基于灰色系统理论和稳健估计的人工源电磁数据处理（英文）
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摘要
针对强干扰导致人工源频率域电磁法测量结果出现偏倚的问题,研究将灰色系统理论和稳健M-估计综合用于数据处理的新方法。由于灰色系统理论对数据分布类型及数量依赖程度低,本文通过灰色建模求解测量数据的标准差,结合阈值法识别、剔除异常值。采用稳健M-估计估算测量结果,以压制异常值影响,提高处理结果的精度。最后将保留数据的M-估计值视为真实值。为验证所述方法处理效果,仿真生成含噪信号,剔除其有效频率频谱数据中的异常值,处理结果可高度逼近理论值,其最大相对误差为3.6676%,最小仅为0.0251%。然后对野外实测数据进行处理,并通过均方根误差、电位差频谱数据和视电阻率曲线形态对处理效果进行评价。研究结果表明:本文方法可以在保留可信数据的同时有效剔除异常值,均方根误差大幅下降,为人工源电磁法资料后续处理解释提供可靠的数据。
We propose a novel method that combines gray system theory and robust M-estimation method to suppress the interference in controlled-source electromagnetic data. We estimate the standard deviation of the data using a gray model because of the weak dependence of the gray system on data distribution and size. We combine the proposed and threshold method to identify and eliminate outliers. Robust M-estimation is applied to suppress the effect of the outliers and improve the accuracy. We treat the M-estimators of the preserved data as the true data. We use our method to reject the outliers in simulated signals containing noise to verify the feasibility of our proposed method. The processed values are observed to be approximate to the expected values with high accuracy. The maximum relative error is 3.6676%, whereas the minimum is 0.0251%. In processing field data, we observe that the proposed method eliminates outliers, minimizes the root-mean-square error, and improves the reliability of controlled-source electromagnetic data in follow-up processing and interpretation.
We propose a novel method that combines gray system theory and robust M-estimation method to suppress the interference in controlled-source electromagnetic data. We estimate the standard deviation of the data using a gray model because of the weak dependence of the gray system on data distribution and size. We combine the proposed and threshold method to identify and eliminate outliers. Robust M-estimation is applied to suppress the effect of the outliers and improve the accuracy. We treat the M-estimators of the preserved data as the true data. We use our method to reject the outliers in simulated signals containing noise to verify the feasibility of our proposed method. The processed values are observed to be approximate to the expected values with high accuracy. The maximum relative error is 3.6676%, whereas the minimum is 0.0251%. In processing field data, we observe that the proposed method eliminates outliers, minimizes the root-mean-square error, and improves the reliability of controlled-source electromagnetic data in follow-up processing and interpretation.
引文
Buselli,G.,and Cameron,M.,1996,Robust statistical methods for reducing sferics noise contaminating transient electromagnetic measurements:Geophysics,61(6),1633-1646.
Cao,M.,Tan,H.D.,and Wang,K.P.,2016,3D LBFGS inversion of controlled source extremely low frequency electromagnetic data:Applied Geophysics,13(4),689-700.
Deng,J.L.,1993,Gray control system:Huazhong University of Science and Technology Press,Wuhan.
Egbert,G.D.,and Booker,J.R.,1986,Robust estimation of geomagnetic transfer functions:Geophysical Journal International,87(1),173-194.
Fisher,R.A.,1950,On the mathematical foundations of theoretical static:Jone Wiley&Sons,New York.
Grayver,A.V.,and Streich,R.,Ritter,O.,2014,3D inversion and resolution analysis of land-based CSEM data from the Ketzin CO_2 storage formation:Geophysics,79(2),E101-E114.
He,J.S.,2010,Wide field electromagnetic sounding methods:Journal of Central South University(in Chinese),41(3),262-269.
He,J.S.,2010,Wide field electromagnetic sounding methods and pseudo-random electrical exploration method:Higher Education Press,Beijing.
Holland,P.W.,and Welsh,R.E.,1977,Robust regression using iteratively reweighted least-squres:Communications in Statistics-Theory and Methods,6(9),813-827.
Huang,Y.P.,Geng,J.Y.,and Guo,T.L.,2015,New seismic attribute:fractal scaling exponent based on gray detrended fluctuation analysis:Applied Geophysics,12(3),343-352.
Huber,P.J.,1964,Robust estimation of a location parameter:The Annals of Mathematical Statistics,35(1),73-101.
Huber,P.J.,1981,Robust statistics:John&Sons Press,New York.
Huber,P.J.,2011,Robust statistics:International Encyclopedia of Statistical Science,Springer Berlin Heidelberg,1248-1251.
Jiang,Q.Y.,2010,Study on the key technology of wide field electromagnetic sounding instrument:PhD Thesis,Central South University,Changsha.
