A nearly analytic exponential time difference method for solving 2D seismic wave equations-中国期刊网

摘要 Inthispaper,weproposeanearlyanalyticexponentialtimedifference(NETD)methodforsolvingthe2Dacousticandelasticwaveequations.Inthismethod,weusethenearlyanalyticdiscreteoperatortoapproximatethehigh-orderspatialdifferentialoperatorsandtransformtheseismicwaveequationsintosemi-discreteordinarydifferentialequations(ODEs).Then,theconvertedODEsystemissolvedbytheexponentialtimedifference(ETD)method.WeinvestigatethepropertiesofNETDindetail,includingthestabilityconditionfor1-Dand2-Dcases,thetheoreticalandrelativeerrors,thenumericaldispersionrelationforthe2-Dacousticcase,andthecomputationalefficiency.Inordertofurthervalidatethemethod,weapplyittosimulatingacoustic/elasticwavepropagationinmultilayermodelswhichhavestrongcontrastsandcomplexheterogeneousmedia,e.g.,theSEGmodelandtheMarmousimodel.Fromourtheoreticalanalysesandnumericalresults,theNETDcansuppressnumericaldispersioneffectivelybyusingthedisplacementandgradienttoapproximatethehigh-orderspatialderivatives.Inaddition,becauseNETDisbasedonthestructureoftheLiegroupmethodwhichpreservesthequantitativepropertiesofdifferentialequations,itcanachievemoreaccurateresultsthantheclassicalmethods.

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A nearly analytic exponential time difference method for solving 2D seismic wave equations

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A nearly analytic exponential time difference method for solving 2D seismic wave equations

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