基于加窗Hilbert变换的复偏振分析方法及其应用
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摘要
考虑到传统Hilbert变换所隐含的无限长序列假设的实际局限性,本文将多窗分析法引入到短时序列Hilbert变换中,通过构建复协方差矩阵和对该矩阵的特征值与特征向量的求解,获得三分量地震记录的时变偏振参数;基于不同波型的偏振特性与实测偏振参数,采用线性_余弦权重函数或高斯权重函数自适应空间滤波,识别与分离具有特定偏振特性的不同地震响应.针对天然地震三分量记录的处理结果表明,该方法在识别、分离具有特定偏振特性的不同地震响应方面具有一定的潜力.
The implying assumption of the traditional Hilbert transform is that the length of time series is infinite. Considering its actual limitation, a multi_taper method (MTM) is introduced into the Hilbert transform of three short_time series to construct a complex covariance matrix. Time_varying polarization parameters can be measured by computing the eigenvalues and eigenvectors of the covariance matrix analytically. Combining with the polarization characteristics of special wave types and the measured parameters of actual seismic data, some signals can be identified, and then be separated using some adaptive filters, such as linear-cosine function or Gaussian weighting function filters. Application example of actual three-component earthquake data demonstrates that this method can be used to identify and separate some special seismic responses with special polarization.
The implying assumption of the traditional Hilbert transform is that the length of time series is infinite. Considering its actual limitation, a multi_taper method (MTM) is introduced into the Hilbert transform of three short_time series to construct a complex covariance matrix. Time_varying polarization parameters can be measured by computing the eigenvalues and eigenvectors of the covariance matrix analytically. Combining with the polarization characteristics of special wave types and the measured parameters of actual seismic data, some signals can be identified, and then be separated using some adaptive filters, such as linear-cosine function or Gaussian weighting function filters. Application example of actual three-component earthquake data demonstrates that this method can be used to identify and separate some special seismic responses with special polarization.
引文
[1]加尔彼林ЕИ著.地震勘探偏振法.何樵登,杨宝俊译.北京:石油工业出版社,1989ГальперинЕИ.PolarizationMethodofSeismicExploration.HeQ D,YangBJtranslate.Beijing:PetroleumIndustryPress,1989
[2]PerelbergAI,HornbostelSC.Applicationsofseismicpolarization analysis.Geophysics,1994,59(1):119～130
[3]陈 ,张中杰,孙春岩等.利用自适应偏振滤波器剔除三分量地震资料中的随机与非随机噪声.见:中国地球物理学会年刊.北京:地震出版社,2002.18ChenY,ZhangZJ,SunCY,etal.Noisereductioninthree componentseismicdatausingdata-adaptivepolarizationfilters.In:AnnualofChineseGeophysicsSociety(inChinese).Beijing:SeismologicalPress,2002.18
[4]李英康,崔作舟.分离纵波和横波的偏振旋转法.地球物理学报,1994,37(增Ⅱ):372～282LiYK,CuiZZ.PandS_wavesseparatedbypolarizationrevolving method.ChineseJ.Geophys.(inChinese),1994,37(Suppl.Ⅱ):372～282
[5]刘 财,董世学,杨宝俊等.极化滤波在广角地震P、S波场分离中的应用.物探化探计算技术,1995,17(2):15～18LiuC,DongSX,YangBJ,etal.Applicationofthepolarization filterintheseismicsoundingdata.ComputingTechniquesfor GeophysicalandGeochemicalExploration(inChinese),1995,17(2):15～18
[6]葛 勇,韩立国,韩文明等.极化分析研究及其在波场分离中的应用.长春地质学院院报,1996,26(1):83～88GeY,HanLG,HanWM,etal.Studyandapplicationof polarizationanalysisinseparationofPandSwaves.Journalof ChangchunUniversityofEarthSciences(inChinese),1996,26(1):83～88