Li,G.,Xiong C.,Wang,H.Q.,et al,2011,Single-trial estimation of dynamic spectrum:Spectroscopy and Spectral Analysis,31(7),1857-1861.
Liu,C.,Wang,D.,Liu,Y.,et al.,2005,Preliminary study of using 2D multilevel median filtering technique to eliminate random noise:Oil Geophysical Prospecting(in Chinese),40(2),163-167.
Liu,N.,2015,Preprocessing and Research of denosing methods for marine controlled source electromangnetic data:Msc.Thesis,Jilin University,Jilin.
Liu,W.Q.,and Chen,R.J.,2016,Coherence analysis formulti-frequency induced polarization signal processing in strong interference environment:The Chinese Journal of Nonferrous Metals(in Chinese),3,022.
Liu,W.Q.,Chen,R.J.,Cai,H.,et al.,2016,Robust statistical methods for impulse noise suppressing of spread spectrum induced polarization data,with application to a mine site,Gansu province,China:Journal of Applied Geophysics,135,397-407.
Liu,Y.,Fomel,S.,and Liu,G.,2010,Nonlinear structureenhancing filtering using plane-wave prediction:Geophysical Prospecting,58(3),415-427.
Meng,Q.X.,Pan,H.P.,and Luo,M.,2015,A study on the discrete image method for calculation of transient electromagnetic fields in geological media:Applied Geophysics,12(4),493-502.
Neelamani,R.,Baumstein,A.I.,Gillard,D.G.,et al.,2008,Coherent and random noise attenuation using the curvelet transform:The Leading Edge,27(2),240-248.
Prata,D.M.,Schwaab,M.,Lima,E.L.,et al.,2010,Simultaneous robust data reconciliation and gross error detection through particle swarm optimization for an industrial polypropylene reactor:Chemical Engineering Science,65(17),4943-4954.
Song,Z.Q.,and Tan,C.Q.,1997,The analysis rule process method and its application for exact evaluation of oilgas reservoirs by using of gray system theory:Systems Engineering-Theory&Practice(in Chinese),17(3),75-83.
Streich,R.,Becken,M.,and Ritter,O.,2013,Robust processing of noisy land-based controlled-source electromagnetic data:Geophysics,78(5),237-247.
Wang,D.L.,Tong,Z.F.,Tang,C.,and Zhu,H.,2010,An iterative curvelet thresholding algorithm for seismic random noise attenuation:Applied Geophysics,7(4),315-324.
Wang,K.,Tan,H.D.,and Wang,T.,2017,2D joint inversion of CSAMT and magnetic data based on crossgradient theory:Applied Geophysics,14(2),279-290.
Wu,G.P.,AO,M.S.,Wu,Y.Q.,et al.,2009,Multi-domain information assessment of oil and gas traps based on cloud model and gray relational analysis:Journal of Southwest Petroleum University,31(5),1-5.
Yang,C.,2012,Study on FIR digital technology in wide field electromagnetic effective signal extracting:Msc.Thesis,Central South University,Changsha.
Zhang,B.M.,Jiang,Q.Y.,Mo,D.,and Xiao,L.Y.,2015,A new method for handling gross errors in electromagnetic prospecting data:Chinese J.Geophys(in Chinese),58(6),2087-2102.
Zhang,L.,and Zhang,X.P.,2011,Eliminating intolerble errors contained in flight rearch data:Journal of Northwestern Polychnical University(in Chinese),29(4),637-640.
Zhu,J.M.,Hong,Z.B.,Wang,Z.Y.,and Zhou,F.Z.,2000,A gray evaluation method of measurement result with standard uncertainty:J.Huazhong Univ.of Sci.&Tech.(in Chinese),28(9),84-86.
Cao,M.,Tan,H.D.,and Wang,K.P.,2016,3D LBFGS inversion of controlled source extremely low frequency electromagnetic data:Applied Geophysics,13(4),689-700.
Deng,J.L.,1993,Gray control system:Huazhong University of Science and Technology Press,Wuhan.
Egbert,G.D.,and Booker,J.R.,1986,Robust estimation of geomagnetic transfer functions:Geophysical Journal International,87(1),173-194.
Fisher,R.A.,1950,On the mathematical foundations of theoretical static:Jone Wiley&Sons,New York.
Grayver,A.V.,and Streich,R.,Ritter,O.,2014,3D inversion and resolution analysis of land-based CSEM data from the Ketzin CO_2 storage formation:Geophysics,79(2),E101-E114.
He,J.S.,2010,Wide field electromagnetic sounding methods:Journal of Central South University(in Chinese),41(3),262-269.
