考虑激发极化效应的瞬变电磁一维Occam反演
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摘要
大地的感应激发极化效应有时会在瞬变电磁晚期响应上产生负值变号现象。常规实电阻率瞬变电磁反演由于没有考虑激发极化效应,对于观测数据负值部分的解释一直存在问题,这影响了反演解释的真实性和可信度。对此,本文首先将Cole-Cole复电阻率模型加入正演计算,并验证了计算的准确性。然后在阻尼最小二乘法的基础上加入Occam平滑约束来构建反演方程,能够同时反演出零频电阻率、充电率、时间常数以及频率相关系数,实现了一维瞬变电磁复电阻率反演算法。最后,建立具有不同程度激发极化效应的典型层状理论模型进行反演试算与结果分析,结果表明,在激发极化效果明显的低阻高极化地层中,复电阻率反演效果更好。与实电阻率反演结果的对比说明,瞬变电磁复电阻率反演既可以达到实电阻率的常规反演效果,也能解决实电阻率无法实现的负值拟合问题。
The transient electromagnetic response sometimes becomes negative at late times,which may be caused by the induced polarization(IP)effect.Because of the fact that there is no consideration of the IP effect in the traditional real resistivity inversion,the interpretation of the negative part of the observed data has always been a problem which affects the accuracy and reliability of the inversion.In this paper,we first introduced the Cole-Cole complex resistivity model into the forward modeling code and tested its accuracy.Then,one-dimensional TEM Occam inversion algorithm was implemented basedon the damped least-squares method.We constructed the inversion equations involving Occam smoothness constraint matrix and inversed simultaneously the four complex resistivity parameters,i.e.DC resistivity,chargeability,time constant and frequency dependence.In order to test the inversion algorithm,we established two different typical theoretical polarized layered models and analyzed their inversion effects.The results show that the complex resistivity parameters can be better recovered in the layer with low resistivity and high chargeability.Comparing with the traditional real resistivity inversion,the complex resistivity inversion can not only perform like the real resistivity inversion,but also solve the fitting problem in the case of the negative response.
The transient electromagnetic response sometimes becomes negative at late times,which may be caused by the induced polarization(IP)effect.Because of the fact that there is no consideration of the IP effect in the traditional real resistivity inversion,the interpretation of the negative part of the observed data has always been a problem which affects the accuracy and reliability of the inversion.In this paper,we first introduced the Cole-Cole complex resistivity model into the forward modeling code and tested its accuracy.Then,one-dimensional TEM Occam inversion algorithm was implemented basedon the damped least-squares method.We constructed the inversion equations involving Occam smoothness constraint matrix and inversed simultaneously the four complex resistivity parameters,i.e.DC resistivity,chargeability,time constant and frequency dependence.In order to test the inversion algorithm,we established two different typical theoretical polarized layered models and analyzed their inversion effects.The results show that the complex resistivity parameters can be better recovered in the layer with low resistivity and high chargeability.Comparing with the traditional real resistivity inversion,the complex resistivity inversion can not only perform like the real resistivity inversion,but also solve the fitting problem in the case of the negative response.
引文
[1]Walker G G,Kawasaki K.Observation of Double Sign Reversals in Transient Electromagnetic Central Induction Soundings[J].Geoexploration,1988,25(3):245-254.
[2]Descloitres M,Guérin R,Albouy Y,et al.Improvement in TDEM Sounding Interpretation in Presence of Induced Polarization:A Case Study in Resistive Rocks of the Fogo Volcano,Cape Verde Islands[J].Journal of Applied Geophysics,2000,45(1):1-18.
[3]Weidelt P.Response Characteristics of Coincident Loop Transient Electromagnetic Systems[J].Geophysics,2012,47(9):1325-1330.
[4]Spies B R.AField Occurrence of Sign Reversals with the Transient Electromagnetic Method[J].Geophysical Prospecting,1980,28(4):620-632.
[5]Pelton W H,Ward S H,Hallof P G,et al.Mineral Discrimination and Removal of Inductive Coupling with Multifrequency IP[J].Geophysics,1978,43(3):588-609.
[6]Flis M F,Newman G A,Hohmann G W.InducedPolarization Effects in Time-Domain Electromagnetic Measurements[J].Geophysics,1989,54(4):514-523.
[7]Kaufman A A,Geoltrain S,Knoshaug R N.Influence of Induced Polarization in Inductive Methods[J].Geoexploration,1989,26(2):75-93.
[8]Smith R S,West G F.Field Examples of Negative Coincident-Loop Transient Electromagnetic Responses Modeled with Polarizable Half-Planes[J].Geophysics,1989,54(11):1491-1498.
