Wave Fields in Real Media Wave Propagation in Anisotropic, Anelastic and Porous Media-[1st]-[J Jose M Carcione].pdf

Wave Fields in Real Media Wave Propagation in Anisotropic, Anelastic and Porous Media-[1st]-[J Jose M Carcione].pdf

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HANDBOOKOFGEOPHYSICALEXPLORATIONSEISMICEXPLORATIONVOLUME31WAVEFIELDSINREALMEDIA:

WAVEPROPAGATIONINANISOTROPIC,ANELASTICANDPOROUSMEDIAHANDBOOKOFGEOPHYSICALEXPLORATIONSEISMICEXPLORATIONEditors:

KlausHelbigandSvenTreitelVolume1.BasicTheoryinReflectioneismolo2.SeismicInstrumentation,2nddition3.SeismicFieldTechniques24A.SeismicInversionandDeconvolution:

ClassicalMethods4B.SeismicInversionandDeconvolution:

Dual-SensorTechnology5.SeismicMigration（TheoryandPractice）6.SeismicVelocitynalsis7.SeismicNoiseAttenuation8.Structural1nterpretation29.SeismicStratigraphy10.ProductionSeismology11.3-DSeismicxloration12.SeismicResolution13.RefractionSeismics14.VerticalSeismicProfiling:

Principles3rdUpdatedandRevisedEdition15A.SeismicShearWaves:

Theory15B.SeismicShearWaves:

Applications16A.SeismicCoalExploration:

Surfaceethods16B.SeismicCoalExploration:

In-SeamSeismics17.MathematicalAspectsofSeismology18.PhysicalPropertiesofRocks19.ShallowHigh-ResolutionReflectionSeismics20.PatternRecognitionandImageProcessing21.SupercomputersinSeismicExploration22.FoundationsofAnisotropyforExplorationSeismics23.SeismicTomographyZ24.Boreholecoustics25.HighFrequencyCrosswellSeismicprofiling226.ApplicationsofAnisotropyinVerticalSeismicprofiling127.SeismicMultipleEliminationTechniques128.WaveletTransformsandTheirApplicationstoSeismicDataAcquisition,Compression,Processingandinterpretationi29.SeismicSignaturesandAnalysisofReflectionDatainAnisotropicMedia30.ComputationalNeuralNetworksforGeophysicalDataProcessing31.WaveFieldsinRealMedia:

WavePropagationinAnisotropic,AnelasticandPorousMedia1npreparation.2lanned.SEISMICEXPLORATIONVolume31WAVEFIELDSINREALMEDIA:

WAVEPROPAGATIONINANISOTROPIC,ANELASTICANDPOROUSMEDIAJoseM.CARCIONEIstitutoNazionalediOceanografiaediGeofisicaSperimentale（OSG）BorgoGrottaGiganta42C34010SgonicoTrieste,Italy2001PERGAMONAnImprintofElsevierScienceAmsterdam-London-NewYork-Oxford-Paris-Shannon-TokyoELSEVIERSCIENCELtdTheBoulevard,LangfordLaneKidlington,OxfordOX5IGB,UK2001ElsevierScienceLtd.Allrightsresewed.ThisworkisprotectedundercopyrightbyElsevierScience,andthefollowingtermsandconditionsapplytoitsuse:

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（+44）2076315500.Othercountriesmayhavealocalreprographicrightsagencyforpayments.DerivativeWorksTablesofcontentsmaybereproducedforinternalcirculation,butpermissionofElsevierScienceisrequiredforexternalresaleordistributionofsuchmaterial.PermissionofthePublisherisrequiredforallotherderivativeworks,includingcompilationsandtranslations.ElectronicStorageorUsagePermissionofthePublisherisrequiredtostoreoruseeleclmnicallyanymaterialcontainedinthiswork,includinganychapterorpartofachapter.Exceptasoutlinedabove,nopartofthisworkmaybereproduced,storedinaretrievalsystemortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,withoutpriorwrittenpermissionofthePublisher.Addresspermissionsrequeststo:

ElsevierScienceGlobalRightsDepartment,atthemail,faxande-mailaddressesnotedabove.NoticeNoresponsibilityisassumedbythePublisherforanyinjuryandlordamagetopersonsorpropertyasamatterofproductsliability,negligenceorotherwise,orfromanyuseoroperationofanymethods,products,instructionsorideascontainedinthematerialherein.Becauseofrapidadvancesinthemedicalsciences,inparticular,independentverificationofdiagnosesanddrugdosagesshouldbemade.Firstedition2001LibraryofCongressCataloginginPublicationDataAcatalogrecordfromtheLibraryofCongresshasbeenappliedfor.BritishLibraryCataloguinginPublicationDataAcataloguerecordfromtheBritishLibraryhasbeenappliedfor.ISBN:

0-08-043929-2ISSN:

