解,如果不对畸变的阻抗张量数据进行畸变消除,将会获得不正确的视电阻率和相位,影响后续的数据处理与解释。
本文从大地电磁场的畸变效应入手,分析了三维／一维与三维／二维电性结构模型下阻抗张量畸变的特征,讨论了畸变分解理论的数学和物理含义,总结了常用的大地电磁阻抗张量分解方法,通过对GB分解方法实现的探讨及分析现有方法的不足,提出了一种改进的阻抗张量分解方法,并推导了该方法实现的计算公式,给出了方法实现的具体流程。在计算过程中首先采用广义逆矩阵算法进行求解,并比较了牛顿法与广义逆算法的性能。然后模型验证表明SWIFT旋转在存在畸变干扰时并不能有效地估计阻抗张量及构造的主轴方向及主阻抗值,但可作为本方法的初值估计。利用依格尔斯特征态分析对各向异性因子进行了初值估计。最后对改进的算法进行了模型验证与比较分析并对实测数据进行了处理。编制的程序代码是在数值计算软件Matlab下面实现的,简洁明了。最后将此方法应用到实际的高频与低频大地电磁资料处理中,获得了反映地下真实电性结构特征的区域阻抗张量等参数,对所求得的结果进行了对比分析,得到比较满意的结果。
通过本文提出的方法获得的阻抗张量分解各种参数,可以定量分析各种畸变参数对区域阻抗张量产生的变化。若表征各向异性的畸变参数的变化,会使得走向主轴方向和倾向主轴方向发生被压缩或是被拉伸的变化；表征扭转和剪切的畸变参数正负值的变化,会使得阻抗张量发生顺时针或是逆时针的旋转。
For the impedance tensor distortion, resulted by horizontal galvanic heterogeneity near surface, it is necessary to decompose the distorted impedance tensor, in order to describe true electrical structural feature. If the distortion of the impedance data is not eliminated, the calculated apparent resistivity and phase may be wrong, which effluence on the result of data processing and interpretation.
In this thesis, based on the distorted impedance tensor feature of 3D/1D or 3D/2D model, we discuss several distortion decomposition methods. By analyzing the process of GB decomposition method, an improved method is introduced, using the generalized inverse matrix algorithm to calculate regional impedance from the data in which the distortions have been eliminated. A computer program to carry out this method is written with Matlab, succinct and clear. By forwardly calculating a theoretical model under the effluence of the distortion factors, we detect the error of the generalized inverse matrix algorithm and prove it to be effective. Finally, the improved method is applied into the calculation of regional impedance from some given magnetotelluric data, which proved to be practical and effective.
The method introduced in this thesis can be used to calculate the distortion factors. Therefore, the quantitative relation between the distortion factors and regional impedance can be studied. Gain enlarges or reduces the amplitude of tensor impedance. Principal axis direction of Strike is compressed and perpendicular axis is stretched if anisotropic parameter is a positive value. Oppositely, perpendicular axis is compressed, and Principal axis direction of Strike is stretched. Tensor impedance rotates in clockwise direction under positive twist parameter. Negative shear parameter makes tensor impedance rotating in anti-clockwise direction.
本文从大地电磁场的畸变效应入手,分析了三维／一维与三维／二维电性结构模型下阻抗张量畸变的特征,讨论了畸变分解理论的数学和物理含义,总结了常用的大地电磁阻抗张量分解方法,通过对GB分解方法实现的探讨及分析现有方法的不足,提出了一种改进的阻抗张量分解方法,并推导了该方法实现的计算公式,给出了方法实现的具体流程。在计算过程中首先采用广义逆矩阵算法进行求解,并比较了牛顿法与广义逆算法的性能。然后模型验证表明SWIFT旋转在存在畸变干扰时并不能有效地估计阻抗张量及构造的主轴方向及主阻抗值,但可作为本方法的初值估计。利用依格尔斯特征态分析对各向异性因子进行了初值估计。最后对改进的算法进行了模型验证与比较分析并对实测数据进行了处理。编制的程序代码是在数值计算软件Matlab下面实现的,简洁明了。最后将此方法应用到实际的高频与低频大地电磁资料处理中,获得了反映地下真实电性结构特征的区域阻抗张量等参数,对所求得的结果进行了对比分析,得到比较满意的结果。
通过本文提出的方法获得的阻抗张量分解各种参数,可以定量分析各种畸变参数对区域阻抗张量产生的变化。若表征各向异性的畸变参数的变化,会使得走向主轴方向和倾向主轴方向发生被压缩或是被拉伸的变化；表征扭转和剪切的畸变参数正负值的变化,会使得阻抗张量发生顺时针或是逆时针的旋转。
For the impedance tensor distortion, resulted by horizontal galvanic heterogeneity near surface, it is necessary to decompose the distorted impedance tensor, in order to describe true electrical structural feature. If the distortion of the impedance data is not eliminated, the calculated apparent resistivity and phase may be wrong, which effluence on the result of data processing and interpretation.
