大定源回线瞬变电磁场数值滤波算法
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摘要
在前人的工作基础上,给出一种新的快速计算框线源激发的瞬变电磁场的数值滤波算法,其中内层积分的Hankel积分式采用47点J1型线性滤波系数,外层积分采用"n点式"Gauss-Legendre数值积分法。通过线性迭加技术,将多个单线源组合成任意多边形的瞬变电磁的发射框源。算例分析表明,数值计算结果和解析解的最大相对误差小于0.007%,单测点、单时间道的计算耗时为0.1s。该方法可应用于瞬变电磁法生产实际中确定出最小延迟时间,以避免"框线效应"对瞬变电磁场的畸变影响。
Based on the studies of Nabighian(1984)and DING Yan-fei(2012),a new digital filtering algorithm is presented to evaluate the transient electromagnetic(TEM)field induced by a line source.Among them,the inner integral Hankel integral formula using 47-point J1 type linear filtering coefficients,outer integral formula using'n-point'Gauss-Legendre numerical integration method.Through linear superposition of a plurality of single line source emission source combined into arbitrary polygon transient electromagnetic.Example analysis shows that the maximum relative error of the numerical results and the analytical solution is less than 0.007%,and the computation time of single point and single time channel is 0.1s.The method can be applied to the production of transient electromagnetic method to determine the minimum delay time,so as to avoid the influence of border effects on the transient electromagnetic field.
Based on the studies of Nabighian(1984)and DING Yan-fei(2012),a new digital filtering algorithm is presented to evaluate the transient electromagnetic(TEM)field induced by a line source.Among them,the inner integral Hankel integral formula using 47-point J1 type linear filtering coefficients,outer integral formula using'n-point'Gauss-Legendre numerical integration method.Through linear superposition of a plurality of single line source emission source combined into arbitrary polygon transient electromagnetic.Example analysis shows that the maximum relative error of the numerical results and the analytical solution is less than 0.007%,and the computation time of single point and single time channel is 0.1s.The method can be applied to the production of transient electromagnetic method to determine the minimum delay time,so as to avoid the influence of border effects on the transient electromagnetic field.
引文
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[13]GUPTASARMA D,SINGH B.New digital linear filters for Hankel J0aand J1transforms[J].Geophysical Prospecting,1997,45:745—762.
[14]ANDERSON W.L.Computer Program Numerical integration of related Hankel transforms of orders 0and 1by adaptive digital filtering[J].Geophysics,1979,44(7):1287—1305.
[15]ALAN D.C.Numerical integration of related Hankel transforms by quadrature and continue fraction expansion[J].Geophysics,1983,48(12):1671—1686.
[16]张伟,王绪本,覃庆炎.汉克尔变换的数值计算与精度的对比[J].物探与化探,2010,34(6):753—755.ZHANG W,WANG X B,QIN Q Y.Research and Application on Numerical Integration of Hankel Transform by Digital Filtering[J].Geophysical&Geochemical Exploration,2010,34(6):753-755.(In Chinese)
[17]徐世良.计算机常用算法(第二版)[M].北京:清华大学出版社,1995.XU S L.Computer algorithms(Second Edition)[M].Beijing:Tsinghua university press,1995.(In Chinese)
[18]刘云,王绪本,段长生.大回线瞬变电磁正演模拟在工程实际中的应用[C].第十届中国国际地球电磁学术讨论会论文集,2011:50—54.LIU Y,WANG X B,DUAN C S.Practical Application of Fixed-loop TEM Forward Modeling[C].The 10th China International Geo-Electromagnetic Workshop,2011:50-54.(In Chinese)
