利用单频双程波动方程计算初至走时及其振幅
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摘要
通过在频率域双程波动方程模拟算法中加入一个复数频率(实部表示频率,虚部表示衰减因子)压制地震波初至走时之后的能量,从而把初至走时及其振幅的计算问题转换为单一频率波场中最大能量走时和振幅的拾取问题,然后利用单一频率域波场的相位项和振幅项分别计算初至走时及其振幅.本文还提出利用参数分析方法求取最优的复数频率,并给出数值计算例子,将本方法的计算结果与有限差分程函方程初至走时和最大能量走时振幅进行比较,结果表明,该方法具有适应于任意复杂介质和多炮多接收点走时和振幅的计算.
By adding one complex frequency (real part is frequency and the imaginary part is damping factor) into the frequency-domain wave equation, the energy or amplitude after first-arrival wave can be damped. Therefore, the first-arrival traveltime and amplitude can be transformed into the pick of maximum energy and its amplitude in the monochromatic wavefield. Then, the first-arrival traveltime and amplitude can be extracted from the phase and amplitude of monochromatic frequency-domain wavefield. In order to obtain the optimum combination of the frequency and damping factor, we propose a parameter analysis scheme for all possible combinations. The numerical examples are compared with finite-difference eikonal solvers and most-energetic amplitude. The results show that our algorithm has good applicability to multi-shot and multi-receiver computation in complex media.
By adding one complex frequency (real part is frequency and the imaginary part is damping factor) into the frequency-domain wave equation, the energy or amplitude after first-arrival wave can be damped. Therefore, the first-arrival traveltime and amplitude can be transformed into the pick of maximum energy and its amplitude in the monochromatic wavefield. Then, the first-arrival traveltime and amplitude can be extracted from the phase and amplitude of monochromatic frequency-domain wavefield. In order to obtain the optimum combination of the frequency and damping factor, we propose a parameter analysis scheme for all possible combinations. The numerical examples are compared with finite-difference eikonal solvers and most-energetic amplitude. The results show that our algorithm has good applicability to multi-shot and multi-receiver computation in complex media.
引文
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[32]ShinC ,YoonK ,MarfurtKJ,etal.Efficientcalculationofapartial derivativewavefieldusingreciprocityforseismicimagingandinversion.Geophysics,2001,66(6):1856～1863
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[34]WangY .Arobustseismicphaseunwrappingmethod.JournalofSeismicExploration,2000,9:93～104
[2]丁志峰,何正勤,孙为国等.青藏高原东部及其边缘地区的地壳上地幔三维速度结构.地球物理学报,1999,42(2):197～205DingZF ,HeZQ ,SunWG ,etal.3DcrustanduppermantlevelocitystructureineasternTibetanPlateauanditssurroundingareas.ChineseJ .Geophys.(inChinese),1999,42(2):197～205
[3]王 辉,常 旭.基于图形结构的三维射线追踪方法.地球物理学报,2000,43(4):534～541WangH ,ChangX .3Draytracingmethodbasedongraphicstructure.ChineseJ.Geophys.(inChinese),2000,43(4):534～541
[4]张建中,陈世军,余大祥.最短路径射线追踪方法及其改进.地球物理学进展,2003,18(1):146～150ZhangJZ ,ChenSJ,YuDX .Shortest pathraytracinganditsimprovement.ProgressinGeophysics(inChinese),2003,18(1):146～150
[5]赵连峰,朱介寿,曹俊兴等.有序波前射线法的射线追踪.地球物理学报,2003,46(3):415～420ZhaoLF ,ZhuJS ,CaoJX ,etal.Raytracingusingordinalwavefrontreconstructionmethod.ChineseJ .Geophys.(inChinese),2003,46(3):415～420
[6]赵爱华,张中杰,王光杰等.非均匀介质中地震波走时与射线路径快速计算技术.地震学报,2000,22(2):151～157ZhaoAH ,ZhangZJ ,WangGJ,etal.Fastcomputationofseismic wavetraveltimeandraypathinheterogeneousmedia.ActaSeismologicaSinica(inChinese),2000,22(2):151～157
[7]SunY .Raytracingin3Dmediabyparametrizedshooting.GeophysicalJournalInternational,1993,114(1):145～155
[8]VirieuxJ,FarraV .Raytracingin3Dcomplexisotropicmedia:ananalysisoftheproblem.Geophysics,1991,56(12):2057～2069