He,J.S.,2010,Wide field electromagnetic sounding methods and pseudo-random electrical exploration method:Higher Education Press,Beijing.
Holland,P.W.,and Welsh,R.E.,1977,Robust regression using iteratively reweighted least-squres:Communications in Statistics-Theory and Methods,6(9),813-827.
Huang,Y.P.,Geng,J.Y.,and Guo,T.L.,2015,New seismic attribute:fractal scaling exponent based on gray detrended fluctuation analysis:Applied Geophysics,12(3),343-352.
Huber,P.J.,1964,Robust estimation of a location parameter:The Annals of Mathematical Statistics,35(1),73-101.
Huber,P.J.,1981,Robust statistics:John&Sons Press,New York.
Huber,P.J.,2011,Robust statistics:International Encyclopedia of Statistical Science,Springer Berlin Heidelberg,1248-1251.
Jiang,Q.Y.,2010,Study on the key technology of wide field electromagnetic sounding instrument:PhD Thesis,Central South University,Changsha.
Li,G.,Xiong C.,Wang,H.Q.,et al,2011,Single-trial estimation of dynamic spectrum:Spectroscopy and Spectral Analysis,31(7),1857-1861.
Liu,C.,Wang,D.,Liu,Y.,et al.,2005,Preliminary study of using 2D multilevel median filtering technique to eliminate random noise:Oil Geophysical Prospecting(in Chinese),40(2),163-167.
Liu,N.,2015,Preprocessing and Research of denosing methods for marine controlled source electromangnetic data:Msc.Thesis,Jilin University,Jilin.
Liu,W.Q.,and Chen,R.J.,2016,Coherence analysis formulti-frequency induced polarization signal processing in strong interference environment:The Chinese Journal of Nonferrous Metals(in Chinese),3,022.
Liu,W.Q.,Chen,R.J.,Cai,H.,et al.,2016,Robust statistical methods for impulse noise suppressing of spread spectrum induced polarization data,with application to a mine site,Gansu province,China:Journal of Applied Geophysics,135,397-407.
Liu,Y.,Fomel,S.,and Liu,G.,2010,Nonlinear structureenhancing filtering using plane-wave prediction:Geophysical Prospecting,58(3),415-427.
Meng,Q.X.,Pan,H.P.,and Luo,M.,2015,A study on the discrete image method for calculation of transient electromagnetic fields in geological media:Applied Geophysics,12(4),493-502.
Neelamani,R.,Baumstein,A.I.,Gillard,D.G.,et al.,2008,Coherent and random noise attenuation using the curvelet transform:The Leading Edge,27(2),240-248.
Prata,D.M.,Schwaab,M.,Lima,E.L.,et al.,2010,Simultaneous robust data reconciliation and gross error detection through particle swarm optimization for an industrial polypropylene reactor:Chemical Engineering Science,65(17),4943-4954.
Song,Z.Q.,and Tan,C.Q.,1997,The analysis rule process method and its application for exact evaluation of oilgas reservoirs by using of gray system theory:Systems Engineering-Theory&Practice(in Chinese),17(3),75-83.
Streich,R.,Becken,M.,and Ritter,O.,2013,Robust processing of noisy land-based controlled-source electromagnetic data:Geophysics,78(5),237-247.
Wang,D.L.,Tong,Z.F.,Tang,C.,and Zhu,H.,2010,An iterative curvelet thresholding algorithm for seismic random noise attenuation:Applied Geophysics,7(4),315-324.
Wang,K.,Tan,H.D.,and Wang,T.,2017,2D joint inversion of CSAMT and magnetic data based on crossgradient theory:Applied Geophysics,14(2),279-290.
Wu,G.P.,AO,M.S.,Wu,Y.Q.,et al.,2009,Multi-domain information assessment of oil and gas traps based on cloud model and gray relational analysis:Journal of Southwest Petroleum University,31(5),1-5.
Yang,C.,2012,Study on FIR digital technology in wide field electromagnetic effective signal extracting:Msc.Thesis,Central South University,Changsha.
Zhang,B.M.,Jiang,Q.Y.,Mo,D.,and Xiao,L.Y.,2015,A new method for handling gross errors in electromagnetic prospecting data:Chinese J.Geophys(in Chinese),58(6),2087-2102.
Zhang,L.,and Zhang,X.P.,2011,Eliminating intolerble errors contained in flight rearch data:Journal of Northwestern Polychnical University(in Chinese),29(4),637-640.
Zhu,J.M.,Hong,Z.B.,Wang,Z.Y.,and Zhou,F.Z.,2000,A gray evaluation method of measurement result with standard uncertainty:J.Huazhong Univ.of Sci.&Tech.(in Chinese),28(9),84-86.