In this thesis, based on the distorted impedance tensor feature of 3D/1D or 3D/2D model, we discuss several distortion decomposition methods. By analyzing the process of GB decomposition method, an improved method is introduced, using the generalized inverse matrix algorithm to calculate regional impedance from the data in which the distortions have been eliminated. A computer program to carry out this method is written with Matlab, succinct and clear. By forwardly calculating a theoretical model under the effluence of the distortion factors, we detect the error of the generalized inverse matrix algorithm and prove it to be effective. Finally, the improved method is applied into the calculation of regional impedance from some given magnetotelluric data, which proved to be practical and effective.
The method introduced in this thesis can be used to calculate the distortion factors. Therefore, the quantitative relation between the distortion factors and regional impedance can be studied. Gain enlarges or reduces the amplitude of tensor impedance. Principal axis direction of Strike is compressed and perpendicular axis is stretched if anisotropic parameter is a positive value. Oppositely, perpendicular axis is compressed, and Principal axis direction of Strike is stretched. Tensor impedance rotates in clockwise direction under positive twist parameter. Negative shear parameter makes tensor impedance rotating in anti-clockwise direction.
引文
[1]Swift C W. A magnetotelluric investigation of an electrical conductivity in the South Western United States [J]. Ph.D.Thesis.M.I.T.Cambridge,Mass,1967.
[2]Bahr K. Geological noise in magnetotelluric data:a classification of distortion types [J]. Earth Planet Inter,1991,66(1):24-38.
[3]Bahr K. Interpretation of the magnetotelluric impedance tensor:regional induction and local telluric distortion [J]. Geophysics,1998,62(1):119-127.
[4]Lilley F E M. Magnetotelluric tensor decomposition:Part Ⅰ, Theory for a basic procedure [J]. Geophysics.1998,63(6):1885-1897.
[5]Lilley F E M. Magnetotelluric tensor decomposition:Part Ⅱ, Example of procedure [J]. Geophysics.1998,63(6):1898-1907.
[6]Lilley F E M. Magnetotelluric analysis using Mohr circles[J]. Geophysis.1993, 58(1):1498-1506.
[7]R. W. Groom, R. C. Bailey. Analytic investigations of the effects of near-surface three-dimension galvanic scatters on MT tensor decomposition[J]. Geophysics, 1995,56(4):496-518.
[8]R. W. Groom, R. C. Bailey. Decomposition of magnetotelluric impedance tensors in the presence of local 3-D galvanic distortion[J]. Geophysics,1989,94: 1913-1925.
[9]晋光文,王家映,王天生.一种大地电磁阻抗张量的计算方法[J].地球物理学,1982,25：650—659.
[10]晋光文.大地电磁测深反演问题综述[C].勘探地球物理专辑,第二辑(电磁测深),北京：地质出版社,1987.
[11]晋光文.大地电磁视电阻率和阻抗相位资料的联合解释[J].地震地质,1987,9(4)：81-86.
[12]晋光文.大地电磁阻抗相位资料的特点和应用[J].地震地质,1988,10(4)：159—168.
[13]晋光文.大地电磁阻抗实部资料和虚部资料的联合反演[J].地球物理学报,1990,33(专辑2)：332—339.
[14]晋光文.大地电磁资料联合反演评述[J].地球科学—中国地质大学学报,1990,15(增刊)：59—68.
