基于灰色判别准则和有理函数滤波的伪随机电磁数据去噪
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摘要
为压制伪随机多频电磁信号中的强干扰、提高数据质量,本文提出一种基于灰色判别准则和有理函数滤波的数据处理方法.首先通过灰色判别准则剔除各个频点频谱数据中的明显异常值,然后进行有理函数滤波得到充分接近真实值的圆滑数据曲线,进而约束数据的二次优化处理,剔除残余噪声的影响.为验证本文方法的处理效果,在实测无明显噪声数据中加入几种不同类型的强噪声,然后用本文方法进行处理.仿真处理结果表明,本文方法能高精度逼近原始数据,处理后数据误差低达8.09%.最后,将本文方法应用于重庆某工区实测伪随机多频电磁数据处理.结果表明,本文方法可以有效压制干扰,在频谱数据个数少、干扰幅值大(高达有效信号幅值的几个数量级)的情况下,仍可有效压制强干扰.处理后的数据相对误差显著下降,视电阻率曲线形态平滑,达到提高信噪比,改善实测数据质量的目的.
We present an adaptive data processing approach mainly based on gray judgment criterion and rational function filtering to suppress strong interference and improve data quality in pseudo-rand multi-frequency electromagnetic method.Firstly,the data with large noise,whose value is bigger or smaller than normal data,can be removed by the gray judgment criterion.Then,the rational function filtering method is applied to filter the remaining data.Furthermore,to eliminate residual noise influence,a smooth curve which closes to the true data is applied to constrain quadratic optimization.Finally,the so-called"pure anomalies"are obtained.To verify our proposed data processing method,firstly the measured data without obvious noises are tested.Different kinds of strong interferences are added into the measured data and our method is adopted to process these signals.Results show that our method can hold down the effects originating from strong noises well,with the relative error being only 8.09%.In addition,we apply the proposed de-noising approach to process the field data with noises acquired in Chongqing.After processing,the relative error of the data decreases,apparent resistivity curve becomes smooth,as well as the SNR increases,which imply that that our method can be well used to eliminate noises and improve the quality of the measured data.
We present an adaptive data processing approach mainly based on gray judgment criterion and rational function filtering to suppress strong interference and improve data quality in pseudo-rand multi-frequency electromagnetic method.Firstly,the data with large noise,whose value is bigger or smaller than normal data,can be removed by the gray judgment criterion.Then,the rational function filtering method is applied to filter the remaining data.Furthermore,to eliminate residual noise influence,a smooth curve which closes to the true data is applied to constrain quadratic optimization.Finally,the so-called"pure anomalies"are obtained.To verify our proposed data processing method,firstly the measured data without obvious noises are tested.Different kinds of strong interferences are added into the measured data and our method is adopted to process these signals.Results show that our method can hold down the effects originating from strong noises well,with the relative error being only 8.09%.In addition,we apply the proposed de-noising approach to process the field data with noises acquired in Chongqing.After processing,the relative error of the data decreases,apparent resistivity curve becomes smooth,as well as the SNR increases,which imply that that our method can be well used to eliminate noises and improve the quality of the measured data.
