矿井全空间三维主轴各向异性介质瞬变电磁场响应特征研究
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摘要
研究瞬变电磁场中的电性各向异性问题,可以为各向异性条件下的地下全空间瞬变电磁法资料处理解释工作提供理论指导,对提高瞬变电磁法探测精度具有重要意义。为了研究矿井全空间条件下主轴各向异性介质的瞬变电磁场响应特征,采用改进的交错网格有限差分方法实现了主轴各向异性介质的瞬变电磁场三维正演。将电导率张量加入麦克斯韦方程组,对Yee氏交错网格进行了改进以便于对主轴各向异性介质中的瞬变电磁场进行差分离散处理,形成了全空间三维主轴各向异性有限差分正演算法。在均匀全空间模型中对比各向异性有限差分数值解及均匀全空间解析解,验证了算法的正确性。建立了不同各向异性类型和不同各向异性对称主轴姿态模型,分别计算了其瞬变电磁场响应,最后结合工程探测实例,通过正演模拟分析了不同主轴各向异性介质对瞬变电磁场的影响特征,解释了探测结果存在偏差的原因。研究表明:在矿井超前探测模式下,对于HTI-X介质,各向异性系数的变化对瞬变电磁场的影响不明显,不同各向异性系数条件下的感应电动势曲线差异较小;对于HTI-Y介质和VTI介质,各向异性系数的变化对瞬变电磁场有明显的影响,随着介质各向异性系数增大,介质瞬变电磁场响应不断变小;随着各向异性介质对称主轴方向与探测方向之间夹角的增大,各向异性介质产生的瞬变电磁场响应不断增大,当对称主轴方向与探测方向一致时(HTI-X介质),各向异性介质产生的感应电动势最弱,而对称主轴方向与探测方向垂直时(VTI介质),各向异性介质产生的感应电动势最强;不同类型的主轴各向异性介质具有明显的各向异性瞬变电磁场响应特征。
The study of the electrical anisotropy in the transient electromagnetic field could provide theoretical guidance for the data processing and interpretation of the underground full-space transient electromagnetic method under the condition of anisotropy,and it has important guiding significance to improve the detection accuracy of transientelectromagnetic method.In order to study the transient electromagnetic field response characteristics of axial anisotropic media in underground whole-space,an improved staggered mesh finite difference method was used to realize a 3 D forward modeling of the transient electromagnetic field of axial anisotropic media. The conductivity tensor was added to Maxwell's equations.Yee's staggered grid was improved to facilitate the differential discretization of axial anisotropic media's transient electromagnetic fields. The whole-space finite difference forward algorithm for axial anisotropic media was developed.The correctness of the algorithm was verified by comparing the anisotropic finite difference numerical solution and the uniform whole-space analytical solution in a uniform whole-space model. Finally,combined with actual engineering detection,the influence characteristics of different axial anisotropic media on transient electromagnetic field were analyzed by forward modeling,and the reasons for the deviation of the detection results were explained.The results show that in the advanced detection mode,the change of anisotropy coefficient of HTI-X medium has no obvious influence on the transient electromagnetic field,the difference of induced electromotive force curves under different anisotropic coefficients is very small. For HTI-Y media and VTI media,the change of anisotropy coefficient has a significant impact on the transient electromagnetic field,as the anisotropy coefficient of the medium increases,the transient electromagnetic field response of the medium decreases continuously.With the increase of the angle between the symmetric axis of anisotropic media and the direction of detection,the transient electromagnetic field response generated by anisotropic media increases continuously.When the symmetric axis of anisotropic medium is consistent with the detection direction(HTI-X medium),the induced electromotive force generated by anisotropic medium is the weakest.When the symmetric axis is perpendicular to the detection direction(VTI medium),the induced electromotive force generated by anisotropic medium is the strongest.Different types of axial anisotropic media have obvious anisotropic transient electromagnetic field response characteristics.
The study of the electrical anisotropy in the transient electromagnetic field could provide theoretical guidance for the data processing and interpretation of the underground full-space transient electromagnetic method under the condition of anisotropy,and it has important guiding significance to improve the detection accuracy of transientelectromagnetic method.In order to study the transient electromagnetic field response characteristics of axial anisotropic media in underground whole-space,an improved staggered mesh finite difference method was used to realize a 3 D forward modeling of the transient electromagnetic field of axial anisotropic media. The conductivity tensor was added to Maxwell's equations.Yee's staggered grid was improved to facilitate the differential discretization of axial anisotropic media's transient electromagnetic fields. The whole-space finite difference forward algorithm for axial anisotropic media was developed.The correctness of the algorithm was verified by comparing the anisotropic finite difference numerical solution and the uniform whole-space analytical solution in a uniform whole-space model. Finally,combined with actual engineering detection,the influence characteristics of different axial anisotropic media on transient electromagnetic field were analyzed by forward modeling,and the reasons for the deviation of the detection results were explained.The results show that in the advanced detection mode,the change of anisotropy coefficient of HTI-X medium has no obvious influence on the transient electromagnetic field,the difference of induced electromotive force curves under different anisotropic coefficients is very small. For HTI-Y media and VTI media,the change of anisotropy coefficient has a significant impact on the transient electromagnetic field,as the anisotropy coefficient of the medium increases,the transient electromagnetic field response of the medium decreases continuously.With the increase of the angle between the symmetric axis of anisotropic media and the direction of detection,the transient electromagnetic field response generated by anisotropic media increases continuously.When the symmetric axis of anisotropic medium is consistent with the detection direction(HTI-X medium),the induced electromotive force generated by anisotropic medium is the weakest.When the symmetric axis is perpendicular to the detection direction(VTI medium),the induced electromotive force generated by anisotropic medium is the strongest.Different types of axial anisotropic media have obvious anisotropic transient electromagnetic field response characteristics.