[15]王立凤,晋光文,孙洁,白登海.一种简单的大地电磁阻抗张量畸变分解方法[J].西北地震学报,2001,23(2)：172-180.
[16]晋光文,孙洁,王继军.大地电磁(MT)阻抗张量的正则分解及其初步应用[J].地震地质,1998,20(3)：243—249.
[17]晋光文,孙洁,白登海,王立凤.川西—藏东大地电磁资料的阻抗张量畸变分解[J].地球物理学报,2003,46(4)：547—552.
[18]Eggers D E. An eigenstate formulation of the magnetotelluric impedance tensor[J]. Geophysics,1982,47:1204-1214.
[19]E. Yee and K. V. Paulson. The canonical decomposition and its relationship to the other forms of magnetotelluric impedance tensor analysis[J]. Journal of Geophysics,1987,61(3):173—189.
[20]E. Yee and K. V. Paulson. Canonical decomposition of the telluric transfer tensor[J]. Journal of Geophysics,1987,61(3):190-199.
[21]刘志,王光锷.MT阻抗张量的正则分解和参数重建[J].现代地质,1998,12(2)：283-288.
[22]刘志.MT阻抗张量的正则分解和参数重建及实用数据处理系统[硕士论文].北京：中国地质大学,1994.
[23]尹兵祥,宋维琪.大地电磁(MT)阻抗张量的正则分解及其应用探讨[J].石油地球物理勘探,2000,35(1)：72—75.
[24]尹兵祥,王光锷.大地电磁阻抗张量正则分解的地质含义分析[J].地球物理学报,2001,44(2)：279—288.
[25]胡玉平,鲍光淑,贾继标.基于畸变3个因子的MT畸变曲线改正方法与应用[J].地质与勘探,2005,41(6)：75—79.
[26]T. Grant Caldwell, Hugh M. Bibby and Colin Brown. The magnetotelluric phase tensor[J]. Geophysics,2004,158:457-469.
[27]晋光文.大地电磁阻抗张量的畸变与分解[M].北京：地震出版社,2006.
[28]La Torraca. G A, Madden T R and Korringa J. An analysis of the magnetotelluric impedance for three-dimensional conductivity structure[J]. Geophysics,1986, 51(9):1819-1829.
[29]何继善.可控源音频大地电磁法[M].长沙：中南工业大学出版社,1990.
[30]苏发,汤井田,何继善等.电磁测深中视电阻率假异常现象分析[J].中国有色金属学报,1995,5(4)：14.
[31]苏鸿尧,何展翔.表层电性不均匀对大地电磁测深曲线的畸变研究[J].地质科技情报,2000,19(3)：103.
[32]陈清礼,张翔,胡文宝.南方碳酸盐岩区大地电磁测深曲线静态偏移校正[J].江汉石油学院学报,1999,21(3)：30—32.
[33]黄潜生,王友胜,汪卫毛.大地电磁曲线校正技术在六盘山盆地研究中的应用 [J].江汉石油学院学报,2004,26(3)：76—78.
[34]阎述,陈明生.频率域电磁测深的静态偏移及校正方法[J].石油地球物理勘探,1996,31(2)：238—247.
[35]Zonge KL. Internal company report on removal of static shift effect[J]. Geophysical Prospecting,1985.
[36]Mallat S, Hwang W L. Singularity detection and processing wit h wavelets [J]. IEEE Trans On Information theory,1992,38:617-643.
[37]何展翔.相权静校正[C].电磁方法研究与进展,1993：117—124.
[38]Zonge K L. Comparison of time frequency and phase measurement in IP[J].Geophysical Prospecting,1972,20:626-648.
[39]方文藻,李予国等.用瞬变电磁测深校正MT静态效应[C].电磁方法研究与进展,1993：111-116.
[40]王若,王妙月.可控源音频大地电磁数据的反演方法[J].地球物理学进展,2003,18(2)：197—202.
[41]解海军,陈明生,阎述.利用小波分析压制静态效应[J].煤田地质与勘探,1998,26(4)：61.
[42]杨生.EMAP处理方法在CSAMT勘查中的应用[J].有色金属矿产与勘查,1994,3(6)：345.
