Formulacion y condiciones para creacion de sismogramas sinteticos
2
8/11/2015 Formulation and Conditions for Synthetic Seismograms http://www.uusatrg.utah.edu/RBSMITH/public_html/TEACHING/GG6220/SynthSeis.html 1/2 GG 6220 Spring 2005 Definitions for Synthetic Seismograms Synthetic seismograms are computed by assuming a mathematical model with a particular geometry of the source and velocity layering that approximates an elastic or anelastic earth.Solutions of varying approximations to the wave equation in the geometry of the model result in theoretical amplitude versus time of arrival times or wavefield seismograms.These may be used for studying wave propagation through various media, calculating amplitude and waveform responses to various sources in different models and for comparison with observed seismograms to infer the model.The calculation of synthetic seismograms normally requires a solution to the wave equation for the geometry and characteristic parameters of the model.This entails application of appropriate boundary conditions exactly or numerically. (1) Models Many are either 1, 2, or 3dimensional as shown in Figure 1 Figure 11, 2 and 3D Models (2) Elastic Parameters ( 1D 2D 3D (3) Seismograms, displacement u, w, v in x 1 ,x 2 ,x 3 in Cartesian coordinates. 1D 2D 3D u(x 1 ,t) u(x 1 ,x 2 ,t) u(x 1 ,x 2 ,x 3 ,t) w(x 1 ,t) w(x 1 ,x 2 ,t) w(x 1 ,x 2 ,x 3 ,t) v(x 1 ,t) v(x 1 ,x 2 ,t) v(x 1 ,x 2 ,x 3 ,t) (Note that a 1D model will produce seismograms that are different for various distances (due to various angles of incidence).In exploration seismology, it is common to refer to a 1D model and 1D synthetic seismograms which are for vertical incident waves only.) (4) Propagation Types Acoustic Elastic Seismic (anelastic) fluid, pressure wave only solid, no absorption solid, including absorption (5) Wave Types Acoustic Elastic Seismic (anelastic) P, SV, SH P SV, SV P Love (SH), Rayleigh higher modes (equivalent to guided waves) (6) Source (at surface or depth) Point Sources Finite Sources Vertical Force Explosive (compressional) Fault Plane Summed vectors Summed Green's functions
-
Upload
lobsang-matos -
Category
Documents
-
view
216 -
download
2
description
Ingenieria sismica y sismologia
Transcript of Formulacion y condiciones para creacion de sismogramas sinteticos
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
