基于小波多尺度分析的奇性指数:一种新地震属性
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摘要
传统的地震解释主要是观测地震振幅及相位的变化,但是地震振幅也会掩盖地下介质中真实的地质情况.在许多情况下,重要的地质信息可能是通过与振幅特征无关的奇异性参数来传递的.本文提出奇异性指数,即Hlder指数α(又被称为Lipschitz指数),可以作为一种新的地震属性,它能够准确反映数据中的奇点的位置和奇异性强度.Hlder指数α是对某一点上或某一点周围很小的范围内的奇异性强度的度量,大的α值表示低的奇异性(或高的正则性).研究表明α可以作为一种自然的能够精确刻画地层边界的地震属性.本文根据这一思想,对合成和实测的地震数据进行了小波基础上的多尺度分析研究,结果表明由本文的算法得到的α提高了对地层边界划分的能力,而这些地层界面在传统的地震振幅显示则不明显.
Seismic interpretation is traditionally based on reflection or amplitude. However, amplitude can also disguise the true nature of subsurface geology and blur stratigraphy boundaries. In many cases important information is carried by singularities that are not necessarily associated to a certain amplitude pattern. We present the Hlder exponent (α) as a new seismic attribute which captures locations and strengths of irregularities in data. The Hlder exponent (α) is a measure of singularity strength defined at or around a point. Higher α indicates a higher degree of regularity. We demonstrate that α is a natural attribute for delineating stratigraphy boundaries due to its excellent ability in detecting detailed geologic features from seismic data. We test our concept and wavelet-based multiscale analyzing algorithm on both synthetic and seismic data, and show that α improves our ability in the delineation of stratigraphy layers that would be otherwise vague in the original amplitude display. α has the potential to bring a major breakthrough in seismic data interpretation.
Seismic interpretation is traditionally based on reflection or amplitude. However, amplitude can also disguise the true nature of subsurface geology and blur stratigraphy boundaries. In many cases important information is carried by singularities that are not necessarily associated to a certain amplitude pattern. We present the Hlder exponent (α) as a new seismic attribute which captures locations and strengths of irregularities in data. The Hlder exponent (α) is a measure of singularity strength defined at or around a point. Higher α indicates a higher degree of regularity. We demonstrate that α is a natural attribute for delineating stratigraphy boundaries due to its excellent ability in detecting detailed geologic features from seismic data. We test our concept and wavelet-based multiscale analyzing algorithm on both synthetic and seismic data, and show that α improves our ability in the delineation of stratigraphy layers that would be otherwise vague in the original amplitude display. α has the potential to bring a major breakthrough in seismic data interpretation.
引文
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[22]陈广军,宋国奇,韩其玉.应用奇性分形反演技术进行储集层描述.石油地球物理勘探,2002,37(2):117～128ChenGJ,SongGQ,HanQY.Trialofapplicationofodd fractal inversiontechnologyinreservoirdescription.OilGeophysical Prospecting(inChinese),2002,37(2):117～128
[23]王忠仁,何樵登.叠前共炮点道集的奇性反演研究.地球物理学报,1998,41(增刊):326～336WangZR,HeJD.Thesingularityinversionfortheunstacked common_sourcegather.ChineseJ.Geophys.(inChinese),1998,41(Suppl.):326～336
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[25]WapenaarK,GouswaardJ,vanWijngaardenA_J.Multiangle,multiscaleinversionofmigratedseismicdata.TheLeadingEdge,1999,18:928～932
[26]LyonsWJ,HerrmannFJ,GrotzingerJ.Singularityanalysis:atool forextractinglithologicandstratigraphiccontentfromseismicdata.
71stAnn.InternatMtg.,Soc.Expl.Geophys.Expanded Abstracts,2001
[27]ArneodoA,BacryE,JaffardS,etal.Singularityspectrumof multifractalfunctionsinvolvingoscillatingsingularities.J.of FourierAnalysisandApplications,1998,4:159～174
[28]TodoeschuckJP,JensonOG.Josephgeologyandseismic deconvolution.Geophysics,1988,53:1410～1414
[29]MisraPC,RoyTK.ExplorationinAndamanfore_arcbasin,its evaluation,faciestrendandprospects_areview.SPEpaper12384,1984
[30]UniversityofTulsa.Wavelet_basedanalysisofsingularitiesin seismicdata.Inventor:LIChun_Feng,LinerC.Int.Cl7:G01V128.U.S.Cl:70217.U.S.patent6745129B1.June01,2004
[2]BahorichMS,FarmerSL.3Dseismicdiscontinuityforfaultsand stratigraphicfeatures:Thecoherencecube.65thAnn.Internat.Mtg:Soc.ofExpl.Geophys.ExpandedAbstracts,1995,93～96
