物探新方法新技术本科课程第八章.docx
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物探新方法新技术本科课程第八章.docx
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物探新方法新技术本科课程第八章
8谱分解技术
Recently,muchattentionhasbeengiventospectraldecomposition(光谱分解)inexplorationgeophysics.Thetechniquehasbeenusedforbothbedthicknessestimationsanddirecthydrocarbon碳氢化合物indications.However,thespectraldecompositionisnotreallyanewinventionofgeophysicists,anditsrootiscloselyrelatedtotheso-calledtime-frequencyrepresentation表现ofstationary稳定的andnon-stationarytimeseriesthathasbeenusedinsignalandimagingprocessingforover50years,thoughgeophysicistshaveplayedacentralroleinitsdevelopment[infact,JeanMorlet,ageophysicist,isoneofthetwo“inventors”ofthecontinuouswavelettransform.Theterm“spectraldecomposition”wascoinedbygeophysicistGregPartykaofBPin1999].TheincreaseuseofthespectraldecompositionmethodsinexplorationseismicinthelastfiveyearscanbelargelyattributedtothepioneeringworkofPartyka(1999)andCastagnaetal(2003).
BecauseoftheHeisenberguncertaintyprinciple,whichpreventsusfromachievingsimultaneous同时的localizationintimeandfrequency,lookingintotheliterature,wemayfindmanytechniquesthatcanbeusedforthesamepurpose.Inthisstudy,wereviewsixmostcommonlyusedtime-frequencyrepresentationandspectral-decompositiontechniquesandcomparethemagainstaseriesofseismicsignals.Weaimtoestablishsomepracticalguidelinesaboutthechoiceofthemethods.Itisnotsurprisedtofindthatallmethodsarecorrect,andthereisnotechniquewhichcanbeclaimedtobesuperiortoothersatalltimeandforallsignals,thoughonetechniquemaygivebetterresults(meaningbettertemporal暂时的ANDfrequencyresolution)thanothersforcertainkindsofsignalorundercertainconditions–hence因此everyonehashis/herownpreferredmethods.
8.1INTRODUCTION
Thereisagrowinginterestinexplorationgeophysicsintheapplicationofspectraldecompositionmethodsforbedthicknessdetermination(Partyka1999);stratigraphic地层的visualization可视化(Marfurt&Kirlin2001);directhydrocarbon(gas)detection(Castagnaetal.2003;Goloshubinetal.2006);detectionoffrequency-dependentseismicanisotropy各向异性(Liuetal.2003);andstudyoftheeffectsofattenuation衰减/dispersion分散onseismicamplitudes-variationswithoffsets(Chapmanetal.2005).Weshallseethattherootofthespectraldecompositionmaybetracedbacktoover50years,however,itisarelativelynewtechniqueanditspopularityhasincreasedingeophysicssincethepioneeringworkofPartykaetal.(1999),Castagnaetal.(2003),andmorerecently,Chapmanetal.(2005),whohaveextendedtheapplicationofspectraldecompositionanalysistoAVOstudiesintheframeworkofRutherfordandWilliamsAVOanalyses分析(Rutherford&Williams1989).Seismicattributesfromthetime-frequencydecompositionhavealsobeenproposed(seereferencesinSection6.4).
AccordingtoCastagna&Sun(2006),spectraldecompositionrefersto参考,涉及anymethodthatproducesacontinuoustime-frequencyanalysisofaseismictrace.Thusafrequencyspectrumisoutputforeachtimesampleoftheseismictrace.Spectraldecompositionisanon-uniqueprocess,thusasingleseismictracecanproducevarioustime-frequencyanalyses.Despitethelonghistorical历史的root,explorationgeophysicistshavefoundmanynewapplicationsoftime-frequencyrepresentationandspectraldecompositionmethodsinthelastfiveyears.
Time-frequencyanalysisisa2Drepresentationofone-dimensionalsignalintime-frequencyplaneanditofferstheabilitytoanalyse分析relativelongcontinuoussegments片段oftimeseries.Thetechniqueissimplyatime-frequencyanalysistechniquewidelyusedinimageprocessing,medicalimaging,acoustics声学,electricalengineering,astrophysics天体物理学,amongothers.Oneapproach方法?