[9]Hohmann G W,Kintzinger P R,Van Voorhis G D,et al.Evaluation of the Measurement of Induced Electrical Polarization with an Inductive System[J].Geophysics,1970,35(5):901-915.
[10]殷长春,刘斌.瞬变电磁法三维问题正演及激电效应特征研究[J].地球物理学报,1994,37(增刊1):486-492.Yin Changchun,Liu Bin.The Research on the 3D TDEM Modeling and IP Effect[J].Acta Geophysica Sinica,1994,37(Sup.1):486-492.
[11]王隆平,温佩琳.论TEM法中的IP效应[J].中南工业大学学报,1998,29(3):209-211.Wang Longping,Wen Peilin.IP Effects in TEM Response[J].Journal of Central South University,1998,29(3):209-211.
[12]徐凯军,李桐林,刘展.激电效应对瞬变电磁影响特征研究[J].物探化探计算技术,2010,32(6):613-616.Xu Kaijun,Li Tonglin,Liu Zhan.The Study of Induced Polarization Effect in Transient Electromagnetic Fields[J].Computing Techniques for Geophysical and Geochemical Exploration,2010,32(6):613-616.
[13]Zhdanov M S,Portniaguine O.Time-Domain Electro-magnetic Migration in the Solution of Inverse Problems[J].Geophysical Journal International,1997,131(2):293-309.
[14]Nabighian M N,Macnae J C.Time Domain Electromagnetic Prospecting Methods[J].Electromagnetic Methods in Applied Geophysics,1991,2(Part A):427-509.
[15]翁爱华.Occam反演及其在瞬变电磁测深中的应用[J].地质与勘探,2007,43(5):74-76.Weng Aihua.Occam’s Inversion and Its Application to Transient Electromagnetic Method[J].Geology and Prospecting,2007,43(5):74-76.
[16]Kozhevnikov N O,Antonov E Y.Inversion of TEM Data Affected by Fast-Decaying Induced Polarization:Numerical Simulation Experiment with Homogeneous Half-Space[J].Journal of Applied Geophysics,2008,66(1):31-43.
[17]El-Kaliouby H M,El-Diwany E A,Hussain S A,et al.Optimum Negative Response of a CoincidentLoop Electromagnetic System Above a Polarizable Half-Space[J].Geophysics,1997,62(1):75-79.
[18]Kozhevnikov N O,Antonov E Y.Inversion of IPAffected TEM Responses of a Two-Layer Earth[J].Russian Geology and Geophysics,2010,51(6):708-718.
[19]Constable S C,Parker R L,Constable C G.Occam’s Inversion:A Practical Algorithm for Generating Smooth Models from Electromagnetic Sounding Data[J].Geophysics,1987,52(3):289-300.
[20]朴英哲,李桐林,刘永亮.在大地电磁二维Occam反演中求取拉格朗日乘子方法改进[J].吉林大学学报(地球科学版),2014,44(2):660-667.Piao Yingzhe,Li Tonglin,Liu Yongliang.Improvement of Choosing Lagrange Multiplier on MT2D Occam Inversion[J].Journal of Jilin University(Earth Science Edition),2014,44(2):660-667.
[21]李建平,李桐林,张亚东.层状介质任意形状回线源瞬变电磁场正反演[J].物探与化探,2012,36(2):256-259.Li Jianping,Li Tonglin,Zhang Yadong.TEM Forward and Inversion of Arbitrary Shape Loop Source in Layered Media[J].Geophysical&Geochemical Exploration,2012,36(2):256-259.
[22]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):329-335.Wang Huajun.Digital Filter Algorithm of the Sine and Cosine Transform[J].Chinese Journal of Engineering Geophysics,2004,1(4):329-335.
[23]Marquardt D W.An Algorithm for Least-Squares Estimation of Nonlinear Parameters[J].Journal of the Society for Industrial and Applied Mathematics,1963,11(2):431-441.
[2]Descloitres M,Guérin R,Albouy Y,et al.Improvement in TDEM Sounding Interpretation in Presence of Induced Polarization:A Case Study in Resistive Rocks of the Fogo Volcano,Cape Verde Islands[J].Journal of Applied Geophysics,2000,45(1):1-18.
[3]Weidelt P.Response Characteristics of Coincident Loop Transient Electromagnetic Systems[J].Geophysics,2012,47(9):1325-1330.
[4]Spies B R.AField Occurrence of Sign Reversals with the Transient Electromagnetic Method[J].Geophysical Prospecting,1980,28(4):620-632.
