8ThefilteringcharacteristicsofHHTanditsapplicationinacousticlogwaveformsignalprocessing*WangZhuwen1◆,LiuJinghua1,YueChongwang1,LiXiaochun1,andLiChangchun1ManuscriptreceivedbytheEditorJuly27,2008;revisedmanuscriptreceivedJanuary24,2009.*ThisresearchissupportedbyNationalNaturalScienceFoundationofChina(GrantNo.40874059)andtheNationalKeyScienceEngineeringProjectsoftheNinthFiveYearPlan([1999]1423).1.GeoExplorationCollegeofScienceandTechnology,JilinUniversity,Changchun130026,China.◆Correspondingauthor(WangZhuwen,email:wangzhuwen@email.jlu.edu.cn).APPLIEDGEOPHYSICS,Vol.6,No.1(March2009),P.8-16,5Figures.DOI:10.1007/s11770-009-0007-0Abstract:Arrayacousticloggingplaysanimportantroleinformationevaluation.Itsdataisanon-linearandnon-stationarysignalandarrayacousticloggingsignalshavetime-varyingspectrumcharacteristics.Traditionalfilteringmethodsareinadequate.WeintroduceaHilbert-Huangtransform(HHT)whichmakesfullpreservationofthenon-linearandnon-stationarycharacteristicsandhasgreatadvantagesintheacousticsignalfiltering.Usingtheempiricalmodedecomposition(EMD)method,theacousticlogwaveformscanbedecomposedintoafiniteandoftensmallnumberofintrinsicmodefunctions(IMF).TheresultsofapplyingHHTtorealarrayacousticloggingsignalfilteringandde-noisingarepresentedtoillustratetheefficiencyandpowerofthisnewmethod.Keywords:Hilbert-Huangtransform,empiricalmodedecomposition,intrinsicmodefunctions,time-frequencyfilterIntroductionAsoneoftheimportantmethodsforreservoirevaluation,theacousticloggingtechniquehasbeendevelopingveryfast.Therearefullwaveformlogging,monopolearrayacousticlogging,anddipoleshearwaveimageloggingemployedinproduction.Thefullwaveformincludesprimary,shear,Stoneley,andpseudo-Rayleighwaves(Chu,1985,WangandWang,2004,ChenandZhang,2002,TaoandZou,2000,ZhangandWang,1998).Whenanalyzingthefullwaves,weneedtoperformfilteringinbothtimeandfrequencydomainsinordertoseparatedifferentcomponentwaves.Theformationcannotbeeffectivelyevaluateduntilallcomponentwavesarepreciselyextracted(Lietal.,1999;ZhuandShen,2006;Liuetal.,2005;Lietal.,1997;Wang,etal.2007aand2007b,2008a,2008b,and2008c).Acousticloggingisstronglyaffectedbyenvironmentalinterferences,makingtheextractionofformationsignalsextremelydifficult.Optimalsignalprocessingisthusanimportanttaskinhandlingacousticloggingdata.OneofthetraditionalmethodsistousetheFourierTransform(FT)technique,mappingtimedomainsignalsintothefrequencydomainforanalysis(Zhangetal.,2008;Wangetal.,2007aand2007b;Donnbo,1995).Thismethodisrelativelyeffectivewhenthesignalisstationaryandhasgoodsignaltonoiseratio.However,forthenon-linearandnon-stationaryarrayacousticloggingsignalinwhicheveryfrequencycomponentateachmomentneedstobeanalyzed,theFTtechniquebecomesinadequate.TheHilbert-HuangTransform(HHT)isanewlydevelopedtime-frequencyanalysismethodfornon-linearandnon-stationarysignalprocessing(Huang,etal.1996,1998,1999).Itcanbeusedtofilterandde-noisethenon-stationarysignalsofarrayacousticlogging9Wangetal.waveforms.Ithasgoodadaptabilityandcananalyzebothtimeandfrequencydomainsignals.WehaveappliedtheHHTtothefilteringanddenoisingofarrayacousticloggingdataandobtainedrelativelypuremodewavesforfurtheranalysis.Inthispaper,weshallbrieflyintroducetheprinciplesofthemethodologyandprovideillustrativeexamplesofitsapplication.TheHilbert-HuangtransformprinciplesHistorically,Fourierspectralanalysishasbeenageneralme...