引文
Ayvaz B,Bolturk E,Ka9to4lu S.2014.A grey system for the forecasting of return product quantity in recycling network.International Journal of Supply Chain Management,3(3):105-112．
Cai J H,Tang J T,Hua X R,et al.2009.An analysis method for magnetotelluric data based on the Hilbert-Huang Transform.Exploration Geophysics,40(2):197-205．
Chave A D,Thomson D J.2003.A bounded influence regression estimator based on the statistics of the hat matrix.Journal of the Royal Statistical Society:Series C(Applied Statistics),52(3):307-322．
Chave A D.2017.Estimation of the magnetotelluric response function:The path from robust estimation to a stable maximum likelihood estimator.Surveys in Geophysics,38(5):837-867．
Chave A D,Mattsson J,Everett M E.2017.On the physics of frequency domain controlled source electromagnetics in shallow water.2:transverse anisotropy.Geophysical Journal International,211(2):1046-1061．
Chen H,Deng J Z,Tan H D,et al.2011.Study on divergence correction method in three-dimensional magnetotelluric modeling with staggered-grid finite difference method.Chinese J.Geophys.(in Chinese),54(6):1649-1659,doi:10.3969/j.issn.0001-5733.2011.06.025．
Deng J W,Deng M,Wei W B,et al.2004.The application of decimation filter in marine bottom magnetotelluric exploration.Journal of Jilin University:Earth Science Edition(in Chinese),34(2):271-276．
Egbert G D,Livelybrooks D W.1996.Single station magnetotelluric impedance estimation:Coherence weighting and the regression M-estimate.Geophysics,61(4):964-970．
Grayver A V,Streich R,Ritter O.2014.3Dinversion and resolution analysis of land-based CSEM data from the Ketzin CO2 storage formation.Geophysics,79(2):E101-E114．
He J S.2010a.Wild Field Electromagnetics and Pseudo-Random Signal Method(in Chinese).Beijing:Higher Education Press．
He J S.2010b.Closed addition in a three-element set and 2n sequence pseudo-random signal coding.Journal of Central South University(Science and Technology)(in Chinese),41(2):632-637．
Huang H P.1991.Electromagnetic data processing using the singular value decomposition method.Chinese J.Geophys.(Acta Geophysica Sinica)(in Chinese),34(5):644-650．
Kayacan E,Ulutas B,Kaynak O.2010.Grey system theory-based models in time series prediction.Expert Systems with Applications,37(2):1784-1789．
Lei D,Zhao G Z,Zhang Z J,et al.2010.A processing method of CSAMT data with strong electromagnetic interferences by using information entropy and rational function filtering.Progress in Geophysics(in Chinese),25(6):2015-2023．
Li G,Xiao X,Tang J T,et al.2017.Near-source noise suppression of AMT by compressive sensing and mathematical morphology filtering.Applied Geophysics,14(4):581-589．
Li J,Tang J T,Yan H,et al.2017.Identification and spearation of magnetotelluric signal and noise based on recurrence analysis and clustering.Chinese J.Geophys.(in Chinese),60(5):1918-1936,doi:10.6038/cjg20170525．
Li J,Zhang X,Tang J T,et al.2019.Audio magnetotelluric signalnoise identification and separation based on multifractal spectrum and matching pursuit.Fractals,27(1):1940007．
Lin Z B,Wang P Y,Wan Y X,et al.2016.A combined wavelet transform algorithm used for de-noising magnetotellurics data in the strong human noise.Chinese J.Geophys.(in Chinese),59(9):3436-3447,doi:10.6038/cjg20160926．
