TEM正演响应计算的几种频-时域转换方法对比
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摘要
在瞬变电磁的一维正演响应模拟中,常用的方法是先在频率域中求解,之后将结果转换到时间域。但该方法在晚期的计算精度通常不高,因此,使用5种频-时域转换方法(正、余弦变换的数值滤波算法,G-S逆拉普拉斯算法、正、余弦变换的折线逼近法)进行了计算,与解析解对比,得出余弦变换的数值滤波算法在晚期计算中精度最高的结论,并对这五种转换方法产生误差问题的原因进行了讨论和分析。本研究有利于瞬变电磁一维正演响应的高精度计算,使其在多维计算中得到更好的应用。
In the forward modeling of transient electromagnetic response,the commonly used method is to calculate the response in the frequency domain,and then the results were converted into the time domain. In this paper,five frequency-time conversion methods( Digital filtering algorithms of sine and cosine transform,G-S inverse Laplace algorithm,polygonal approximations method of sine and cosine transform) were used to conduct calculation. it is concluded that the digital filtering method based on cosine transform has the highest computing precision among these five methods,as shown by the comparison with the analytical algorithm,and the reasons of the error caused by these five kinds of conversion methods were discussed and analyzed,which is beneficial to the high precision calculation of one- dimensional forward modeling of transient electromagnetic response,so that these methods can be better applied to the calculation of multi-dimensional frequency-time conversion.
In the forward modeling of transient electromagnetic response,the commonly used method is to calculate the response in the frequency domain,and then the results were converted into the time domain. In this paper,five frequency-time conversion methods( Digital filtering algorithms of sine and cosine transform,G-S inverse Laplace algorithm,polygonal approximations method of sine and cosine transform) were used to conduct calculation. it is concluded that the digital filtering method based on cosine transform has the highest computing precision among these five methods,as shown by the comparison with the analytical algorithm,and the reasons of the error caused by these five kinds of conversion methods were discussed and analyzed,which is beneficial to the high precision calculation of one- dimensional forward modeling of transient electromagnetic response,so that these methods can be better applied to the calculation of multi-dimensional frequency-time conversion.
引文
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[18]罗延钟,昌彦君.G-S变换的快速算法[J].地球物理学报,2000,43(5):684-690.
[19]王华军.正余弦变换的数值滤波算法[J].工程地球物理学报,2004,1(4):329-333.
[20]陈入云,向淑晃.一种正余弦变换的改进高效算法[J].工程地球物理学报,2008,5(4):416-419.
[21]徐振平,胡文宝.一种高精度瞬变电磁响应正演的数值滤波算法[J].石油物探,2011,50(03):213-219.
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[23]Villinger H.Solving cylindrical geothermal problems using GaverStehfest inverse Laplace transform[J].Geophysics,1985,50(10):1581-1587.
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[25]向淑晃.一些高振荡积分、高振荡积分方程的高性能计算[J].中国科学:数学,2012,42(7):651-670,doi:10.3969/j.issn.1000-1441.2011.03.001.
[26]朴化荣,殷长春.利用G-S逆拉氏变换法计算瞬变测深正演问题[J].物探化探计算技术,1987,9(4):297-302.
[27]罗回国.瞬变电磁大定源回线一维正演模拟研究[D].北京:中国地质大学,2012.
[28]牛之琏.时间域电磁法原理[M].长沙:中南大学出版社,2007.
[29]郭嵩巍.中心回线瞬变电磁一维正反演算法研究[D].成都:成都理工大学,2010.
[30]唐宝山.瞬变电磁法中心回线装置一维正反演研究[D].北京:中国地质大学,2008.
[31]华军,蒋延生,汪文秉.双重贝塞尔函数积分的数值计算[J].煤田地质与勘探,2001,29(3):58-61.
[32]Johansen H K,Sorensen K.Fast Hankel transforms[J].Geophysical Prospecting,1979,27:876-901.
[33]李星.瞬变电磁响应正反演及其特殊问题研究[D].成都:成都理工大学,2013.
[34]李建慧,朱自强,刘树才,等.基于Gaver-Stehfest算法的矩形发射回线激发的瞬变电磁场[J].石油地球物理勘探,2011,46(3):489-492.
[2]Ali Moradi Tehrani.Quasi-analytcal method for frequency-to-time conversion in CSEM applications[J].Geophysics,2012,77(5):357-363,doi:10.1190/GEO2011-0432.1.
[3]李貅.瞬变电磁测深的理论与应用[M].西安:陕西科学技术出版社,2002.
