8/11/2015 FormulationandConditionsforSyntheticSeismogramshttp://www.uusatrg.utah.edu/RBSMITH/public_html/TEACHING/GG6220/SynthSeis.html 1/2GG6220Spring2005DefinitionsforSyntheticSeismogramsSyntheticseismogramsarecomputedbyassumingamathematicalmodelwithaparticulargeometryofthesourceandvelocitylayeringthatapproximatesanelasticoranelasticearth.Solutionsofvaryingapproximationstothewaveequationinthegeometryofthemodelresultintheoreticalamplitudeversustimeofarrivaltimesorwavefieldseismograms.Thesemaybeusedforstudyingwavepropagationthroughvariousmedia,calculatingamplitudeandwaveformresponsestovarioussourcesindifferentmodelsandforcomparisonwithobservedseismogramstoinferthemodel.Thecalculationofsyntheticseismogramsnormallyrequiresasolutiontothewaveequationforthegeometryandcharacteristicparametersofthemodel.Thisentailsapplicationofappropriateboundaryconditionsexactlyornumerically.(1)ModelsManyareeither1,2,or3dimensionalasshowninFigure1Figure11,2and3DModels(2)ElasticParameters(1D 2D 3D(3)Seismograms,displacementu,w,vinx1,x2,x3inCartesiancoordinates.1D 2D 3Du(x1,t) u(x1,x2,t) u(x1,x2,x3,t)w(x1,t) w(x1,x2,t) w(x1,x2,x3,t)v(x1,t) v(x1,x2,t) v(x1,x2,x3,t)(Note that a 1D model will produce seismograms that are different for various distances (due to various angles of incidence).Inexplorationseismology,itiscommontorefertoa1Dmodeland1Dsyntheticseismogramswhichareforverticalincidentwavesonly.)(4)PropagationTypesAcoustic Elastic Seismic(anelastic)fluid,pressurewaveonly solid,noabsorption solid,includingabsorption(5)WaveTypesAcoustic Elastic Seismic(anelastic)P,SV,SHP SV,SV PLove(SH),Rayleighhighermodes(equivalenttoguidedwaves)(6)Source(atsurfaceordepth)PointSources FiniteSourcesVerticalForceExplosive(compressional)FaultPlaneSummedvectorsSummedGreen'sfunctions8/11/2015 FormulationandConditionsforSyntheticSeismogramshttp://www.uusatrg.utah.edu/RBSMITH/public_html/TEACHING/GG6220/SynthSeis.html 2/2DoubleCouple Sourcetimehistory(7)WaveTheoryorRayTheoryWaveApproach RayTheoryApproach(8)AnelasticityWaveTheorycausaloracausalQintroductionbycomplexvelocitiesRayTheorycausalQoperator(A(t,t*))There is an extensive literature pertaining to various synthetic seismogram methods. However, much confusion on theterminology of various methods exists and only a few reviewtype papers are available Chapman, 1977 Helmberger and Burdick,1979 Cerveny and Ravindra, 1971and Cerveny et al., 1977, Lay and Wallace, 1996). For bodywave problems Chapman (1977)reviewsvariousraytheoreticalandwavetheoreticalsyntheticseismogrammethodsforthecaseof1Dmodels.Heshowsthatinthiscasethebasicequationconsistsofadoubleintegraltransformationwhereuistheseismogramof(vector)displacement,u(,p,z)isthefrequencydomaindisplacementresponsefunction(complexreflectioncoefficients),andtheexponentialtermrepresentsaplaneharmonicwavewithfrequency,andslownessp.ThevarioussyntheticseismogrammethodssolvethisintegralequationusingavarietyofapproacheswhicharerelatedbyTable1.InadditionabriefdescriptionofthevarioussyntheticseismogrammethodsisgiveninTable2.ReturntoGG6220homeReturntolecturehandoutsThispagewaslastmodifiedMar6,2007.Contactrbsmith@mines.utah.eduwithquestionsaboutthispage.URLofthispageishttp://www.mines.utah.edu/~rbsmith/TEACHING/GG6220/SynthSeis.html