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利用25点有限差分方法对二维弹性波正演模拟.docx

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利用25点有限差分方法对二维弹性波正演模拟 Title:Two-DimensionalElasticWaveForwardModelingusingthe25-PointFiniteDifferenceMethod Abstract: Theaccurateandefficientsimulationofelasticwavesiscrucialinvariousapplications,includingseismicexploration,earthquakeengineering,andundergroundimaging.Inthispaper,weproposeatwo-dimensionalelasticwaveforwardmodelingtechniqueutilizingthe25-pointfinitedifferencemethod.Thismethodaccuratelycapturesthecomplexbehaviorofelasticwaves,allowingustosimulateandanalyzewavepropagationindifferentgeologicalsettings. 1.Introduction: Elasticwaveforwardmodelingisanessentialtoolinunderstandingthebehaviorofseismicwavesandtheirinteractionswithsubsurfacestructures.Itplaysavitalroleinseismicimaging,reservoircharacterization,andearthquakeanalysis.The25-pointfinitedifferencemethodisawidelyusednumericaltechniqueforsolvingthewaveequationduetoitsaccuracyandcomputationalefficiency.Inthispaper,wewillpresentthedetailsofimplementingthe25-pointfinitedifferencemethodfortwo-dimensionalelasticwaveforwardmodeling. 2.GoverningEquations: Thegoverningequationsforelasticwavepropagationintwodimensionscanbeexpressedbythefollowingcoupledpartialdifferentialequations:theequationofmotion,thecontinuityequation,andthestress-strainrelationship.Utilizingtheseequations,wecannumericallysolveforthedisplacementcomponentsandanalyzetheresultingwavefield. 3.DiscretizationandFiniteDifferenceMethod: Inthefinitedifferencemethod,wediscretizethedomainintoagridofequallyspacednodes.Here,weemploya25-pointstenciltoapproximatethesecond-orderspatialderivativesinthegoverningequations.Byapplyingcentraldifferences,weachieveahighaccuracyinapproximatingthederivatives.Thewaveequationsarethensolvedusingiterativetime-steppingschemessuchastheleapfrogorRunge-Kuttamethods. 4.BoundaryConditions: Toaccuratelysimulatewavepropagation,properboundaryconditionsmustbeimplemented.Commonlyusedboundaryconditionsincludetheperfectlymatchedlayer(PML)forabsorbingwavesandthefreesurfaceboundarycondition.Theseboundaryconditionsensurethatincident,ref