基于节点有限元与矢量有限元的可控源电磁三维正演对比
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摘要
基于电场的可控源电磁三维有限元正演模拟早期主要采用节点有限元法,但因存在伪解问题而影响求解效率和精度;避免出现伪解的有效手段之一是采用基于棱边元的矢量有限元法,该方法近年在电磁三维模拟中逐步得到应用推广。为了更具体地了解两种方法在三维电磁正演中的实际应用效果,开展了两种方法的对比试验。首先从边值问题的建立进行讨论,之后分别通过一个水平层状介质模型和单一低阻体模型对两种方法的正演结果及效率进行比较。实际模拟结果表明:同等条件下,矢量有限元法计算精度更高,但其计算速度较节点有限元法约慢一半。
In the early stage,the nodal element was mainly used for the forward modeling of the 3D controlled-source electromagnetic(EM)responses,but its spurious mode affected calculation efficiency and solution accuracy.The edge-based finite element method is increasingly adopted in the 3D EM modeling since it can avoid spurious solutions.To study details of the efficiency and accuracy between these two methods,comparison experiments are carried out.First the construction of the boundary-value problem is discussed.Then the forward modeling based on these two methods are achieved on both a horizontal-layered model and a single low-resistivity body model.Our comparison experiments show that under the same modeling condition,the result accuracy with the edge-based finite element is better than that with the nodal element while the edge element is slower than the nodal element as the first one spends about twice of calculation time of the latter one.
In the early stage,the nodal element was mainly used for the forward modeling of the 3D controlled-source electromagnetic(EM)responses,but its spurious mode affected calculation efficiency and solution accuracy.The edge-based finite element method is increasingly adopted in the 3D EM modeling since it can avoid spurious solutions.To study details of the efficiency and accuracy between these two methods,comparison experiments are carried out.First the construction of the boundary-value problem is discussed.Then the forward modeling based on these two methods are achieved on both a horizontal-layered model and a single low-resistivity body model.Our comparison experiments show that under the same modeling condition,the result accuracy with the edge-based finite element is better than that with the nodal element while the edge element is slower than the nodal element as the first one spends about twice of calculation time of the latter one.
引文
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[21]严波,李予国,韩波等.任意方位电偶源的MCSEM电磁场三维正演.石油地球物理勘探,2017,52(4):859-868.Yanbo,Li Yuguo,Hanbo et al.The 3Dforward modeling of the EM field for MCSEM using the electrical dipole source with arbitrary azimuth.OGP,2017,52(4):859-868.
[22]李建慧,胡祥云,陈斌等.复杂形态回线源激发电磁场的矢量有限元解.石油地球物理勘探,2017,52(6):1324-1332.Li Jianhui,Hu Xiangyun,Chen Bin et al.The vector finite element solution for the EM field induced by the loop source with complex form.OGP,2017,52(6):1324-1332.
[23]赵慧,刘颖,李予国.自适应有限元海洋大地电磁场二维正演模拟.石油地球物理勘探,2014,49(3):578-585.Zhao Hui,Liu Ying,Li Yuguo.The adaptive finite element forward modeling for 2D marine MT.OGP,2014,49(3):578-585.
[24]考夫曼A A,凯勒G V.频率域和时间域电磁测深.北京:地质出版社,1987.Kaufman A A,Keller G V.Frequency and Transient Sounding.Geological Publishing House,Beijing,1987.
[25]Guptasarma D,Singh B.New digital linear filters for Hankel J0 and J1 transforms.Geophysical Prospecting,1997,45(5):745-762.
[2]Nabighian M,Corbett J.Electromagnetic Methods in Applied Geophysics:Theory.SEG,1988.
[3]杨怀杰,潘和平,孟庆鑫等.导电围岩对井中三维瞬变电磁响应的影响规律研究.石油物探,2016,55(2):288-293.Yang Huaijie,Pan Heping,Meng Qingxin et al.Influence laws of conductive host on borehole 3Dtransient electromagnetic responses.GPP,2016,55(2):288-293.
[4]柳建新,麻昌英,孙丽影等.可控源音频大地电磁测深法在地热勘探中的应用.工程地球物理学报,2014,11(3):319-325.Liu Jianxin,Ma Changying,Sun Liying et al.The application of CSAMT to the geothermal exploration.Chinese Journal of Engineering Geophysics,2014,11(3):319-325.
[5]He Z,Liu X,Qiu W et al.Mapping reservoir boundary by borehole-surface TFEM:Two case studies.The Leading Edge,2005,24(9):896-900.
[6]Wirianto M,Mulder W A,Slob E C.A feasibility study of land CSEM reservoir monitoring in a complex 3-Dmodel.Geophysical Journal of the Royal Astronomical Society,2010,181(2):741-755.
