对称非各向同性体大地电磁法二维异常特征
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摘要
大量观测资料表明,地下介质的物性普遍存在非各向同性现象,只有建立非各向同性模型才能真实地反应地下介质情况。在分析前人研究成果的基础上,从实际地质情况出发,以层状介质的电学性质为基础引入非各向同性系数到对称非各向同性体的研究当中,推导出对称非各向同性体二维大地电磁场的变分方程,实现了模拟对称非各向同性体的有限单元法。将计算结果与Pek的有限差分法的计算结果进行对比验证了程序的正确性。通过固定非各向同性系数在不同倾角下的模型,说明倾角对非各向同性效应的影响;通过固定倾角在不同非各向同性系数下的模型,说明非各向同性系数对非各向同性效应的影响;通过不同倾角和不同非各向同性系数模型的正演拟断面图,更加形象地展示两者与非各向同性效应之间的关系。
Lots of observational data have indicated that anisotropic physical properties are common in rocks in the depth. This requires the construction of anisotropic models to obtain a true reflection of the underground medium. The basis of the present study is a review of previous research results and an investigation of the electrical properties of a layered medium representing actual geological conditions. For a symmetrical anisotropic body,an anisotropy coefficient is proposed,together with an equation for the variation of the Earth's electromagnetic field regarded as two-dimensional. Finally,a finite element simulation of a symmetrical anisotropic body is described.The finite element calculation results are compared with finite difference results to verify the accuracy of the FE program. Three sets of model conditions are considered: (1) fixed anisotropy coefficient and different dip angles,showing the effect of dip angle on an anisotropic body; (2) fixed dip angle and different anisotropy coefficients,showing the effect of the anisotropy coefficient on an anisotropic body; (3) different dip angles and different anisotropy coefficients. Forward pseudo section maps clearly demonstrate the relationship between dip angle,anisotropy coefficient and their anisotropic effect.
Lots of observational data have indicated that anisotropic physical properties are common in rocks in the depth. This requires the construction of anisotropic models to obtain a true reflection of the underground medium. The basis of the present study is a review of previous research results and an investigation of the electrical properties of a layered medium representing actual geological conditions. For a symmetrical anisotropic body,an anisotropy coefficient is proposed,together with an equation for the variation of the Earth's electromagnetic field regarded as two-dimensional. Finally,a finite element simulation of a symmetrical anisotropic body is described.The finite element calculation results are compared with finite difference results to verify the accuracy of the FE program. Three sets of model conditions are considered: (1) fixed anisotropy coefficient and different dip angles,showing the effect of dip angle on an anisotropic body; (2) fixed dip angle and different anisotropy coefficients,showing the effect of the anisotropy coefficient on an anisotropic body; (3) different dip angles and different anisotropy coefficients. Forward pseudo section maps clearly demonstrate the relationship between dip angle,anisotropy coefficient and their anisotropic effect.
引文
[1]李金铭.地电场与电法勘探[M].北京:地质出版社,2005.Li J M.Electric and electrical prospecting[M].Beijing:Geology Publishing House,2005.
[2]内吉J G,萨拉夫P D.大地介质电磁各向异性问题[M].邹永辉,陈德志,译.北京:地质出版社,1992.Negi J G,Saraf P D(translated by Zou Y H,Chen D Z).Anisotropy in geoelectromagnetism[M].Beijing:Geology Publishing House,1992.
[3]O'Brueb D P,Morrison H F.Electromagnetic fields in an N-layered anisotropic half-space[J].Geophysics,1967,32(4):668-677.
[4]Pek J,Santos F A M.Magnetotelluric impedances and parametric sensitivities for 1-D anisotropic layered media[J].Computers&Geosciences,2002,28:939-950.
[5]霍光谱,胡祥云,方慧,等.层状各向异性介质大地电磁联合反演研究[J].物理学报,2012,61(12):129101(1-10).Huo G P,Hu X Y,Fang H,et al.Magnetotelluric joint inversion for anisotropic conductivities in layered media[J].Acta Physica Sinica,2012,61(12):129101(1-10).
[6]Reddy I K,Rankin D.Magnetotelluric response of latterlly inhomogeneous and anisotropic media[J].Geophysics,1975,40(6):1035-1045.
[7]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元解法[J].地震学报,1985,7(1):80-90.Xu S Z,Zhao S K.Solution of magnetotelluric field equations for a two-dimensional,anisotropic geoelectric section by the finite element method[J].Acta Seismologica Sinica,1985,7(1):80-90.
[8]Pek J,Verner T.Finite-difference modeling of magnetotelluric fields in two-dimensional anisotropic media[J].Geophysics Journal International,1997,128(1):505-521.
[9]Li Y.A finite-element algorithm for electromagnetic induction in two-dimensional anisotropic conductivity structures[J].Geophysics Journal International,2002,148:389-401.
