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三维声波方程优化有限差分正演（英文）.docx

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三维声波方程优化有限差分正演（英文） OptimizationofThree-DimensionalWaveEquationusingFiniteDifferenceForwardModeling Abstract Thefinitedifferencemethodiswidelyusedtosolvethewaveequationinexplorationseismology.However,theaccuracyofthesolutionsobtainedusingthefinitedifferencemethoddependsonthegridsize,whichcanbecomputationallyexpensiveforlarge-scalethree-dimensionalproblems.Inthispaper,weproposeanoptimizationtechniqueforthefinitedifferencemethodusedinthree-dimensionalwaveequationmodeling.Ourtechniqueisbasedonamodifiedimplicitschemethatutilizesanadaptivegridsize,allowingforefficientandaccuratemodelingofcomplexgeologicstructures. Introduction Thewaveequationisafundamentalequationinexplorationseismologyusedtodescribethepropagationofseismicwavesinthesubsurface.Thefinitedifferencemethodiscommonlyusedtosolvethewaveequationasitisastraightforwardandcomputationallyefficientmethod.Thefinitedifferencemethoddiscretizesthewaveequationbyapproximatingthepartialderivativesusingnumericaldifferences.However,theaccuracyofthesolutionsobtainedusingfinitedifferencemethoddependsonthegridsize,whereasmallergridsizeleadstomoreaccuratesolutions,butalsoincreasesthecomputationalcost.Therefore,thereisaneedtooptimizethefinitedifferencemethodusedinthree-dimensionalwaveequationmodelingforefficientandaccuratemodelingoflarge-scalegeologicstructures. Methods Weproposeanoptimizationtechniqueforthefinitedifferencemethodusingamodifiedimplicitschemethatutilizesanadaptivegridsize.Theadaptivegridsizeisbasedonacombinationofbothlocalandglobalrefinementcriteria.Localrefinementisbasedontheminimumwavelengthoftheseismicwave,whichcanbeestimatedusingtheNyquistfrequencyoftheseismicsource.Globalrefinementisbasedonthemaximumwavevelocity,whereweincreasethegridsizeasthewavevelocitydecreases.Inthisway,wecanefficientlymodelcomplexgeologicstructuresusingthefinitedifferencemethodwithoutsacrificingaccuracy. Results Wedemonstratetheeffectivenessofouroptimizationtechniqueusingsyntheticdatawithacomplexgeologicmodel.Wecomparetheaccuracyandcomputati