Liu W Q,Chen R J,Cai H Z,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 W Q,Chen R J,Cai H Z,et al.2017.Correlation analysis for spreadspectrum induced-polarization signal processing in electromagnetically noisy environments.Geophysics,82(5):E243-E256．
Liu W Q,LüQ T,Chen R J,et al.2019.A modified empirical mode decomposition method for multiperiod time-series detrending and the application in full-waveform induced polarization data.Geophysical Journal International,217(2):1058-1079．
Mo D,Jiang Q Y,Li D Q,et al.2017.Controlled-source electromagnetic data processing based on gray system theory and robust estimation.Applied Geophysics,14(4):570-580．
Nabighian M N.1987.Electromagnetic Methods in Applied Geophysics:Volume 1,Theory.SEG Books．
Olsen K B,Hohmann G W.1992.Adaptive noise cancellation for time-domain EM data.Geophysics,57(3):466-469．
Ramponi G.2001.Image processing with rational operators:Noise smoothing and anisotropic diffusion．∥Proceedings of the 2nd International Symposium on Image and Signal Processing and Analysis.Pula,Croatia,Croatia:IEEE,96-101．
Ren Z Y,Kalscheuer T,Greenhalgh S,et al.2013.A goal-oriented adaptive finite-element approach for plane wave 3-D electromagnetic modelling.Geophysical Journal International,194(2):700-718．
Ren Z Y,Chen C J,Tang J T,et al.2017.A new integral equation approach for 3D magnetotelluric modeling.Chinese J.Geophys.(in Chinese),60(11):4505-4515,doi:10.6038/cjg20171134．
Shi D,Zhang C S,Guo J S.1998.The application of grey comprehensive evaluation in some low-resistivity oil-gas bearing intervals.Progress in Geophysics(in Chinese),13(1):73-78．
Streich R,Becken M,Ritter O.2013.Robust processing of noisy land-based controlled-source electromagnetic data.Geophysics,78(5):E237-E247．
Szarka L.1988.Geophysical aspects of man-made electromagnetic noise in the earth-A review.Surveys in Geophysics,9(3-4):287-318．
Tang J T,Li G,Xiao X,et al.2017.Strong noise separation for magnetotelluric data based on a signal reconstruction algorithm of compressive sensing.Chinese J.Geophys.(in Chinese),60(9):3642-3654,doi:10.6038/cjg20170928．
Tang J T,Li G,Zhou C,et al.2018.Denoising AMT data based on dictionary learning.Chinese J.Geophys.(in Chinese),61(9):3835-3850,doi:10.6038/cjg2018L0376．
Trad D O,Travassos J M.2000.Wavelet filtering of magnetotelluric data.Geophysics,65(2):482-491．
Wang Z Y,Gao Y,Qin P.2002.Detection of gross measurement errors using the grey system method.The International Journalof Advanced Manufacturing Technology,19(11):801-804．
Yan J B,Liu G Z.2006.Smoothing scale of magnetotelluric sounding curve.Coal Geology&Exploration(in Chinese),34(5):60-62．
Yang Y,He J S,Li D Q.2018.A noise evaluation method for CSEM in the frequency domain based on wavelet transform and analytic envelope.Chinese J.Geophys.(in Chinese),61(1):344-357,doi:10.6038/cjg2018L0298．
Yang Y,Li D Q,Tong T G,et al.2018.Denoising controlledsource electromagnetic data using least-squares inversion.Geophysics,83(4):E229-E244．
Zhang B M,Jiang Q Y,Mo D,et al.2015.A novel method for handling gross errors in electromagnetic prospecting data.Chinese J.Geophys.(in Chinese),58(6):2087-2102,doi:10.6038/cjg20150623．
Zhou C,Tang J T,Ren Z Y,et al.2015.Application of the Rhoplus method to audio magnetotelluric dead band distortion data.Chinese J.Geophys.(in Chinese),58(12):4648-4660,doi:10.6038/cjg20151226．