[10]Li Y,Key K.2D marine controlled-source electromagnetic modeling,part 1:an adaptive finite-element algorithm[J].Geophysics,2007,72(2):WA51-WA62.
[11]Li Y,Pek J.Adaptive finite element modelling of two-dimensional magnetotelluric fields in general anisotropic media[J].Geophysics Journal International,2008,175:942-954.
[12]林长佑,武玉霞,杨长福,等.水平层状对称各向异性介质的大地电磁资料反演[J].地球物理学报,1996,39(S1):342-348.Lin C Y,Wu Y X,Yang C F,et al.Magnetotelluric inversion for symmetrically anisotropic layered medium[J].Chinese Journal of Geophysics,1996,39(S1):342-348.
[13]霍光谱,胡祥云,刘敏.各向异性介质中大地电磁正演研究综述[J].地球物理学进展,2011,26(6):1976-1982.Huo G P,Hu X Y,Liu M.Review of the forward modeling of magnetotelluric in the anisotropy medium research[J].Progress in Geophysics,2011,26(6):1976-1982.
[14]胡祥云,霍光谱,高锐,等.大地电磁各向异性二维模拟及实例分析[J].地球物理学报,2013,56(12):4268-4277.Hu X Y,Huo G P,Gao R,et al.The magnetotelluric anisotropic two-dimensional simulation and case analysis[J].Chinese Journal of Geophysics,2013,56(12):4268-4277.
[15]徐世浙.地球物理中的有限单元法[M].北京:科学出版社,1994.Xu S Z.The finite element method in geophysics[M].Beijing:Science Press,1994.
[2]内吉J G,萨拉夫P D.大地介质电磁各向异性问题[M].邹永辉,陈德志,译.北京:地质出版社,1992.Negi J G,Saraf P D(translated by Zou Y H,Chen D Z).Anisotropy in geoelectromagnetism[M].Beijing:Geology Publishing House,1992.
[3]O'Brueb D P,Morrison H F.Electromagnetic fields in an N-layered anisotropic half-space[J].Geophysics,1967,32(4):668-677.
[4]Pek J,Santos F A M.Magnetotelluric impedances and parametric sensitivities for 1-D anisotropic layered media[J].Computers&Geosciences,2002,28:939-950.
[5]霍光谱,胡祥云,方慧,等.层状各向异性介质大地电磁联合反演研究[J].物理学报,2012,61(12):129101(1-10).Huo G P,Hu X Y,Fang H,et al.Magnetotelluric joint inversion for anisotropic conductivities in layered media[J].Acta Physica Sinica,2012,61(12):129101(1-10).
[6]Reddy I K,Rankin D.Magnetotelluric response of latterlly inhomogeneous and anisotropic media[J].Geophysics,1975,40(6):1035-1045.
[7]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元解法[J].地震学报,1985,7(1):80-90.Xu S Z,Zhao S K.Solution of magnetotelluric field equations for a two-dimensional,anisotropic geoelectric section by the finite element method[J].Acta Seismologica Sinica,1985,7(1):80-90.
[8]Pek J,Verner T.Finite-difference modeling of magnetotelluric fields in two-dimensional anisotropic media[J].Geophysics Journal International,1997,128(1):505-521.
[9]Li Y.A finite-element algorithm for electromagnetic induction in two-dimensional anisotropic conductivity structures[J].Geophysics Journal International,2002,148:389-401.
[10]Li Y,Key K.2D marine controlled-source electromagnetic modeling,part 1:an adaptive finite-element algorithm[J].Geophysics,2007,72(2):WA51-WA62.
[11]Li Y,Pek J.Adaptive finite element modelling of two-dimensional magnetotelluric fields in general anisotropic media[J].Geophysics Journal International,2008,175:942-954.
[12]林长佑,武玉霞,杨长福,等.水平层状对称各向异性介质的大地电磁资料反演[J].地球物理学报,1996,39(S1):342-348.Lin C Y,Wu Y X,Yang C F,et al.Magnetotelluric inversion for symmetrically anisotropic layered medium[J].Chinese Journal of Geophysics,1996,39(S1):342-348.
[13]霍光谱,胡祥云,刘敏.各向异性介质中大地电磁正演研究综述[J].地球物理学进展,2011,26(6):1976-1982.Huo G P,Hu X Y,Liu M.Review of the forward modeling of magnetotelluric in the anisotropy medium research[J].Progress in Geophysics,2011,26(6):1976-1982.
[14]胡祥云,霍光谱,高锐,等.大地电磁各向异性二维模拟及实例分析[J].地球物理学报,2013,56(12):4268-4277.Hu X Y,Huo G P,Gao R,et al.The magnetotelluric anisotropic two-dimensional simulation and case analysis[J].Chinese Journal of Geophysics,2013,56(12):4268-4277.
[15]徐世浙.地球物理中的有限单元法[M].北京:科学出版社,1994.Xu S Z.The finite element method in geophysics[M].Beijing:Science Press,1994.
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