[7]黄中玉,高 林,徐亦鸣等.三分量数据的偏振分析及其应用.石油物探,1996,35(2):9～16HuangZY,GaoL,XuYM,etal.Theanalysisofpolarizationin three-componentseismicdataanditsapplication.Geophysical ProspectingforPetroleum(inChinese),1996,35(2):9～16
[8]DuZJ,FoulgerGR,MaoWJ,etal.Noisereductionforbroad band,three componentseismogramsusingdata adaptivepolarization filters.Geophy.J.Int.,2000,141:820～828
[9]SamsonJC,OlsonJV.Data adaptivepolarizationfiltersfor multichannelgeophysicaldata.Geophysics,1981,46(10):1423～1431
[10]黄忠贤,陈 虹,王贵华等.面波偏振与中国大陆岩石层横向不均匀性.地球物理学报,1994,37(4):456～468HuangZX,ChenH,WangGH,etal.Surfacewavepolarization andlateralheterogeneitiesofthelithosphereinChina.ChineseJ.Geophys.(inChinese),1994,37(4):456～468
[11]张中杰.多分量地震资料的各向异性处理与解释方法.哈尔滨:黑龙江教育出版社,2002ZhangZJ.MethodsofAnisotropicProcessingandInterpretationfor Multi_ComponentSeismicData.Harbin:HeilongjiangEducation Press,2002
[12]詹正彬,姚 姚.多波及横波地震勘探.北京:地质出版社,1994ZhanZB,YaoY.SeismicExplorationwithMulti_waveandShear Wave.Beijing:GeologicalPublishingHouse,1994
[13]SherriffRE,GeldartLP著.勘探地震学.徐中信,张中杰,于占元等译.长春:吉林科学技术出版社,1992SherriffRE,GeldartLP.ExplorationSeismology.XuZX,Zhang ZJ,YuZY,etal.translate.Changchun:JilinScienceand TechnologyPress,1992
[14]TanerMT,KoehlerF,SheriffRE.Complexseismictrace analysis.Geophysics,1979,44(6):1041～1063
[15]JohnEV.Complexpolarizationanalysisofparticlemotion.Bull.Seismol.Soc.Am.,1986,76(5):1393～1405
[16]Ren啨RM,FitterJL.Multicomponentseismicstudiesusing complextraceanalysis.Geophysics,1986,51(6):1235～1251
[17]LuoY,DossarySA,MarhoonM,etal.GeneralizedHilbert transformanditsapplicationsingeophysics.TheLeadingEdge,2003,March:198～202
[18]ThomsonDJ.Spectrumestimationandharmonicanalysis.IEEE Proc.,1982,70(9):1055～1096
[19]ParkJ.Multi_taperspectralanalysisofhigh_frequencyseismograms.J.Geophys.Res.,1987,92:12675～12684
[20]ParkJ,VernonIII.Frequencydependentpolarizationanalysisof high_frequencyseismograms.J.Geophys.Res.,1987,92:12664～12674
[21]LillyJM,ParkJ.Multiwaveletspectralandpolarizationanalysesof seismicrecords.Geophy.J.Int.,1995,122:1001～1021
[22]RiedelKS,AlexanderSidorenko.Minimumbiasmultipletaper spectralestimation.IEEETrans.SignalProcessing,1995,43(1):188～200
[23]BatailleK,ChiuJM.Polarizationanalysisofhigh_frequency,three_componentseismicdata.Bull.Seismol.Soc.Am,1991,81(2):622～642
[24]SamsonJC.Purestate,polarizedwaves,andprincipalcomponents inthespectraofmultiple,geophysicaltime series.Geophys.J.R.Astr.Soc.,1983,72:647～664
[25]JurkevicsA.Polarizationanalysisofthree componentarraydata.Bull.Seismol.Soc.Am,1988,78(5):1725～1743
[26]SamsonJC,OlsonJV.Somecommentsonthedescriptionsofthe polarizationstatesofwaves.Geophys.J.R.Astr.Soc.,1980,61:115～129
[27]FlinnEA.Signalanalysisusingrectilinearityanddirectionof particlemotion.Proc.IEEE,1965,12:1874～1876
[28]AlkazVG,OnofrashNI,PerelbergAI.PolarizationAnalysisof SeismicWaves(inRussian).ShtiintcaPress.1977
[2]PerelbergAI,HornbostelSC.Applicationsofseismicpolarization analysis.Geophysics,1994,59(1):119～130
[3]陈 ,张中杰,孙春岩等.利用自适应偏振滤波器剔除三分量地震资料中的随机与非随机噪声.见:中国地球物理学会年刊.北京:地震出版社,2002.18ChenY,ZhangZJ,SunCY,etal.Noisereductioninthree componentseismicdatausingdata-adaptivepolarizationfilters.In:AnnualofChineseGeophysicsSociety(inChinese).Beijing:SeismologicalPress,2002.18
[4]李英康,崔作舟.分离纵波和横波的偏振旋转法.地球物理学报,1994,37(增Ⅱ):372～282LiYK,CuiZZ.PandS_wavesseparatedbypolarizationrevolving method.ChineseJ.Geophys.(inChinese),1994,37(Suppl.Ⅱ):372～282