totime-frequencyanalysisistorepresentthesignalasasumofwaveforms波形withwell-definedtime-frequencyproperties.InFourieranalysis,thesewaveformsaresimplycosineandsinefunctionsthatprovidegoodlocalization定位infrequencybutnotintime.ToachieveagoodlocalizationbothintimeANDinfrequency,thereareavarietyoftime-frequencymethods,includingtheshort-timeFouriertransformorwindowedFourierTransform(WFT),maximumentropy熵method(MEM),Wigner-Villetransform(WVT)andvariousextensions,continuouswavelettransform(CWT),StockwellorS-transform(SWT),andmatchingpursuitmethod(MPM).Aswewillseefromthisreview,someofthesetechniquesarenotcompletedindependentandarecloserelativesofeachothers.AsCastagan&Sun(2006)correctlystatethatnoneofthesemethodsare,strictlyspeaking,rightorwrong.Eachmethodhasitsownadvantagesanddisadvantages,anddifferentapplicationsrequiredifferentmethods.Amongthemethodsmentionedabove,theWFTinvolvesexplicit明确的useoffixed-lengthwindows,andthenatureofthewindowinghasasignificanteffectonthetimeandspectralresolutionoftheoutput.TheMEMworksinthesimilarwayastheWFT,wherethepowerspectrum功率谱ofasignaliscomputedusingthemaximumentropymethodinsteadoftheconventionalFouriertransform.TheCWTisequivalenttotemporalnarrow-bandfilteringofthesignalandhasanadvantageovertheWFTforbroadbandsignalsinthatthewindowisfrequencydependent,i.e.varyingwindowlengths.Analternativemethod,usedinseveralmotivatingstudies,istheS-transforminventedbyStockwelletal.(1996),whichisanextensionofthewindowedFouriertransformwhichusesfrequency-dependentscalingwindowsinanalogy类推tothewavelettransform(however,itisnotthewavelettransformbecauseS-transformdoesnotsatisfyadmissibility容许性).Thispermitsafrequency-dependentresolutionwithnarrowerwindowsathigherfrequenciesandwiderwindowsatlowerfrequencies.Anotherpowerfultechnique,MPM,developedbyMallat&Zhang(1993),isbasedonthewavelettransform,butusesafamilyofwavelets(“waveletatom原子”orwaveletdictionary)composedofGaborfunctionssupplementedwithacanonical正则basisofdiscrete离散的DiracfunctionsanddiscreteFourierbasisofcosineandsincefunctions.Thisdictionaryprovidesarichcollectionofatomicwaveformswhicharelocatedonamuchfinergridinthetime-frequencyspacethanwaveletandcosinepackettables.TheMPMisamorecomputationallyintensiveprocessthantheothers,andCastagna&Sun(2006)claimthatithassuperiortemporalandspectralresolutionifacompactmotherwaveletisutilized被利用的.
Inthispaper,weprovideasystematic系统的overviewofthemostcommonlyusedmethodsabouttime-frequencyrepresentationofatime-variantsignal,andcomparethemagainstsomecommonsignals.Ourgoalistoprovidesomepracticalguidelinestothechoiceofthemethodsinthecontextofexplorationseismicapplications.
8.2FOURIERTRANSFORMANDHEISENBERGUNCERTAINTY
Westartwiththemostbasictechniquefordeterminingthefrequencydistributionofasignalu(t),i.e.theFouriertransform.Thisisgivenbythefamiliarintegral积分的transform
.(8-1)
TheFouriertransformisinvertible可逆的,implyingthesignalu(t)canberecoveredby
.(8-2)
Thewell-knownpropertyoftheFourierspectrumofasignalisthatitislocalizedinfrequency,butnotintime.Forexample,aninfinite无穷的lengthcosinesignalwilltransformedtoadelta(δ)pulse(singlefrequency).Figure8-1showsaseismicsignalanditsFourierspectrum.Wecannottellthetimecorrespondingtothefrequencycontents–thearrivaltimeofthelowfrequencypulse,whichiscentredat0.08sec,cannotberevealedfromthesignal’sspectralplot.Notethemulti-taperspectralalgorithmofParketal.(1987)maybeusedwhichcanproducemuchsmootherspectralthantheconventionalsingletaperFFT.
Figure8-1.Achirp-likeguidedwave导波fromaninseamseismicexperimentanditsFourierspectrum.
Ouraimistoobtainthetime-dependentspectra光谱ofasignal.ThiscanbeachievedbytakingtheFouriertransformwithashortmovingwindowalongthesignaltoobtainthetime-frequencyspectrumcalledspectrogram光谱图.ThoughtheFourierrepresentationofasignalisunique,thetime-frequencyrepresentationofthissignalwillnotbeunique.Asaresult,therearemanymethodsthathavebeenproposed建议,打算torepresentatransient短暂的,瞬时的signalaimingtoachievelocalizedspectrum.ThemovingwindowFouriertransformorsimplycalledwindowedFouriertransformisoneofthesimplestmethods.Herewelistsixmostpopularmethodsthatcanusuallybefoundingeophysicalandothersignalprocessingliterature:
a.Short-timeFouriertransformorwindowedFouriertransform(WFT)
b.Maximumentropymethod(MEM)
c.Wigner-Villetransform(WVT)
d.Continuouswavelettransform(CWT)
e.StockwellorS-transform(SWT)
f.Matchingpursuitmethod(MPM)
8.3METHODCOMPARISON:
TESTEXAMPLES
Wetestthemethodsintheprevioussectionson3signals:
(a)aguidedwavefromanin-seamseismicexperimentinaUKcoalmine(afterLiuetal.1992);(b)asimpleRickerwaveletwithapeakfrequencyof50Hz,and(c)asynthetic合成的timeseriescontainingaseriesofRickerwaveletsatdifferentseparations.
8.3.1Dispersive分散的channel/guidedwaves
Figures8-8to8-11comparetime-frequencyspectrogramsfromvariousmethods.Weusethissignalinourfirsttestexamplebecauseitshowsobviousdispersivecharacteristicsofguidedorchannelwaves(whichareverysimilartochirp线性调频脉冲signals).Infact,amajorapplicationoftime-frequencyrepresentationoftimeseriessignalsinseismologyhasbeentheextraction抽取ofdispersioncharacteristics(velocityasafunctionoffrequency)ofsurfacewavesgeneratedfromteleseismic远震events.TheguidedwavedisplayedinFigures8-8to8-10isverysimilartoatypicalRayleighorLovesurfacewavesfromearthquakeexcep
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