基于GEMTIP模型的CR三维有限元数值模拟
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摘要
本文提出了基于广义等效介质激电(GEMTIP)模型的复电阻率三维有限元数值模拟方法,首先介绍了GEMTIP模型及在不同参数影响下的复电阻率变化特征,而后给出双点电源的复电阻率法三维正演所满足的变分问题,采用六面体单元对研究区域进行网格剖分,在单元内对复电位、复电导率均进行线性插值,将变分方程转为线性方程组;采用不完全LU分解的稳定双共轭梯度算法(BICGSTAB算法)求解线性方程组,得到异常复电位值.设计一个两层极化大地模型,将数值解与解析解进行对比,验证了文中算法的正确性.设计两个典型地电模型的数值模拟结果表明,采用GEMTIP模型研究宏观尺度下的激电效应是有效的,可为进一步研究复电阻率异常响应特征提供一种新的途径.
A 3D finite element method for complex resistivity simulation based on generalized equivalent medium induced polarization( GEMTIP) model was introduced. First,the GEMTIP model and the complex resistivity variation characteristics of GEMTIP model under the influence of different parameters was introduced,Then,the variation equations were established for two – point sources of 3D modeling of complex resistivity method. The computing area was divided into hexahedral elements. The complex potential and the complex conductivity of rocks within each triangular lattice were described by a linear interpolation to create a linear equations system from the variation equation. The BICGSTAB( Bi-conjugate gradient stabilized method) algorithm with incomplete LU decomposition for preconditioning was used to solve the system linear equation to calculate the anomalous complex potential of all nodes and the apparent complex resistivity on the surface. Finally,this approach was verified through the calculations of a two layered model. Two typical geoelectric models were designed to test the correctness and efficiency of the algorithm. The results show that it provide new way to further study the induced polarization effect of rock and ore on the acroscopic scale.
A 3D finite element method for complex resistivity simulation based on generalized equivalent medium induced polarization( GEMTIP) model was introduced. First,the GEMTIP model and the complex resistivity variation characteristics of GEMTIP model under the influence of different parameters was introduced,Then,the variation equations were established for two – point sources of 3D modeling of complex resistivity method. The computing area was divided into hexahedral elements. The complex potential and the complex conductivity of rocks within each triangular lattice were described by a linear interpolation to create a linear equations system from the variation equation. The BICGSTAB( Bi-conjugate gradient stabilized method) algorithm with incomplete LU decomposition for preconditioning was used to solve the system linear equation to calculate the anomalous complex potential of all nodes and the apparent complex resistivity on the surface. Finally,this approach was verified through the calculations of a two layered model. Two typical geoelectric models were designed to test the correctness and efficiency of the algorithm. The results show that it provide new way to further study the induced polarization effect of rock and ore on the acroscopic scale.
引文
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[11]李冠男,邓居智,陈辉.改进的Dias复电阻率模型在江西相山铀矿田中适用性研究[J].工程地球物理学报,2015,12(6):732-740.
[12]Farias V J C,Da Rocha B R P.Induced polarization modelling using the fractal model to complex resistivity for environmental application[J].Journal of Environmental Informatics,2005,6(1):25-32.
[13]Farias V J C,Da Rocha B R P,Da Rocha M P C.The use of the fractal model to complex resistivity in the interpretation of induced polarization data[J].Applied Mathematical Modelling,2013,37(3):1347-1361.
[14]Zhdanov M S.Generalized effective medium theory of induced polarization[J].Geophysics,2008,73(5):197-211.
[15]张锐锋,严良俊,孙社敏,等.时频电磁法时域激电参数提取与应用[J].石油地球物理勘探,2016,51(6):1227-1232.
[16]Phillips C.Experimental study of the induced polarization effect using cole-cole and GEMTIP models[D].Salt lake city:The University of Utah,2010.
[17]Zhdanov M S,Burtman V,Endo M,et al.Laboratory-based GEMTIP analysis of spectral IP data for mineral discrimination[C]//SEG Technical Program Expanded Abstracts,2008:1-5.
[18]吴延强,熊彬,罗天涯,等.基于广义等效激电模型的频谱特性分析[J].工程地球物理学报,2017,14(2):217-224.
[19]刘云龙,熊彬,罗天涯,等.基于广义等效CR模型的激电法2.5维响应特征研究[J].地球物理学进展,2015,30(3):1337-1344.
[20]柳建新,蒋鹏飞,童孝忠,等.不完全LU分解预处理的BICGSTAB算法在大地电磁二维正演模拟中的应用[J].中南大学学报(地球科学版),2009,40(2):485-491.
[2]王大勇,李桐林,李建平,等.三维复电阻率模型电磁场正演模拟研究[J].地球物理学进展,2010,25(1):266-271.
[3]李勇,林品荣,李桐林,等.基于异常复电位的2.5维CR有限元数值模拟[J].吉林大学学报(地球科学版),2011,41(5):1597-1603.
[4]梁盛军.复电阻率三维正反演问题研究[D].北京:中国地质大学(北京),2011.
[5]万文涛.长导线源复电阻率法三维正演研究[D].北京:中国地质大学(北京),2016.
[6]杨振威,许江涛,赵秋芳,等.复电阻率法(CR)发展现状与评述[J].地球物理学进展,2015,30(2):899-904.
[7]王珺璐,刘明文,李荡,等.基于cole-cole复电阻率模型的线源可控源有限元数值模拟[J].物探化探计算技术,2015,37(1):32-39.
[8]范翠松,李桐林,王大勇,等.起伏地形下复电阻率法2.5维反演研究[J].地质学报,2014,88(4):755-762.
[9]欧鸥.起伏地形条件下2.5维复电阻率法数值模拟与反演成像研究[D].成都:成都理工大学,2015.
[10]代小威,严良俊,周磊,等.CSAMT中的不同激电模型效果的对比研究[J].西部资源,2015(1):112-113.
[11]李冠男,邓居智,陈辉.改进的Dias复电阻率模型在江西相山铀矿田中适用性研究[J].工程地球物理学报,2015,12(6):732-740.
[12]Farias V J C,Da Rocha B R P.Induced polarization modelling using the fractal model to complex resistivity for environmental application[J].Journal of Environmental Informatics,2005,6(1):25-32.
[13]Farias V J C,Da Rocha B R P,Da Rocha M P C.The use of the fractal model to complex resistivity in the interpretation of induced polarization data[J].Applied Mathematical Modelling,2013,37(3):1347-1361.
[14]Zhdanov M S.Generalized effective medium theory of induced polarization[J].Geophysics,2008,73(5):197-211.
[15]张锐锋,严良俊,孙社敏,等.时频电磁法时域激电参数提取与应用[J].石油地球物理勘探,2016,51(6):1227-1232.
[16]Phillips C.Experimental study of the induced polarization effect using cole-cole and GEMTIP models[D].Salt lake city:The University of Utah,2010.
[17]Zhdanov M S,Burtman V,Endo M,et al.Laboratory-based GEMTIP analysis of spectral IP data for mineral discrimination[C]//SEG Technical Program Expanded Abstracts,2008:1-5.
[18]吴延强,熊彬,罗天涯,等.基于广义等效激电模型的频谱特性分析[J].工程地球物理学报,2017,14(2):217-224.
[19]刘云龙,熊彬,罗天涯,等.基于广义等效CR模型的激电法2.5维响应特征研究[J].地球物理学进展,2015,30(3):1337-1344.
[20]柳建新,蒋鹏飞,童孝忠,等.不完全LU分解预处理的BICGSTAB算法在大地电磁二维正演模拟中的应用[J].中南大学学报(地球科学版),2009,40(2):485-491.