[9]EhingerA ,JuradoF ,MonestieC .Calculationofmulti valuedtraveltimeswitharaybendingmethod.68thAnn.Internat.Mtg.,Soc.Expl.Geophys..ExpandedAbstracts,1998.1893～1896
[10]VinjeV ,IversenE ,GjystdalH .Traveltimeandamplitudeestimationusingwavefrontconstruction.Geophysics,1993,58(8):1157～1166
[11]VinjeV ,IversenE ,AsteblK ,etal.Estimationofmulti valuedarrivalsusingwavefrontconstructionPartI.GeophysicalProspecting,1996,44(5):819～842
[12]VinjeV ,IversenE , steblK ,etal.EstimationofmultivaluedarrivalsusingwavefrontconstructionPartII :Tracingandinterpolation.GeophysicalProspecting,1996,44(5):843～858
[13]ComanR ,GajewskiD .Estimationofmultivaluedarrivalsin3Dmodelsusingwavefrontraytracing.71stAnn.Internat.Mtg.,Soc.Expl.Geophys..ExpandedAbstracts,2001.1265～1268
[14]GibsonJrR .Raytracingbywavefrontconstructionforanisotropicmedia.70 thAnn.Internat.Mtg.,Soc.Expl.Geophys..ExpandedAbstracts,2000.2305～2308
[15]ChangT ,DownieAL .3Dmultivaluedray tracingbywavefrontconstruction.58thMtg.,Eur.Assn.Geosci.Eng..1996.109～110
[16]VidaleJE .Finite differencecalculationoftraveltimes.Bull.Seis.Soc.Am.,1988,78(6):2062～2076
[17]PodvinP ,LecompteI.Finitedifferencecomputationoftraveltimesinverycontrastedvelocitymodels:amassivelyparallelapproachanditsassociatedtools.GeophysicalJournalInternational,1991,105(1):271～284
[18]QinF ,LuoY ,OlsenKB ,etal.Finitedifferencesolutionoftheeikonalequationalongexpandingwavefronts.Geophysics,1992,57(3):478～487
[19]HoleJA ,ZeltBC .3Dfinite differencereflectiontraveltime.GeophysicalJournalInternational,1995,121(2):427～434
[20]Afnimar,KoketsuK .Finitedifferencetraveltimecalculationforheadwavestravelingalonganirregularinterface.GeophysicalJournalInternational,2000,143(3):729～734
[21]MoLW ,HarrisJM .Finite differencecalculationofdirect arrivaltraveltimesusingtheeikonalequation.Geophysics,2002,67(6):1270～1274
[22]SethianJA ,PopoviciAM .3Dtraveltimecomputationusingthefastmarchingmethod.Geophysics,1999,64(3):516～523
[23]AlkhalifahT ,FomelS .Implementingthefastmarchingeikonalsolver:sphericalversusCartesiancoordinates.GeophysicalProspecting,2001,49(2):165～178
[24]FomelS .Avariationalformulationofthefastmarchingeikonalsolver.StanfordExplorationProject,ReportSERGEY ,2000.127～147
[25]PopoviciAM ,SethianJA .3Dimagingusinghigherorderfastmarchingtraveltimes.Geophysics,2002,67(2):604～609
[26]RawlinsonN ,SambridgeM .Wavefrontevolutioninstronglyheterogeneouslayeredmediausingthefastmarchingmethod. GeophysicalJournalInternational,2004,156(3):631～647
[27]NicholsDE .Maximumenergytraveltimescalculatedintheseismicfrequencyband.Geophysics,1996,61(1):253～263
[28]ShinCS ,KoSW ,MarfurtK ,etal.WaveequationcalculationofmostenergetictraveltimesandamplitudesforKirchhoffprestackmigration.Geophysics,2003,68(6):2040～2042
[29]ShinC ,KoS ,KimW ,etal.Traveltimecalculationsfromfrequency domaindownward continuationalgorithms.Geophysics,2003,68(4):1380～1388
[30]ShinS ,ShinC ,KimW .Traveltimecalculationusingmonochromaticone waywaveequation.70 thAnn.Internat.Mtg.,Soc.Expl.Geophys..ExpandedAbstracts,2000.2313～2316
[31]JoCH ,ShinC ,SuhJH .Anoptimal9 point,finite differencefrequency space2Dscalarwaveextrapolator.Geophysics,1996,61(2):529～537
[32]ShinC ,YoonK ,MarfurtKJ,etal.Efficientcalculationofapartial derivativewavefieldusingreciprocityforseismicimagingandinversion.Geophysics,2001,66(6):1856～1863
[33]WangY ,HousemanGA .Continousunwrappedphase.JournalofSeismicExploration,1998,7:109～116
[34]WangY .Arobustseismicphaseunwrappingmethod.JournalofSeismicExploration,2000,9:93～104
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