[4]薛国强,李貅,底青云.瞬变电磁法理论与应用研究进展[J].地球物理学进展,2007,22(4):1195-1200.
[5]薛国强,李貅,底青云.瞬变电磁法正反演问题研究进展[J].地球物理学进展,2008,23(4):1165-1172.
[6]昌彦君,张桂青.电磁场从频率域转换到时间域的几种算法比较[J].物探化探计算技术,1995,17(3):25-29.
[7]陈向斌,胡社荣,张超.瞬变电磁场响应计算的频-时域转换方法综述[J].工程地球物理学报,2008,5(2):242-246.
[8]Guptasarma D.Computation of the time-domain response of a polarizable ground[J].Geophysics,1982,47(11):1574-1576,doi:10.1190/1.1441307.
[9]阮百尧.Guptasarma算法在瞬变电磁正演计算中的应用[J].桂林工学院学报,1996,16(2):167-170.
[10]Knight J H,Raichei A P.Transient electromagnetic calculations using the Gaver-Stehfest inverse Laplace transform method[J].Geophysics,1982,47(1):47-50.
[11]长谷川健.水平电气双极子によろ层状大地のスチツア应答と见挂导电率について[J].物理探查,1985,38(3):21-31.
[12]Newman G A,Hohmann G W,Anderson W L.Transient electromagnetic response of three-dimensional body in a layered earth[J].Geophysics,1986,51(8):1680-1626.
[13]Kaufman A A,Keller G V.Frequency and transient sounding(in chinese)[M].Beijing:Ecological Publishing House,1987.
[14]李建慧,朱自强,曾思红,等.瞬变电磁法正演计算进展[J].地球物理学进展,2012,27(4):1393-1400.doi:10.6038/j.issn.1004-2903.2012.04.013.
[15]朴化荣.电磁测深法原理[M].地质出版社,1990.
[16]陈乐寿,王光锷.构造电法勘探[M].武汉:中国地质大学出版社,1991,1-203.
[17]李吉松,朴化荣.电偶源瞬变测深一维正演及视电阻率响应研究[J].物探化探计算技术,1993,15(2):108-116.
[18]罗延钟,昌彦君.G-S变换的快速算法[J].地球物理学报,2000,43(5):684-690.
[19]王华军.正余弦变换的数值滤波算法[J].工程地球物理学报,2004,1(4):329-333.
[20]陈入云,向淑晃.一种正余弦变换的改进高效算法[J].工程地球物理学报,2008,5(4):416-419.
[21]徐振平,胡文宝.一种高精度瞬变电磁响应正演的数值滤波算法[J].石油物探,2011,50(03):213-219.
[22]Raiche A P.Transient electromagnetic field computations for polygonal loops on layered earth[J].Geophysics,1987,526:785-793.
[23]Villinger H.Solving cylindrical geothermal problems using GaverStehfest inverse Laplace transform[J].Geophysics,1985,50(10):1581-1587.
[24]考夫曼A A,凯勒G V.频率域和时间域电磁测深[M].北京:地质出版社,1987.
[25]向淑晃.一些高振荡积分、高振荡积分方程的高性能计算[J].中国科学:数学,2012,42(7):651-670,doi:10.3969/j.issn.1000-1441.2011.03.001.
[26]朴化荣,殷长春.利用G-S逆拉氏变换法计算瞬变测深正演问题[J].物探化探计算技术,1987,9(4):297-302.
[27]罗回国.瞬变电磁大定源回线一维正演模拟研究[D].北京:中国地质大学,2012.
[28]牛之琏.时间域电磁法原理[M].长沙:中南大学出版社,2007.
[29]郭嵩巍.中心回线瞬变电磁一维正反演算法研究[D].成都:成都理工大学,2010.
[30]唐宝山.瞬变电磁法中心回线装置一维正反演研究[D].北京:中国地质大学,2008.
[31]华军,蒋延生,汪文秉.双重贝塞尔函数积分的数值计算[J].煤田地质与勘探,2001,29(3):58-61.
[32]Johansen H K,Sorensen K.Fast Hankel transforms[J].Geophysical Prospecting,1979,27:876-901.
[33]李星.瞬变电磁响应正反演及其特殊问题研究[D].成都:成都理工大学,2013.
[34]李建慧,朱自强,刘树才,等.基于Gaver-Stehfest算法的矩形发射回线激发的瞬变电磁场[J].石油地球物理勘探,2011,46(3):489-492.