[7]Newman G A,Alumbaugh D L.Frequency-domain modelling of airborne electromagnetic responses using staggered finite differences.Geophysical Prospecting,1995,43(8):1021-1042.
[8]Weiss C,Newman G.Electromagnetic induction in a generalized 3Danisotropic earth,Part 2:The LIN preconditioner.Geophysics,2003,68(3):922-930.
[9]Streich R.3Dfinite-difference frequency-domain modeling of controlled-source electromagnetic data:Direct solution and optimization for high accuracy.Geophysics,2009,74(5):F95-F105.
[10]Badea E A,Everett M E,Newman G A et al.Finiteelement analysis of controlled-source electromagnetic induction using Coulomb-gauged potentials.Geophysics,2001,66(3):786-799.
[11]Stalnaker J L.A Finite Element Approach to the 3DCSEM Modeling Problem and Applications to the Study of the Effect of Target Interaction and Topography[D].Texas A&M University,2004.
[12]Farquharson C G,Miensopust M P.Three-dimensional finite-element modelling of magnetotelluric data with a divergence correction.Journal of Applied Geophysics,2011,75(4):699-710.
[13]Puzyrev V,Koldan J,Puente Jdl et al.A parallel finite-element method for three-dimensional controlledsource electromagnetic forward modelling.Geophysical Journal International,2013,193(2):678-693.
[14]Tong X Z,Liu J X,Xie W et al.Three-dimensional forward modeling for magnetotelluric sounding by finite element method.Journal of Central South University of Technology,2009,16(1):136-142.
[15]徐志锋,吴小平.可控源电磁三维频率域有限元模拟.地球物理学报,2010,53(8):1931-1939.Xu Zhifeng,Wu Xiaoping.Controlled source electromagnetic 3-D modeling in frequency domain for finite element method.Chinese Journal of Geophysics,2010,53(8):1931-1939.
[16]付长民,底青云,王妙月.海洋可控源电磁法三维数值模拟.石油地球物理勘探,2009,44(3):358-363.Fu Changmin,Di Qingyun,Wang Miaoyue.The 3Dnumerical modeling for MCSEM.OGP,2009,44(3):358-363.
[17]殷长春,贲放,刘云鹤等.三维任意各向异性介质中海洋可控源电磁法正演研究.地球物理学报,2014,57(12):4110-4122.Yin Changchun,Ben Fang,Liu Yunhe et al.MCSEM3D modeling for arbitrarily anisotropic media.Chinese Journal of Geophysics,2014,57(12):4110-4122.
[18]王超.海洋可控源电磁法三维正演研究[学位论文].北京:中国地质大学(北京),2014.Wang Chao.Marine CSEM 3D Forward Modeling[D].China University of Geosciences(Beijing),Beijing,2014.
[19]韩波,胡祥云,Schultz A等.复杂场源形态的海洋可控源电磁三维正演.地球物理学报,2015,58(3):1059-1071.Han bo,Hu Xiangyun,Schultz A et al.Three dimensional forward modeling of marine controlled source electromagnetic field of complex source geometries.Chinese Journal of Geophysics,2015,58(3):1059-1071.
[20]汤文武,李耀国,柳建新等.基于二次电场的可控源电磁法三维矢量有限元正演模拟.石油物探,2015,54(6):665-673.Tang Wenwu,Li Yaoguo,Liu Jianxin et al.Three-dimensional controlled-source electromagnetic forward modeling by edge-based finite element using secondary electrical field.GPP,2015,54(6):665-673.
[21]严波,李予国,韩波等.任意方位电偶源的MCSEM电磁场三维正演.石油地球物理勘探,2017,52(4):859-868.Yanbo,Li Yuguo,Hanbo et al.The 3Dforward modeling of the EM field for MCSEM using the electrical dipole source with arbitrary azimuth.OGP,2017,52(4):859-868.
[22]李建慧,胡祥云,陈斌等.复杂形态回线源激发电磁场的矢量有限元解.石油地球物理勘探,2017,52(6):1324-1332.Li Jianhui,Hu Xiangyun,Chen Bin et al.The vector finite element solution for the EM field induced by the loop source with complex form.OGP,2017,52(6):1324-1332.
[23]赵慧,刘颖,李予国.自适应有限元海洋大地电磁场二维正演模拟.石油地球物理勘探,2014,49(3):578-585.Zhao Hui,Liu Ying,Li Yuguo.The adaptive finite element forward modeling for 2D marine MT.OGP,2014,49(3):578-585.
[24]考夫曼A A,凯勒G V.频率域和时间域电磁测深.北京:地质出版社,1987.Kaufman A A,Keller G V.Frequency and Transient Sounding.Geological Publishing House,Beijing,1987.
[25]Guptasarma D,Singh B.New digital linear filters for Hankel J0 and J1 transforms.Geophysical Prospecting,1997,45(5):745-762.