[5]刘 财,董世学,杨宝俊等.极化滤波在广角地震P、S波场分离中的应用.物探化探计算技术,1995,17(2):15～18LiuC,DongSX,YangBJ,etal.Applicationofthepolarization filterintheseismicsoundingdata.ComputingTechniquesfor GeophysicalandGeochemicalExploration(inChinese),1995,17(2):15～18
[6]葛 勇,韩立国,韩文明等.极化分析研究及其在波场分离中的应用.长春地质学院院报,1996,26(1):83～88GeY,HanLG,HanWM,etal.Studyandapplicationof polarizationanalysisinseparationofPandSwaves.Journalof ChangchunUniversityofEarthSciences(inChinese),1996,26(1):83～88
[7]黄中玉,高 林,徐亦鸣等.三分量数据的偏振分析及其应用.石油物探,1996,35(2):9～16HuangZY,GaoL,XuYM,etal.Theanalysisofpolarizationin three-componentseismicdataanditsapplication.Geophysical ProspectingforPetroleum(inChinese),1996,35(2):9～16
[8]DuZJ,FoulgerGR,MaoWJ,etal.Noisereductionforbroad band,three componentseismogramsusingdata adaptivepolarization filters.Geophy.J.Int.,2000,141:820～828
[9]SamsonJC,OlsonJV.Data adaptivepolarizationfiltersfor multichannelgeophysicaldata.Geophysics,1981,46(10):1423～1431
[10]黄忠贤,陈 虹,王贵华等.面波偏振与中国大陆岩石层横向不均匀性.地球物理学报,1994,37(4):456～468HuangZX,ChenH,WangGH,etal.Surfacewavepolarization andlateralheterogeneitiesofthelithosphereinChina.ChineseJ.Geophys.(inChinese),1994,37(4):456～468
[11]张中杰.多分量地震资料的各向异性处理与解释方法.哈尔滨:黑龙江教育出版社,2002ZhangZJ.MethodsofAnisotropicProcessingandInterpretationfor Multi_ComponentSeismicData.Harbin:HeilongjiangEducation Press,2002
[12]詹正彬,姚 姚.多波及横波地震勘探.北京:地质出版社,1994ZhanZB,YaoY.SeismicExplorationwithMulti_waveandShear Wave.Beijing:GeologicalPublishingHouse,1994
[13]SherriffRE,GeldartLP著.勘探地震学.徐中信,张中杰,于占元等译.长春:吉林科学技术出版社,1992SherriffRE,GeldartLP.ExplorationSeismology.XuZX,Zhang ZJ,YuZY,etal.translate.Changchun:JilinScienceand TechnologyPress,1992
[14]TanerMT,KoehlerF,SheriffRE.Complexseismictrace analysis.Geophysics,1979,44(6):1041～1063
[15]JohnEV.Complexpolarizationanalysisofparticlemotion.Bull.Seismol.Soc.Am.,1986,76(5):1393～1405
[16]Ren啨RM,FitterJL.Multicomponentseismicstudiesusing complextraceanalysis.Geophysics,1986,51(6):1235～1251
[17]LuoY,DossarySA,MarhoonM,etal.GeneralizedHilbert transformanditsapplicationsingeophysics.TheLeadingEdge,2003,March:198～202
[18]ThomsonDJ.Spectrumestimationandharmonicanalysis.IEEE Proc.,1982,70(9):1055～1096
[19]ParkJ.Multi_taperspectralanalysisofhigh_frequencyseismograms.J.Geophys.Res.,1987,92:12675～12684
[20]ParkJ,VernonIII.Frequencydependentpolarizationanalysisof high_frequencyseismograms.J.Geophys.Res.,1987,92:12664～12674
[21]LillyJM,ParkJ.Multiwaveletspectralandpolarizationanalysesof seismicrecords.Geophy.J.Int.,1995,122:1001～1021
[22]RiedelKS,AlexanderSidorenko.Minimumbiasmultipletaper spectralestimation.IEEETrans.SignalProcessing,1995,43(1):188～200
[23]BatailleK,ChiuJM.Polarizationanalysisofhigh_frequency,three_componentseismicdata.Bull.Seismol.Soc.Am,1991,81(2):622～642
[24]SamsonJC.Purestate,polarizedwaves,andprincipalcomponents inthespectraofmultiple,geophysicaltime series.Geophys.J.R.Astr.Soc.,1983,72:647～664
[25]JurkevicsA.Polarizationanalysisofthree componentarraydata.Bull.Seismol.Soc.Am,1988,78(5):1725～1743
[26]SamsonJC,OlsonJV.Somecommentsonthedescriptionsofthe polarizationstatesofwaves.Geophys.J.R.Astr.Soc.,1980,61:115～129
[27]FlinnEA.Signalanalysisusingrectilinearityanddirectionof particlemotion.Proc.IEEE,1965,12:1874～1876
[28]AlkazVG,OnofrashNI,PerelbergAI.PolarizationAnalysisof SeismicWaves(inRussian).ShtiintcaPress.1977
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