Zhu J M,Bin H Z,Wang Z Y,et al.2000.A grey evaluation method of measurement result with standard uncertainty.Journal of Huazhong University of Science and Technology(in Chinese),28(9):84-86．
Ziolkowski A,Wright D,Mattsson J.2011.Comparison of pseudorandom binary sequence and square-wave transient controlledsource electromagnetic data over the Peon gas discovery,Norway.Geophysical Prospecting,59(6):1114-1131．
陈辉，邓居智，谭捍东等．2011．大地电磁三维交错网格有限差分数值模拟中的散度校正方法研究．地球物理学报，54(6):1649-1659,doi:10.3969/j.issn.0001-5733.2011.06.025．
邓靖武，邓明，魏文博等．2004．抽取滤波在海底大地电磁探测中的应用．吉林大学学报：地球科学版，34(2):271-276．
何继善．2010a．广域电磁法和伪随机信号电法．北京：高等教育出版社．
何继善．2010b．三元素集合中的自封闭加法与2n系列伪随机信号编码．中南大学学报（自然科学版），41(2):632-637．
黄皓平．1991．电磁法数据处理的奇异值分解法．地球物理学报，34(5):644-650．
雷达，赵国泽，张忠杰等．2010．强干扰地区CSAMT数据信息熵与有理函数滤波的处理方法．地球物理学进展，25(6):2015-2023．
李晋，汤井田，燕欢等．2017．基于递归分析和聚类的大地电磁信噪辨识及分离．地球物理学报，60(5):1918-1936,doi:10.6038/cjg20170525．
凌振宝，王沛元，万云霞等．2016．强人文干扰环境的电磁数据小波去噪方法研究．地球物理学报，59(9):3436-3447,doi:10.6038/cjg20160926．
任政勇，陈超健，汤井田等．2017．一种新的三维大地电磁积分方程正演方法．地球物理学报，60(11):4506-4515,doi:10.6038/cjg20171134．
施冬，张春生，郭甲世．1998．灰色综合评判法在低阻油气层中的应用．地球物理学进展，13(1):73-78．
汤井田，李广，肖晓等．2017．基于压缩感知重构算法的大地电磁强干扰分离．地球物理学报，60(9):3642-3654,doi:10.6038/cjg20170928．
汤井田，李广，周聪等．2018．基于字典学习的音频大地电磁数据处理．地球物理学报，61(9):3835-3850,doi:10.6038/cjg2018L0376．
严家斌，刘贵忠．2006．大地电磁测深曲线平滑尺度．煤田地质与勘探，34(5):60-62．
杨洋，何继善，李帝铨．2018．在频率域基于小波变换和Hilbert解析包络的CSEM噪声评价．地球物理学报，61(1):344-357,doi:10.6038/cjg2018L0298．
张必明，蒋奇云，莫丹等．2015．电磁勘探数据粗大误差处理的一种新方法．地球物理学报，58(6):2087-2102,doi:10.6038/cjg20150623．
周聪，汤井田，任政勇等．2015．音频大地电磁法“死频带”畸变数据的Rhoplus校正．地球物理学报，58(12):4648-4660,doi:10.6038/cjg20151226．
朱坚民，宾鸿赞，王中宇等．2000．测量结果标准不确定度的灰色评定方法．华中理工大学学报，28(9):84-86.
Cai J H,Tang J T,Hua X R,et al.2009.An analysis method for magnetotelluric data based on the Hilbert-Huang Transform.Exploration Geophysics,40(2):197-205．
Chave A D,Thomson D J.2003.A bounded influence regression estimator based on the statistics of the hat matrix.Journal of the Royal Statistical Society:Series C(Applied Statistics),52(3):307-322．
Chave A D.2017.Estimation of the magnetotelluric response function:The path from robust estimation to a stable maximum likelihood estimator.Surveys in Geophysics,38(5):837-867．
Chave A D,Mattsson J,Everett M E.2017.On the physics of frequency domain controlled source electromagnetics in shallow water.2:transverse anisotropy.Geophysical Journal International,211(2):1046-1061．
Chen H,Deng J Z,Tan H D,et al.2011.Study on divergence correction method in three-dimensional magnetotelluric modeling with staggered-grid finite difference method.Chinese J.Geophys.(in Chinese),54(6):1649-1659,doi:10.3969/j.issn.0001-5733.2011.06.025．
Deng J W,Deng M,Wei W B,et al.2004.The application of decimation filter in marine bottom magnetotelluric exploration.Journal of Jilin University:Earth Science Edition(in Chinese),34(2):271-276．
Egbert G D,Livelybrooks D W.1996.Single station magnetotelluric impedance estimation:Coherence weighting and the regression M-estimate.Geophysics,61(4):964-970．
Grayver A V,Streich R,Ritter O.2014.3Dinversion and resolution analysis of land-based CSEM data from the Ketzin CO2 storage formation.Geophysics,79(2):E101-E114．