[2]蒋邦远.实用近区磁源瞬变电磁勘探[M].北京:地质出版社,1998.JIANG B Y.Near field magnetic source transient electromagnetic exploration[M].Beijing:Geological Publishing House,1998.(In Chinese)
[3]陈贵生.瞬变电磁法在金属矿产勘查上的应用效果及存在问题探讨[J].矿产与地质,2006,20(4):543—547.CHEN G S.Application result of transient electromagnetic method to metallic mineral resources exploration and existing problems[J].Mineral resources and geology,2006,20(4):543-547.(In Chinese)
[4]薛国强,李貅.瞬变电磁隧道超前预报成像技术[J].地球物理学报,2008,51(3):894—900.XUE G Q,LI X.The technology of TEM tunnel prediction imaging[J].Chinese J.Geophysics,2008,51(3):894-900.(In Chinese)
[5]李宁,张文博,刘域田,等.瞬变电磁法在红旗岭铜镍矿3号岩体勘查中的应用与研究[J].吉林地质,2014,33(2):69—72.LI N,ZHANG W B,LIU Y T,et al.Application and research of the transient electromagnetic method in No.3Rock mass of Hongqiling copper-nickle mine[J].Jilin Geology,2014,33(2):69-72.(In Chinese)
[6]韩自强,罗姣,刘涛,等.定源回线瞬变电磁法在煤矿富水区调查中的应用[J].地球物理学进展,2015,30(4):1705—1711.HAN Z Q,LUO J,LIU T,et al.The application of fixed source loop transient electromagnetic method in the coal mine rich water area survey[J].Progress in Geophysics,2015,30(4):1705-1711.(In Chinese)
[7]包乃利,刘鸿福,余传涛.大定源瞬变电磁法激励场及边框效应研究[J].煤田地质与勘探,2014,42(2):80—84.BAO N L,LIU H F,YU C T.The research on the primary field and rim effect of transient electromagnetic method with large fixed loop[J].Coal Geology&Exploration,2014,42(2):80-84.(In Chinese)
[8]NABIGHIAN M.N,ORISTAGLIO M.L.On the approximation of finite loop sources by two-dimensional line source[J].Geophysics,1984,49(7):1027—1029.
[9]丁艳飞,白登海,许诚.均匀半空间表面大定源瞬变电磁响应的快速算法[J].地球物理学报,2012,55(6):2087—2096.DING Y F,BAI D H,XU C.A rapid algorithm for calculating time domain transient electromagnetic responses of a large fixed loop on the half space[J].Chinese J.Geophysics,2012,55(6):2087-2096.(In Chinese)
[10]何光渝,高永利.Visual Fortran常用算法集[M].北京:科学出版社,2002.HE G Y,GAO Y L.Visual Fortran common algorithm set[M].Beijing:Science Press,2002.(In Chinese)
[11]阮百尧.均匀水平大地上频率域垂直磁偶源电磁场数值滤波解法[J].桂林工学院学报,2005,25(1):14—18.RUAN B Y.Digital filter method of evaluating electromagnetic field from a vertical magnetic dipole above the homogeneous earth[J].Journal of Guilin University of Technology,2005,25(1):14-18.(In Chinese)
[12]程志平.电法勘探教程[M].北京:冶金工业出版社,2007.CHENG Z P.Electric exploration course[M].Beijing:Metallurgical industry press,2007.(In Chinese)
[13]GUPTASARMA D,SINGH B.New digital linear filters for Hankel J0aand J1transforms[J].Geophysical Prospecting,1997,45:745—762.
[14]ANDERSON W.L.Computer Program Numerical integration of related Hankel transforms of orders 0and 1by adaptive digital filtering[J].Geophysics,1979,44(7):1287—1305.
[15]ALAN D.C.Numerical integration of related Hankel transforms by quadrature and continue fraction expansion[J].Geophysics,1983,48(12):1671—1686.
[16]张伟,王绪本,覃庆炎.汉克尔变换的数值计算与精度的对比[J].物探与化探,2010,34(6):753—755.ZHANG W,WANG X B,QIN Q Y.Research and Application on Numerical Integration of Hankel Transform by Digital Filtering[J].Geophysical&Geochemical Exploration,2010,34(6):753-755.(In Chinese)
[17]徐世良.计算机常用算法(第二版)[M].北京:清华大学出版社,1995.XU S L.Computer algorithms(Second Edition)[M].Beijing:Tsinghua university press,1995.(In Chinese)
[18]刘云,王绪本,段长生.大回线瞬变电磁正演模拟在工程实际中的应用[C].第十届中国国际地球电磁学术讨论会论文集,2011:50—54.LIU Y,WANG X B,DUAN C S.Practical Application of Fixed-loop TEM Forward Modeling[C].The 10th China International Geo-Electromagnetic Workshop,2011:50-54.(In Chinese)