复杂地电结构AMT有限元数值模拟
摘要
实际野外环境,地表起伏不平,地下地质结构十分复杂,往往是向斜、背斜、断层等复杂地质体的组合,这些都使得数据解释十分困难。音频大地电磁(Audio-frequency magnetotelluric,简称“AMT”)以大地电磁理论为基础,研究音频段电磁信号的响应,正好能很好的反映地表的电阻率分布信息,因此,实现复杂地电结构下AMT的数值正演模拟对实践就显得十分必要。
论文采用矩形网格双线性插值的有限单元法,编制了AMT的二维正演程序；研究了截断边界及网格尺寸对有限元计算精度的影响；模拟了水平地面条件下,复杂地电结构以及纯山脊和山谷的AMT响应；实现了起伏地形下三层背斜和向斜的数值模拟。
研究表明：网格剖分对求解极为重要,左右边界对一维介质的计算无影响,可不用放置在无穷远；对于二维介质,左右边界取目标体尺寸的5倍以上就能显著削弱其影响；下边界的远近及网格横纵比不会影响计算精度；纵向网格尺寸越小精度越高,在满足最大相对误差小于1%的前提下,一个趋肤深度范围内,线性插值用四个网格就可以达到要求,地表以下连续三个网格不能跨越物性分界面。TM模式的横向分辨能力高于TE模式,水平地形下的复杂地电结构的视电阻率断面图的等值线地形并不是真实构造的反映。纯地形的影响不可忽略,TE模式总是在山脊处出现极大值,在山谷处出现极小值,TM模式则相反。三层的背斜或向斜的视电阻率曲线剖面图和拟断面图的特征是有规律可循的,在不做地形改正的前提下,按照其视电阻率拟断面图中两种极化模式的等值线所呈现不同形状,以及所反映的幅值信息,可以对复杂地电结构做定性的分析。为指导实践提供了有利的依据。
As the geological structure is very complex, not only for terrain but also for the structure underground, often syncline, anticline, fault and other complex combination of geological bodies, which make AMT forward modeling very difficult. Audio-frequency magnetotelluric (AMT) based on the magnetotelluric (MT) theory is researched on the response to the audio section of electromagnetic signals. It is necessary to achieve the simulation of AMT data under complex structure to practice.
The rectangular elements with bilinear interpolation finite element method (FEM) was used to compiled the two dimensional AMT forward modeling program in this paper. Meanwhile, the effects of grid size and its boundaries to the accuracy of MT forward modeling using FEM were discussed. Besides that, complex geological structure responses with terrain and without terrain were detailed simulated in this paper, so were anticline and syncline models.
The results show that, for one-dimensional media, left and right boundaries are not necessary to place at infinity, for two dimensional media, the effects of boundaries could be weakened seriously only laid at 5 times the size of object distance. Both lower boundary and ratio of horizontal to vertical have little effect on accuracy; vertical grid is closely related to the smallest skin depth and it can not larger than 1/4 skin depth to make sure maximum relative less than 1% for bilinear interpolation. There consecutive elements below the surface should not cross the interface. The horizontal resolution of TM mode is higher than TE mode and the shape of isoline about apparent resistivity section is not a true reflection of structure. Topography can not be ignored. The maximum value is always on the ridge and minimum on the valley for TE mode, however, TM mode on the contrary. The apparent resistivity profiles and their pseudo-sections on anticline and syncline of three layers are regular. Without terrain correction, referred to the characteristics of apparent resistivity profiles and their pseudo-sections, it can make a qualitative analysis and be guided for practice.