He J S.2010a.Wild Field Electromagnetics and Pseudo-Random Signal Method(in Chinese).Beijing:Higher Education Press．
He J S.2010b.Closed addition in a three-element set and 2n sequence pseudo-random signal coding.Journal of Central South University(Science and Technology)(in Chinese),41(2):632-637．
Huang H P.1991.Electromagnetic data processing using the singular value decomposition method.Chinese J.Geophys.(Acta Geophysica Sinica)(in Chinese),34(5):644-650．
Kayacan E,Ulutas B,Kaynak O.2010.Grey system theory-based models in time series prediction.Expert Systems with Applications,37(2):1784-1789．
Lei D,Zhao G Z,Zhang Z J,et al.2010.A processing method of CSAMT data with strong electromagnetic interferences by using information entropy and rational function filtering.Progress in Geophysics(in Chinese),25(6):2015-2023．
Li G,Xiao X,Tang J T,et al.2017.Near-source noise suppression of AMT by compressive sensing and mathematical morphology filtering.Applied Geophysics,14(4):581-589．
Li J,Tang J T,Yan H,et al.2017.Identification and spearation of magnetotelluric signal and noise based on recurrence analysis and clustering.Chinese J.Geophys.(in Chinese),60(5):1918-1936,doi:10.6038/cjg20170525．
Li J,Zhang X,Tang J T,et al.2019.Audio magnetotelluric signalnoise identification and separation based on multifractal spectrum and matching pursuit.Fractals,27(1):1940007．
Lin Z B,Wang P Y,Wan Y X,et al.2016.A combined wavelet transform algorithm used for de-noising magnetotellurics data in the strong human noise.Chinese J.Geophys.(in Chinese),59(9):3436-3447,doi:10.6038/cjg20160926．
Liu W Q,Chen R J,Cai H Z,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 W Q,Chen R J,Cai H Z,et al.2017.Correlation analysis for spreadspectrum induced-polarization signal processing in electromagnetically noisy environments.Geophysics,82(5):E243-E256．
Liu W Q,LüQ T,Chen R J,et al.2019.A modified empirical mode decomposition method for multiperiod time-series detrending and the application in full-waveform induced polarization data.Geophysical Journal International,217(2):1058-1079．
Mo D,Jiang Q Y,Li D Q,et al.2017.Controlled-source electromagnetic data processing based on gray system theory and robust estimation.Applied Geophysics,14(4):570-580．
Nabighian M N.1987.Electromagnetic Methods in Applied Geophysics:Volume 1,Theory.SEG Books．
Olsen K B,Hohmann G W.1992.Adaptive noise cancellation for time-domain EM data.Geophysics,57(3):466-469．
Ramponi G.2001.Image processing with rational operators:Noise smoothing and anisotropic diffusion．∥Proceedings of the 2nd International Symposium on Image and Signal Processing and Analysis.Pula,Croatia,Croatia:IEEE,96-101．
Ren Z Y,Kalscheuer T,Greenhalgh S,et al.2013.A goal-oriented adaptive finite-element approach for plane wave 3-D electromagnetic modelling.Geophysical Journal International,194(2):700-718．
Ren Z Y,Chen C J,Tang J T,et al.2017.A new integral equation approach for 3D magnetotelluric modeling.Chinese J.Geophys.(in Chinese),60(11):4505-4515,doi:10.6038/cjg20171134．
Shi D,Zhang C S,Guo J S.1998.The application of grey comprehensive evaluation in some low-resistivity oil-gas bearing intervals.Progress in Geophysics(in Chinese),13(1):73-78．
Streich R,Becken M,Ritter O.2013.Robust processing of noisy land-based controlled-source electromagnetic data.Geophysics,78(5):E237-E247．
