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1、GEOPHYSICS,VOL.71,NO.1(JANUARY-FEBRUARY2006);P.T7T11,4FIGS.10.1190/1.2149900Anexactsolutionoftheconversionpointfortheconvertedwavesfromadippingreflectorwithhomogeneous(isotropic)overburdenChunfangYuan1,SupingPeng1,andChunmingLi2forP-SVconvertedwavesinhomogeneousisotropicmedi
2、a.ABSTRACTThatsolutioniscalculatedasafunctionofoffset,velocityratiovP/vS,andreflectordepth.Taylor(1989)findsasimilarsolu-Forconvertedwaves,stackingtraceswithacommontion.Schneider(2002)givesanotheranalyticsolutionforthereflectionpoint,forminggathers,andperformingdipconversionpo
3、intforP-SVconvertedwavesinhomogeneousmoveout(DMO)allrequireaccuratelycalculatingtheisotropicmedia.Thatsolutionisafunctionofoffset,velocitylocationofconversionpoints.Becauseoftheasymmet-ratio,andtwo-wayreflectiontraveltimeoftheP-SVconvertedricalpathsofconvertedwaves,evenforho
4、rizontallylay-waves.eredmedia,thecalculationofaconversionpointforInthisstudy,adippingreflectorwithahomogeneousconvertedwavesiscomplicated.Previousauthorshaveisotropicoverburdenisconsidered(Figure1).WefirstuseobtainedanalyticsolutionsfortheconversionpointforSnellslawtoderiveaq
5、uarticequationfortheP-SVconvertedconvertedwavesinahorizontallylayeredmedia.Wewaves.Auniqueanalyticsolutionoftheconversionpointisextendthoseresultstothemoregeneralcaseofcon-thenobtainedfromthequarticequation.Thissolutionisgivenvertedwavesfromadippingreflectorwithahomoge-asafu
6、nctionnotonlyoftheoffset,velocitiesvPandvS,andneous,isotropicoverburden.ByusingSnellslaw,wenormaldepthbutalsoofthedipangleattheconversionpoint.deriveaquarticequationandsolveituniquelyfortheconversionpoint.TheresultantanalyticexpressionisaP-SVCONVERSION-POINTEQUATIONFORfunct
7、ionofoffset,compressional-,andshear-waveve-ADIPPINGREFLECTORMODELlocities;normalreflectordepth;anddipangleattheconversionpoint.ThissolutioncanbereadilyusedtoAnearthmodelconsistingofadippinglayerisconsidered,generateaccuratesyntheticseismicresponsesforcon-asshowninFigure1.The
8、P-wavetravelsfromsourcepointSvertedwavesbasedonraytheory.Italsocanbeex-tothedippin