[43]宋守根、汤井田、何继善.小波分析与电磁测深中静态效应的识别、分离及压制[J].地球物理学报,1995,38(1)：120—128.
[44]李金铭,罗延钟.电法勘探新进展[M].北京：地质出版社,1996：37—41.
[45]Gersztenkorn A, Marfurt K J. Eigenstructure-based coherence computation as an aid to 3-D structural and stratigphicmapping[J].Geophysics,1999,64(5):14-68.
[46]王立凤,晋光文,孙洁,白登海.电磁响应函数的旋转不变量特征[J].物探化探计算计算,2000,22(4)：306—321.
[47]杨长福,林长佑,徐世浙.大地电磁GB张量分解法的改进[J].地球物理学报,2002,45(增刊)：356—364.
[48]胡玉平.大地电磁阻抗的地质噪声的畸变研究及校正方法[硕士论文].长沙：中南大学,2002.
[49]A G Jones, Gray W. Static shift of magnetotelluric data and its removal in a sedimentary basic environment [J]. Geophysics,1988,49(7):967-978.
[50]李艳青.张量阻抗分解的实现及在藏南构造走向研究中的应用[硕士论文].北京：中国地质大学,2008.
[2]Bahr K. Geological noise in magnetotelluric data:a classification of distortion types [J]. Earth Planet Inter,1991,66(1):24-38.
[3]Bahr K. Interpretation of the magnetotelluric impedance tensor:regional induction and local telluric distortion [J]. Geophysics,1998,62(1):119-127.
[4]Lilley F E M. Magnetotelluric tensor decomposition:Part Ⅰ, Theory for a basic procedure [J]. Geophysics.1998,63(6):1885-1897.
[5]Lilley F E M. Magnetotelluric tensor decomposition:Part Ⅱ, Example of procedure [J]. Geophysics.1998,63(6):1898-1907.
[6]Lilley F E M. Magnetotelluric analysis using Mohr circles[J]. Geophysis.1993, 58(1):1498-1506.
[7]R. W. Groom, R. C. Bailey. Analytic investigations of the effects of near-surface three-dimension galvanic scatters on MT tensor decomposition[J]. Geophysics, 1995,56(4):496-518.
[8]R. W. Groom, R. C. Bailey. Decomposition of magnetotelluric impedance tensors in the presence of local 3-D galvanic distortion[J]. Geophysics,1989,94: 1913-1925.
[9]晋光文,王家映,王天生.一种大地电磁阻抗张量的计算方法[J].地球物理学,1982,25：650—659.
[10]晋光文.大地电磁测深反演问题综述[C].勘探地球物理专辑,第二辑(电磁测深),北京：地质出版社,1987.
[11]晋光文.大地电磁视电阻率和阻抗相位资料的联合解释[J].地震地质,1987,9(4)：81-86.
[12]晋光文.大地电磁阻抗相位资料的特点和应用[J].地震地质,1988,10(4)：159—168.
[13]晋光文.大地电磁阻抗实部资料和虚部资料的联合反演[J].地球物理学报,1990,33(专辑2)：332—339.
[14]晋光文.大地电磁资料联合反演评述[J].地球科学—中国地质大学学报,1990,15(增刊)：59—68.
[15]王立凤,晋光文,孙洁,白登海.一种简单的大地电磁阻抗张量畸变分解方法[J].西北地震学报,2001,23(2)：172-180.
[16]晋光文,孙洁,王继军.大地电磁(MT)阻抗张量的正则分解及其初步应用[J].地震地质,1998,20(3)：243—249.
[17]晋光文,孙洁,白登海,王立凤.川西—藏东大地电磁资料的阻抗张量畸变分解[J].地球物理学报,2003,46(4)：547—552.
[18]Eggers D E. An eigenstate formulation of the magnetotelluric impedance tensor[J]. Geophysics,1982,47:1204-1214.
[19]E. Yee and K. V. Paulson. The canonical decomposition and its relationship to the other forms of magnetotelluric impedance tensor analysis[J]. Journal of Geophysics,1987,61(3):173—189.