0950-1401（Series）8ThepaperusedinthispublicationmeetstherequirementsofANSVNISO239.48-1992（PermanenceofPaper）.PrintedinTheNetherlands.Thisbookisdedicatedtomyparents,AngelaandAntonioThisPageIntentionallyLeftBlankContentsPrefacexvAcknowledgmentsxxAbouttheauthorxxiBasicnotationxxiiGlossaryofmainsymbolsxxiii1Anisotropicelasticmedia1.1.1Strain-energydensityandstress-strainrelation11.2Dynamicalequations.4.1.2.1Symmetriesandtransformationproperties6.Symmetryplaneofamonoclinicmedium7Transformationofthestiffnessmatrix.91.3Kelvin-Christoffelequation,phasevelocityandslowness.101.3.1Transverselyisotropicmedia.111.3.2Symmetryplanesofanorthorhombicmedium.131.3.3Orthogonalityofpolarizations.141.4Energybalanceandenergyvelocity.151.4.1Groupvelocity.17.1.4.2Equivalencebetweenthegroupandenergyvelocities191.4.3Envelopevelocity.20Transverselyisotropicmedia.20.1.4.4Elasticityconstantsfromphaseandgroupvelocities22.1.4.5Relationshipbetweentheslownessandwavesurfaces24SH-wavepropagation.241.5Finelylayeredmedia.251.6Anomalouspolarizations.29.1.7Analyticalsolutionsfortransverselyisotropicmedia341.7.12-DGreensfunction.341.7.23-DGreensfunction.361.8Reflectionandtransmissionofplanewaves.361.8.1Cross-planeshearwaves.38CONTENTS2Viscoelasticityandwavepropagation452.1Energydensitiesandstress-strainrelations.462.1.1Fadingmemoryandsymmetriesoftherelaxationtensor.482.2Stress-strainrelationfor1-Dviscoelasticmedia.492.2.1Complexmodulusandstorageandlossmoduli.492.2.2Energyandsignificanceofthestorageandlossmoduli.512.2.3Non-negativeworkrequirementsandotherconditions.512.2.4Consequencesofrealityandcausality.522.2.5Summaryofthemainproperties.54.Relaxationfunction54Complexmodulus.542.3Wavepropagationconceptsfor1-Dviscoelasticmedia.552.4Mechanicalmodelsandwavepropagation.592.4.1Maxwellmodel.612.4.2Kelvin-Voigtmodel.642.4.3Zenerorstandardlinearsolidmodel.652.4.4GeneralizedZenermodel.69NearlyconstantQ.712.4.5Nearlyconstant-Qmodelwithacontinuousspectrum.732.5Constant-Qmodelandwaveequation.732.5.1Phasevelocityandattenuationfactor.742.5.2Waveequationindifferentialform.Fractionalderivatives.75PropagationinPierreshale.762.6Memoryvariablesandequationofmotion.772.6.1Maxwellmodel.772.6.2Kelvin-Voigtmodel.792.6.3Zenermodel.792.6.4GeneralizedZenermodel.803Isotropicanelasticmedia833.1Stress-strainrelation.843.2Equationsofmotionanddispersionrelations.843.3Vectorplanewaves.863.3.1Slowness,phasevelocityandattenuationfactor.863.3.2ParticlemotionofthePwave.883.3.3ParticlemotionoftheSwaves.903.3.4Polarizationandorthogonality.923.4Energybalance,energyvelocityandqualityfactor.933.4.1Pwave.94.3.4.2Swaves1003.5BoundaryconditionsandSnellslaw.1003.6Thecorrespondenceprinciple.102.3.7Rayleighwaves1023.7.1Dispersionrelation.1033.7.2Displacementfield.1043.7.3Phasevelocityandattenuationfactor.105CONTENTSix.3.7.4Specialviscoelasticsolids106.Incompressiblesolid106.Poissonssolid106.Hardtwigssolid106.3.7.5TwoRayleighwaves1063.8Reflectionandtransmissionofcross-planeshearwaves.107.3.9Memoryvariablesandequationofmotion110.3.10Analyticalsolutions112.3.10.1Viscoacousticmedia112.3.10.2Constant-Qviscoacousticmedia113.3.10.3Viscoelasticmedia114.3.11Theelastodynamicofanon-idealinterface115.3.11.1Theinterfacemodel116.Boundaryconditionsindifferentialform117.3.11.2ReflectionandtransmissioncoefficientsofSHwaves117.Energyloss1183.11.3ReflectionandtransmissioncoefficientsofP-SVwaves.119.Energyloss1214Anisotropicanelasticmedia125.4.1Stress-strainrelations126.4.1.1Model1:

Effectiveanisotropy1284.1.2Model2:

Attenuationviaeigenstrains.1284.1.3Model3:

Attenuationviameananddeviatoricstresses.1304.2Wavevelocities,slownessandattenuationvector.1314.3Energybalanceandfundamentalrelations.133.4.3.1Planewaves.Energyvelocityandqualityfactor135.4.3.2Polarizations1394.4ThephysicsofwavepropagationforviscoelasticSHwaves.140.4.4.1Energyvelocity140.4.4.2Groupvelocity142.4.4.3Envelopevelocity143.4.4.4Perpendicularityproperties143.4.4.5Numericalevaluationoftheenergyvelocity1454.4.6Forbiddendirectionsofpropagation.1464.5Memoryvariablesandequationofmotioninthetimedomain.1474.5.1Strainmemoryvariables.1484.5.2Memory-variableequations.150.4.5.3SHequationofmotion151.4.5.4qP-qSVequationofmotion151.4.6AnalyticalsolutionforSHwavesinmonoclinicmedia1535Thereciprocityprinciple155.5.1Sources.receiversandreciprocity156.5.2Thereciprocityprincipl