[3]TanerMT,KoehlerF,SheriffRE.Complexseismictrace analysis.Geophysics,1979,44:1041～1063
[4]HerrmannFJ,StarkC.Monoscaleanalysisofedges reflectorsusing fractionaldifferentiations integrations.69thAnn.InternatMtg.,Soc.Expl.Geophys.ExpandedAbstracts,1999
[5]HerrmannFJ,StarkC.Ascaleattributefortextureinwell_and seismicdata.70thAnn.InternatMtg.,Soc.Expl.Geophys.ExpandedAbstracts,2000
[6]LIChun_Feng.Scalingandwavelet_basedsingularityanalysesfor geologicalandgeophysicalinterpretation[Ph.D.dissertation].Tulsa:Univ.ofTulsa,2002
[7]LIChun Feng.Informationpassagefromacousticimpedanceto seismograms:perspectivefromwavelet basedmultiscaleanalysis.J.Geophys.Res.,2004,109,B07301,doi:10.10292003JB002882
[8]StruzikZR.Determininglocalsingularitystrengthsandtheirspectra withthewavelettransform.Fractals,2000,8(2):163～179
[9]SeuretS,GilbertA.PointwiseH lderexponentestimationindata networktraffic.InternationalTeletrafficCongressWorkshop,Monterey,Canada.2000
[10]KolwankarKM,LevyVehelJ.Atimedomaincharacterizationof thefinelocalregularityoffunctions.JFAA,2002,8:319～334
[11]LevyVehelJ,LuttonE.Evolutionarysignalenhancementbasedon H lderregularityanalysis.EVOLASP,LakeComo,Italy,Springer Verlag,2001
[12]HerrmannFJ.Singularitycharacterizationbymonoscaleanalysis:Applicationtoseismicimaging.Appl.Comput.Harmon.Anal.,2001,11:64～88
[13]MallatS,HwangW_L.Singularitydetectionandprocessingwith wavelets.IEEETransactionsonInformationTheory,1992,38:617～642
[14]LIChun_Feng.Rescaled_rangeandpowerspectrumanalysesonwell_loggingdata.Geophys.J.Int.,2003153:201～212
[15]GuiheneufB,LevyVehelJ.2-microlocalanalysisandapplications insignalprocessing.In:ProceedingsofInternationalWavelets Conference,Tangier,1998
[16]李世雄.一维波动方程的奇性反演与小波.地球物理学报,1995,38(1):93～104LiSX.Analysisandinversionofsingularitiesofone_dimensional waveequationsandwavelets.ChineseJ.Geophys.(inChinese),1995,38(1):93～104
[17]杨云雁,李世雄.一维有耗散波动方程的奇性分析与小波.地球物理学报,1999,42(1):94～101YangYY,LiSX.Analysisofsingularitiesofone dimensionalwave equationswithdissipationsandwavelets.ChineseJ.Geophys.(in Chinese),1999,42(1):94～101
[18]曹聿明.地震道的奇性特征与分辨率.石油地球物理勘探,1995,30(4):480～486CaoYM.Resolutionandsingularityofseismictrace.Oil GeophysicalProspecting(inChinese),1995,30(4):480～486
[19]郑继明.小波变换在地震道奇异性检测中的应用.重庆邮电学院学报,1997,9(1):66～69ZhengJM.Theapplicationofwavelettransforminthesingularity detectionofseismictrace.J.ChongqingUniv.PostsTel.(in Chinese),1997,9(1):66～69
[20]李庆春,朱光明.基于小波变换的薄层地震信号奇点的检测.地震学报,2000,22(1):54～58LiQC,ZhuGM.Wavelet_basedsingularitydetectionofthin_layer seismicsignal.ActaSeismologicaSinica(inChinese),2000,22(1):54～58
[21]田金文,高 谦,杜拥军.基于小波变换模极大值的地震信号去噪处理方法.江汉石油学院学报,2001,23(1):22～25TianJW,GaoQ,DuYJ.Aseismicdataprocessingmethodbased onmodularmaximumofwavelettransforms.J.JianghanPetro.Inst.(inChinese),2001,23(1):22～25
[22]陈广军,宋国奇,韩其玉.应用奇性分形反演技术进行储集层描述.石油地球物理勘探,2002,37(2):117～128ChenGJ,SongGQ,HanQY.Trialofapplicationofodd fractal inversiontechnologyinreservoirdescription.OilGeophysical Prospecting(inChinese),2002,37(2):117～128
[23]王忠仁,何樵登.叠前共炮点道集的奇性反演研究.地球物理学报,1998,41(增刊):326～336WangZR,HeJD.Thesingularityinversionfortheunstacked common_sourcegather.ChineseJ.Geophys.(inChinese),1998,41(Suppl.):326～336
[24]Dessing,FJ.Awavelettransformapproachtoseismicprocessing[Ph.D.thesis].Delft:DelftUniv.ofTechnology,Netherlands,1997
[25]WapenaarK,GouswaardJ,vanWijngaardenA_J.Multiangle,multiscaleinversionofmigratedseismicdata.TheLeadingEdge,1999,18:928～932
[26]LyonsWJ,HerrmannFJ,GrotzingerJ.Singularityanalysis:atool forextractinglithologicandstratigraphiccontentfromseismicdata.
71stAnn.InternatMtg.,Soc.Expl.Geophys.Expanded Abstracts,2001
[27]ArneodoA,BacryE,JaffardS,etal.Singularityspectrumof multifractalfunctionsinvolvingoscillatingsingularities.J.of FourierAnalysisandApplications,1998,4:159～174
[28]TodoeschuckJP,JensonOG.Josephgeologyandseismic deconvolution.Geophysics,1988,53:1410～1414
[29]MisraPC,RoyTK.ExplorationinAndamanfore_arcbasin,its evaluation,faciestrendandprospects_areview.SPEpaper12384,1984
[30]UniversityofTulsa.Wavelet_basedanalysisofsingularitiesin seismicdata.Inventor:LIChun_Feng,LinerC.Int.Cl7:G01V128.U.S.Cl:70217.U.S.patent6745129B1.June01,2004
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