[20]E. Yee and K. V. Paulson. Canonical decomposition of the telluric transfer tensor[J]. Journal of Geophysics,1987,61(3):190-199.
[21]刘志,王光锷.MT阻抗张量的正则分解和参数重建[J].现代地质,1998,12(2)：283-288.
[22]刘志.MT阻抗张量的正则分解和参数重建及实用数据处理系统[硕士论文].北京：中国地质大学,1994.
[23]尹兵祥,宋维琪.大地电磁(MT)阻抗张量的正则分解及其应用探讨[J].石油地球物理勘探,2000,35(1)：72—75.
[24]尹兵祥,王光锷.大地电磁阻抗张量正则分解的地质含义分析[J].地球物理学报,2001,44(2)：279—288.
[25]胡玉平,鲍光淑,贾继标.基于畸变3个因子的MT畸变曲线改正方法与应用[J].地质与勘探,2005,41(6)：75—79.
[26]T. Grant Caldwell, Hugh M. Bibby and Colin Brown. The magnetotelluric phase tensor[J]. Geophysics,2004,158:457-469.
[27]晋光文.大地电磁阻抗张量的畸变与分解[M].北京：地震出版社,2006.
[28]La Torraca. G A, Madden T R and Korringa J. An analysis of the magnetotelluric impedance for three-dimensional conductivity structure[J]. Geophysics,1986, 51(9):1819-1829.
[29]何继善.可控源音频大地电磁法[M].长沙：中南工业大学出版社,1990.
[30]苏发,汤井田,何继善等.电磁测深中视电阻率假异常现象分析[J].中国有色金属学报,1995,5(4)：14.
[31]苏鸿尧,何展翔.表层电性不均匀对大地电磁测深曲线的畸变研究[J].地质科技情报,2000,19(3)：103.
[32]陈清礼,张翔,胡文宝.南方碳酸盐岩区大地电磁测深曲线静态偏移校正[J].江汉石油学院学报,1999,21(3)：30—32.
[33]黄潜生,王友胜,汪卫毛.大地电磁曲线校正技术在六盘山盆地研究中的应用 [J].江汉石油学院学报,2004,26(3)：76—78.
[34]阎述,陈明生.频率域电磁测深的静态偏移及校正方法[J].石油地球物理勘探,1996,31(2)：238—247.
[35]Zonge KL. Internal company report on removal of static shift effect[J]. Geophysical Prospecting,1985.
[36]Mallat S, Hwang W L. Singularity detection and processing wit h wavelets [J]. IEEE Trans On Information theory,1992,38:617-643.
[37]何展翔.相权静校正[C].电磁方法研究与进展,1993：117—124.
[38]Zonge K L. Comparison of time frequency and phase measurement in IP[J].Geophysical Prospecting,1972,20:626-648.
[39]方文藻,李予国等.用瞬变电磁测深校正MT静态效应[C].电磁方法研究与进展,1993：111-116.
[40]王若,王妙月.可控源音频大地电磁数据的反演方法[J].地球物理学进展,2003,18(2)：197—202.
[41]解海军,陈明生,阎述.利用小波分析压制静态效应[J].煤田地质与勘探,1998,26(4)：61.
[42]杨生.EMAP处理方法在CSAMT勘查中的应用[J].有色金属矿产与勘查,1994,3(6)：345.
[43]宋守根、汤井田、何继善.小波分析与电磁测深中静态效应的识别、分离及压制[J].地球物理学报,1995,38(1)：120—128.
[44]李金铭,罗延钟.电法勘探新进展[M].北京：地质出版社,1996：37—41.
[45]Gersztenkorn A, Marfurt K J. Eigenstructure-based coherence computation as an aid to 3-D structural and stratigphicmapping[J].Geophysics,1999,64(5):14-68.
[46]王立凤,晋光文,孙洁,白登海.电磁响应函数的旋转不变量特征[J].物探化探计算计算,2000,22(4)：306—321.
[47]杨长福,林长佑,徐世浙.大地电磁GB张量分解法的改进[J].地球物理学报,2002,45(增刊)：356—364.
[48]胡玉平.大地电磁阻抗的地质噪声的畸变研究及校正方法[硕士论文].长沙：中南大学,2002.
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