论文采用矩形网格双线性插值的有限单元法,编制了AMT的二维正演程序；研究了截断边界及网格尺寸对有限元计算精度的影响；模拟了水平地面条件下,复杂地电结构以及纯山脊和山谷的AMT响应；实现了起伏地形下三层背斜和向斜的数值模拟。
研究表明：网格剖分对求解极为重要,左右边界对一维介质的计算无影响,可不用放置在无穷远；对于二维介质,左右边界取目标体尺寸的5倍以上就能显著削弱其影响；下边界的远近及网格横纵比不会影响计算精度；纵向网格尺寸越小精度越高,在满足最大相对误差小于1%的前提下,一个趋肤深度范围内,线性插值用四个网格就可以达到要求,地表以下连续三个网格不能跨越物性分界面。TM模式的横向分辨能力高于TE模式,水平地形下的复杂地电结构的视电阻率断面图的等值线地形并不是真实构造的反映。纯地形的影响不可忽略,TE模式总是在山脊处出现极大值,在山谷处出现极小值,TM模式则相反。三层的背斜或向斜的视电阻率曲线剖面图和拟断面图的特征是有规律可循的,在不做地形改正的前提下,按照其视电阻率拟断面图中两种极化模式的等值线所呈现不同形状,以及所反映的幅值信息,可以对复杂地电结构做定性的分析。为指导实践提供了有利的依据。
As the geological structure is very complex, not only for terrain but also for the structure underground, often syncline, anticline, fault and other complex combination of geological bodies, which make AMT forward modeling very difficult. Audio-frequency magnetotelluric (AMT) based on the magnetotelluric (MT) theory is researched on the response to the audio section of electromagnetic signals. It is necessary to achieve the simulation of AMT data under complex structure to practice.
The rectangular elements with bilinear interpolation finite element method (FEM) was used to compiled the two dimensional AMT forward modeling program in this paper. Meanwhile, the effects of grid size and its boundaries to the accuracy of MT forward modeling using FEM were discussed. Besides that, complex geological structure responses with terrain and without terrain were detailed simulated in this paper, so were anticline and syncline models.
The results show that, for one-dimensional media, left and right boundaries are not necessary to place at infinity, for two dimensional media, the effects of boundaries could be weakened seriously only laid at 5 times the size of object distance. Both lower boundary and ratio of horizontal to vertical have little effect on accuracy; vertical grid is closely related to the smallest skin depth and it can not larger than 1/4 skin depth to make sure maximum relative less than 1% for bilinear interpolation. There consecutive elements below the surface should not cross the interface. The horizontal resolution of TM mode is higher than TE mode and the shape of isoline about apparent resistivity section is not a true reflection of structure. Topography can not be ignored. The maximum value is always on the ridge and minimum on the valley for TE mode, however, TM mode on the contrary. The apparent resistivity profiles and their pseudo-sections on anticline and syncline of three layers are regular. Without terrain correction, referred to the characteristics of apparent resistivity profiles and their pseudo-sections, it can make a qualitative analysis and be guided for practice.
引文
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[2]Tikhonov A H. Determination of the electrical characteristics of the deep strata of the Earth's crust. Dokl Akad. Nauk SSR,1950,73:295～311
[3]Saraev A K, Pertel M I, Malkin Z M. Monitoring of tidal variations of apparent resistivity. Geologica acta: an international earth science journal,2010,8(1):5～13
[4]田宗勇,姚姚,赵晓明.大地电磁法在沪蓉国道地质勘察中的应用.长江科学院院报,2007,24(2)：55～57
[5]Chiang C W, Martyn, Chen, C S, et al. Fault Zone Resistivity Structure and Monitoring at the Taiwan Chelungpu Drilling Project (TCDP). Terr. Atmos. Ocean. Sci.,2008,19 (5):473～479
[6]高利华.大地电磁测深在北天山前缘油气勘探中的应用.石油物探,2006,45(4)：427～431
[7]Garcia X, Jones A G. Atmospheric sources for audio-magnetotelluric (AMT) sounding. Geophysics,2002,67 (2):448～459