引文
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[15]周建美,李貅,戚志鹏.浅水域各向异性地层中的瞬变电磁响应分析[J].石油地球物理勘探,2016,51(4):821-830.ZHOU Jianmei,LI Xiu,QI Zhipeng. Transient electromagnetic response analysis for anisotropic media in shallow water[J].Oil Geophysical Prospecting,2016,51(4):821-830.
[16]周建美,刘文韬,李貅,等.双轴各向异性介质中回线源瞬变电磁三维拟态有限体积正演算法[J].地球物理学报,2018,61(1):368-378.ZHOU J M,LIU W T,LI X,et al.Research on the 3D mimetic finite volume method for loop-source TEM response in biaxial anisotropic formation[J].Chinese Journal of Geophysics,2018,61(1):368-378.
[17] WANG T,HOHMANN G W.A finite-difference time-domain solution for three-dimensional electromagnetic modeling[J]. Geophysics,1993,58(6):797-809.
[18]考夫曼A A,凯勒G V.频率域和时间域电磁测深[M].王建谋,译.北京:地质出版社,1987:25-57.
[19]阮爱国.地壳介质弹性、电性各向异性理论及对地震过程的联合解释[D].北京:中国地震局地球物理研究所,2000.
[2] O’BRIEN DOUGLAS P,MORRIS H-F. Electromagnetic fields in an n-layer anisotropic half-space[J]. Geophysics,1967,32(4):668-677.
[3] LI Xiaobo,PEDERS Laust B.The electromagnetic response of an azimuthally anisotropic half-space[J]. Geophysics,1991(56):1462-1473.
[4] WANG T,FANG S,3-D electromagnetic anisotropy modeling using finite differences[J].Geophysics,2001,66:1386-1398.
[5]胡祥云,霍光谱,高锐.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 Xiangyun,HUO Guangpu,GAO Rui,et al. The magnetotelluric anisotropic two-dimensional simulation and case analysis[J]. Chinese Journal of Geophysics,2013,56(12):4268-4277.
[6]罗鸣,李予国.一维电阻率各向异性对海洋可控源电磁响应的影响研究[J].地球物理学报,2015,58(8):2851-2861.LUO Ming,LI Yuguo. Effects of the electric anisotropy on marine controlled-source electromagnetic responses[J]. Chinese Journal of Geophysics,2015,58(8):2851-2861.
[7]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[J].地球物理学报,2014,57(12):4110-4122.YIN Chancun,BEN Fang,LIU Yunhe,et al. MCSEM 3D modeling for arbitrarily anisotropic media[J]. Chinese Journal of Geophysics,2014,57(12):4110-4122.
[8] WANG T,WANG K P,TAN H D.Forward modeling and inversion of tensor CSAMT in 3D anisotropic media[J]. Applied Geophysics,2017,14(4):590-605.
[9] FRIDN J,KRISTENSSON G,STEWART R D. Transient electromagnetic wave propagation in anisotropic dispersive media[J].Journal of the Optical Society of America,1993,10(12):2618-2627.
[10] FERNANDO L Teixeira,WENG CHO Chew.Finite-difference computation of transient electromagnetic waves for cylindrical geometries[J]. IEEE Transactions on Geoscience and Remote Sensing,2000,38(4):1530-1543.
[11] JAMIE L Collins,MARK E Everett,BRANN Johnson. Detection of near-surface horizontal anisotropy in a weathered metamorphic schist at Llano Uplift(Texas)by transient electromagnetic induction[J]. Physics of the Earth and Planetary Interiors,2006,158(26):158-173.
[12] HOBBS B,WERTHMLLER D,ENGELMARK F.The effect of resistivity anisotropy on transient electromagnetic earth responses[J].ASEG Extended Abstracts,2009.
[13] TERUHIKO Hagiwara. Determination of dip and anisotropy from transient[J].Geophysics,2012,77(4):105-112.
[14]严良俊,周磊,谢兴兵,等.储层电各向异性模型的瞬变电磁响应[J].工程地球物理学报,2014,11(3):346-350.YAN Liangjun,ZHOU Lei,XIE Xingbing,et al. The transient electromagnetic response of electrical anisotropic reservoir model[J].Chinese Journal of Engineering Geophysics,2014,11(3):346-350.
[15]周建美,李貅,戚志鹏.浅水域各向异性地层中的瞬变电磁响应分析[J].石油地球物理勘探,2016,51(4):821-830.ZHOU Jianmei,LI Xiu,QI Zhipeng. Transient electromagnetic response analysis for anisotropic media in shallow water[J].Oil Geophysical Prospecting,2016,51(4):821-830.
[16]周建美,刘文韬,李貅,等.双轴各向异性介质中回线源瞬变电磁三维拟态有限体积正演算法[J].地球物理学报,2018,61(1):368-378.ZHOU J M,LIU W T,LI X,et al.Research on the 3D mimetic finite volume method for loop-source TEM response in biaxial anisotropic formation[J].Chinese Journal of Geophysics,2018,61(1):368-378.
[17] WANG T,HOHMANN G W.A finite-difference time-domain solution for three-dimensional electromagnetic modeling[J]. Geophysics,1993,58(6):797-809.
[18]考夫曼A A,凯勒G V.频率域和时间域电磁测深[M].王建谋,译.北京:地质出版社,1987:25-57.
[19]阮爱国.地壳介质弹性、电性各向异性理论及对地震过程的联合解释[D].北京:中国地震局地球物理研究所,2000.
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