Szarka L.1988.Geophysical aspects of man-made electromagnetic noise in the earth-A review.Surveys in Geophysics,9(3-4):287-318．
Tang J T,Li G,Xiao X,et al.2017.Strong noise separation for magnetotelluric data based on a signal reconstruction algorithm of compressive sensing.Chinese J.Geophys.(in Chinese),60(9):3642-3654,doi:10.6038/cjg20170928．
Tang J T,Li G,Zhou C,et al.2018.Denoising AMT data based on dictionary learning.Chinese J.Geophys.(in Chinese),61(9):3835-3850,doi:10.6038/cjg2018L0376．
Trad D O,Travassos J M.2000.Wavelet filtering of magnetotelluric data.Geophysics,65(2):482-491．
Wang Z Y,Gao Y,Qin P.2002.Detection of gross measurement errors using the grey system method.The International Journalof Advanced Manufacturing Technology,19(11):801-804．
Yan J B,Liu G Z.2006.Smoothing scale of magnetotelluric sounding curve.Coal Geology&Exploration(in Chinese),34(5):60-62．
Yang Y,He J S,Li D Q.2018.A noise evaluation method for CSEM in the frequency domain based on wavelet transform and analytic envelope.Chinese J.Geophys.(in Chinese),61(1):344-357,doi:10.6038/cjg2018L0298．
Yang Y,Li D Q,Tong T G,et al.2018.Denoising controlledsource electromagnetic data using least-squares inversion.Geophysics,83(4):E229-E244．
Zhang B M,Jiang Q Y,Mo D,et al.2015.A novel method for handling gross errors in electromagnetic prospecting data.Chinese J.Geophys.(in Chinese),58(6):2087-2102,doi:10.6038/cjg20150623．
Zhou C,Tang J T,Ren Z Y,et al.2015.Application of the Rhoplus method to audio magnetotelluric dead band distortion data.Chinese J.Geophys.(in Chinese),58(12):4648-4660,doi:10.6038/cjg20151226．
Zhu J M,Bin H Z,Wang Z Y,et al.2000.A grey evaluation method of measurement result with standard uncertainty.Journal of Huazhong University of Science and Technology(in Chinese),28(9):84-86．
Ziolkowski A,Wright D,Mattsson J.2011.Comparison of pseudorandom binary sequence and square-wave transient controlledsource electromagnetic data over the Peon gas discovery,Norway.Geophysical Prospecting,59(6):1114-1131．
陈辉，邓居智，谭捍东等．2011．大地电磁三维交错网格有限差分数值模拟中的散度校正方法研究．地球物理学报，54(6):1649-1659,doi:10.3969/j.issn.0001-5733.2011.06.025．
邓靖武，邓明，魏文博等．2004．抽取滤波在海底大地电磁探测中的应用．吉林大学学报：地球科学版，34(2):271-276．
何继善．2010a．广域电磁法和伪随机信号电法．北京：高等教育出版社．
何继善．2010b．三元素集合中的自封闭加法与2n系列伪随机信号编码．中南大学学报（自然科学版），41(2):632-637．
黄皓平．1991．电磁法数据处理的奇异值分解法．地球物理学报，34(5):644-650．
雷达，赵国泽，张忠杰等．2010．强干扰地区CSAMT数据信息熵与有理函数滤波的处理方法．地球物理学进展，25(6):2015-2023．
李晋，汤井田，燕欢等．2017．基于递归分析和聚类的大地电磁信噪辨识及分离．地球物理学报，60(5):1918-1936,doi:10.6038/cjg20170525．
凌振宝，王沛元，万云霞等．2016．强人文干扰环境的电磁数据小波去噪方法研究．地球物理学报，59(9):3436-3447,doi:10.6038/cjg20160926．
任政勇，陈超健，汤井田等．2017．一种新的三维大地电磁积分方程正演方法．地球物理学报，60(11):4506-4515,doi:10.6038/cjg20171134．
施冬，张春生，郭甲世．1998．灰色综合评判法在低阻油气层中的应用．地球物理学进展，13(1):73-78．
汤井田，李广，肖晓等．2017．基于压缩感知重构算法的大地电磁强干扰分离．地球物理学报，60(9):3642-3654,doi:10.6038/cjg20170928．
汤井田，李广，周聪等．2018．基于字典学习的音频大地电磁数据处理．地球物理学报，61(9):3835-3850,doi:10.6038/cjg2018L0376．
严家斌，刘贵忠．2006．大地电磁测深曲线平滑尺度．煤田地质与勘探，34(5):60-62．
杨洋，何继善，李帝铨．2018．在频率域基于小波变换和Hilbert解析包络的CSEM噪声评价．地球物理学报，61(1):344-357,doi:10.6038/cjg2018L0298．
张必明，蒋奇云，莫丹等．2015．电磁勘探数据粗大误差处理的一种新方法．地球物理学报，58(6):2087-2102,doi:10.6038/cjg20150623．
周聪，汤井田，任政勇等．2015．音频大地电磁法“死频带”畸变数据的Rhoplus校正．地球物理学报，58(12):4648-4660,doi:10.6038/cjg20151226．
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