[8]Farquharson C G, Craven J A. Three-dimensional inversion of magnetotelluric data for mineral exploration:An example from the McArthur River uranium deposit, Saskatchewan, Canada. Journal of Applied Geophysics,2009,68 (4):450～458
[9]Parry J R, Ward S H. Electromagnetic scattering from cylinders investigation of finite-element modeling for electromagnetic data in three dimensions. Geophysics, 1971,36:67～100
[10]Ting, Hohmann. S C. Ting and G.W. Hohmann, Integral equation modeling of three-dimensional magnetotelluric response. Geophysics,1981,46:182～197
[11]Wannamaker P E, Hohmann G W, Ward S H. Magnetotelluric responses of two-dimensional bodies in layered earths. Geophysics,1984,49:1517～1533
[12]Ku C C, Hsieh M S, Lim, S H. The topographic effect on electromagnetic fields. Can. J. Earth Sci.,1973,10:645～656
[13]Ngoc P V. Magnetotelluric survey of the mount Meager region of the Squamish Valley (British Columbia). Geomagnetic Service of Canada, Earth Physics Branch of the Dept.of Energy, Mines and Resources Canada, of Rep.1980,80-8-E
[14]Jiracek G R. Numerical comparisons of a modified Rayleigh approach with other surface scattering solutions. Trans., Inst. Electo. Electron. Eng. Anten. Prop.,1973, 393～396
[15]Kojima R K. Application of the Rayleigh-FFT Technique to Magnetotelluric Modeling. M.S. Thesis, San Diego State University,1985
[16]Jiracek G R, Redding R P, Kojima R K. Application of the Rayleigh-FFT technique to magnetotelluric modeling and correction. M.S. Thesis, San Diego State University,1986
[17]Pek J. Finite-difference modeling of magnetotelluric fields in two-dimensional anisotropic media. Geophysical Journal International,1997
[18]Mackie R L, Smith J T. Three-dimensional electromagnetic modeling using finite difference equations:The magnetotelluric example. Radio Science,1994,29: 923～975
[19]徐世浙,王庆乙,王军.用边界单元法模拟二维地形对大地电磁场的影响.地球物理学报,1992,35(3)：380～388
[20]徐世浙,阮百尧,周辉,等.用边界元法模拟三维地形对MT场的影响.科学通报,1996,14(23)：2162-2164
[21]Ruan B Y, Xu S Z, Xu Z F. Modeling the 3D Terrain Effect on MT by the Boundary Element Method. Journal of China University of Geosciences,2006,17 (2): 163～127
[22]阮百尧,徐世浙,徐志锋.三维地形大地电磁场的边界元模拟方法.地球科学(中国地质大学学报),2007,32(1)：163～167
[23]Coggon G H. Electromagnetic and electrical modeling by the finite element. Geophysics,1971,36:132～155
[24]Rodi W L A technique for improving the accuracy of finite element solutions for magnetotelluric data. Geophysical Journal of the Royal Astronomical,1976, E34-458
[25]Rijo L. Modeling of electric and electromagnetic data. Ph.D. Thesis Utah Univ. 1977
[26]Wannamaker P E, Stodt J A, Rijo L. PW2D-Finite element program for solution of magnetotelluric responses of two-dimensional earth resistivity structure. Univ. of Utah Res. Inst. Rep, ESL,1985
[27]Wannamaker P E, Stodt J A, Rijo L. Two-dimensional topographic responses in magnetotellurics modeled using finite elements. Geophysics,1986,51:2131～2144
[28]Mogi T. Three-dimensional modeling of magnetotelluric data using finite element method. Journal of Applied Geophysics,1996,35:185～189
[29]Mitsuhata Y, Uchida T.3D magnetotelluric modeling using the T-Ω finite-element method. Geophysics,2004,69:108～119
[30]陈乐寿.有限元法在大地电磁场正演计算中的应用及改进.地球科学,1981,(2)：241～260
[31]徐世浙,刘斌.电导率分层连续变化的水平层的大地电磁正演。地球物理学报,1995,38(2)：262～268
[32]徐世浙,李予国,刘斌.电导率分块连续变化的二维MT有限元模拟_1.高校地质学报.1995,1(2)：65～73
[33]徐世浙,李予国,刘斌.电导率分块连续变化的二维MT有限元模拟_2.高校地质学报.1996,2(4)：448～452
[34]阮百尧,徐世浙.电导率分块线性变化二维地电断面电阻率测深有限元数值模拟.中国地质大学报,1998,23(3)：303～307
[35]陈小斌.有限元直接迭代算法.物探化探计算技术.1999,21(2)：165～171
[36]杨长福.大地电磁二维对称各向异性介质的有限元数值模拟.西北地震学报,1997,19(2)：27～33
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