[5]Pelton W H,Ward S H,Hallof P G,et al.Mineral Discrimination and Removal of Inductive Coupling with Multifrequency IP[J].Geophysics,1978,43(3):588-609.
[6]Flis M F,Newman G A,Hohmann G W.InducedPolarization Effects in Time-Domain Electromagnetic Measurements[J].Geophysics,1989,54(4):514-523.
[7]Kaufman A A,Geoltrain S,Knoshaug R N.Influence of Induced Polarization in Inductive Methods[J].Geoexploration,1989,26(2):75-93.
[8]Smith R S,West G F.Field Examples of Negative Coincident-Loop Transient Electromagnetic Responses Modeled with Polarizable Half-Planes[J].Geophysics,1989,54(11):1491-1498.
[9]Hohmann G W,Kintzinger P R,Van Voorhis G D,et al.Evaluation of the Measurement of Induced Electrical Polarization with an Inductive System[J].Geophysics,1970,35(5):901-915.
[10]殷长春,刘斌.瞬变电磁法三维问题正演及激电效应特征研究[J].地球物理学报,1994,37(增刊1):486-492.Yin Changchun,Liu Bin.The Research on the 3D TDEM Modeling and IP Effect[J].Acta Geophysica Sinica,1994,37(Sup.1):486-492.
[11]王隆平,温佩琳.论TEM法中的IP效应[J].中南工业大学学报,1998,29(3):209-211.Wang Longping,Wen Peilin.IP Effects in TEM Response[J].Journal of Central South University,1998,29(3):209-211.
[12]徐凯军,李桐林,刘展.激电效应对瞬变电磁影响特征研究[J].物探化探计算技术,2010,32(6):613-616.Xu Kaijun,Li Tonglin,Liu Zhan.The Study of Induced Polarization Effect in Transient Electromagnetic Fields[J].Computing Techniques for Geophysical and Geochemical Exploration,2010,32(6):613-616.
[13]Zhdanov M S,Portniaguine O.Time-Domain Electro-magnetic Migration in the Solution of Inverse Problems[J].Geophysical Journal International,1997,131(2):293-309.
[14]Nabighian M N,Macnae J C.Time Domain Electromagnetic Prospecting Methods[J].Electromagnetic Methods in Applied Geophysics,1991,2(Part A):427-509.
[15]翁爱华.Occam反演及其在瞬变电磁测深中的应用[J].地质与勘探,2007,43(5):74-76.Weng Aihua.Occam’s Inversion and Its Application to Transient Electromagnetic Method[J].Geology and Prospecting,2007,43(5):74-76.
[16]Kozhevnikov N O,Antonov E Y.Inversion of TEM Data Affected by Fast-Decaying Induced Polarization:Numerical Simulation Experiment with Homogeneous Half-Space[J].Journal of Applied Geophysics,2008,66(1):31-43.
[17]El-Kaliouby H M,El-Diwany E A,Hussain S A,et al.Optimum Negative Response of a CoincidentLoop Electromagnetic System Above a Polarizable Half-Space[J].Geophysics,1997,62(1):75-79.
[18]Kozhevnikov N O,Antonov E Y.Inversion of IPAffected TEM Responses of a Two-Layer Earth[J].Russian Geology and Geophysics,2010,51(6):708-718.
[19]Constable S C,Parker R L,Constable C G.Occam’s Inversion:A Practical Algorithm for Generating Smooth Models from Electromagnetic Sounding Data[J].Geophysics,1987,52(3):289-300.
[20]朴英哲,李桐林,刘永亮.在大地电磁二维Occam反演中求取拉格朗日乘子方法改进[J].吉林大学学报(地球科学版),2014,44(2):660-667.Piao Yingzhe,Li Tonglin,Liu Yongliang.Improvement of Choosing Lagrange Multiplier on MT2D Occam Inversion[J].Journal of Jilin University(Earth Science Edition),2014,44(2):660-667.
[21]李建平,李桐林,张亚东.层状介质任意形状回线源瞬变电磁场正反演[J].物探与化探,2012,36(2):256-259.Li Jianping,Li Tonglin,Zhang Yadong.TEM Forward and Inversion of Arbitrary Shape Loop Source in Layered Media[J].Geophysical&Geochemical Exploration,2012,36(2):256-259.
[22]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):329-335.Wang Huajun.Digital Filter Algorithm of the Sine and Cosine Transform[J].Chinese Journal of Engineering Geophysics,2004,1(4):329-335.
[23]Marquardt D W.An Algorithm for Least-Squares Estimation of Nonlinear Parameters[J].Journal of the Society for Industrial and Applied Mathematics,1963,11(2):431-441.