利用高阶交错网格有限差分法模拟地震波在非均匀孔隙介质中的传播
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摘要
烃类储集层是一种复合多相介质 ,在固体颗粒的空隙中含有气体或液体 .研究弹性波在该类地层中的传播规律对于油气勘探开发 ,特别对于全波列声波测井有重要意义 .为了提高孔隙弹性介质数值模拟的计算效率 ,本文采用改进显式交错网格有限差分算法取代常用的空间域四阶和时间域二阶的速度 -应力有限差分算法 ,算法的空间域为八阶、时间域为二阶 .虽然计算的时间步长略小于空间域四阶的情形 ,但高阶有限差分算法可以选择较粗糙的网格 ,因此补偿了计算的低效 ;同时高阶交错网格有限差分算法的空间频散性比低阶算法小 .利用该算法计算了一个两层模型的波场 ,同时还模拟了等效弹性和孔隙弹性模型中波的传播 .结果表明慢波及其影响明显 ,尽管慢波衰减很快 ,但被某一界面反射后 ,转换形成的P波和S波仍以正常的方式传播 ,且比慢波衰减小 .
Hydrocarbon reservoirs are composite multiphase media with gas and/or liquid contained in voids between solid grains. In this work, instead of using the velocity-stress finite-difference scheme of fourth-order in space and second order in time, we propose an improved explicit eighth-order staggered finite-difference algorithm in space and second order in time for poroelastic media to enhance the computation efficiency. Although the time step is a little smaller than that in fourth-order, the high-order FD scheme can use much coarser grids than that for the fourth-order. This feature compensates its inefficiency in time domain. Using this scheme, we calculate the snapshots and time series on a two-layered model. We also simulate the wave propagation in equivalent elastic and poroelastic models. Slow waves and their effects are clearly seen. Our numerical modeling shows that, although slow waves are attenuated strongly, when they are reflected by an interface, the converted P- and shear waves propagate in a normal way with much less attenuation than the slow waves.
Hydrocarbon reservoirs are composite multiphase media with gas and/or liquid contained in voids between solid grains. In this work, instead of using the velocity-stress finite-difference scheme of fourth-order in space and second order in time, we propose an improved explicit eighth-order staggered finite-difference algorithm in space and second order in time for poroelastic media to enhance the computation efficiency. Although the time step is a little smaller than that in fourth-order, the high-order FD scheme can use much coarser grids than that for the fourth-order. This feature compensates its inefficiency in time domain. Using this scheme, we calculate the snapshots and time series on a two-layered model. We also simulate the wave propagation in equivalent elastic and poroelastic models. Slow waves and their effects are clearly seen. Our numerical modeling shows that, although slow waves are attenuated strongly, when they are reflected by an interface, the converted P- and shear waves propagate in a normal way with much less attenuation than the slow waves.
引文
[1] ParraJO .Poroelasticmodeltorelateseismicwaveattenuationanddispersiontopermeabilityanisotropy.Geophysics,2000,65(1):202～210
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[13] OzdenvarT ,McMechanA .Causesandreductionofnumericalarte factsinpseudo spectralwavefieldextrapolation.Geophys.J.Int.,1996,126:819～828
[14] OzdenvarT ,McMechanA .Algorithmsforstaggered gridcomputa tionsforporoelastic,elastic,acousticandscalarwaveequations.GeophysicalProspecting,1997,45(4):403～420
[15] TalEzerH .Spectralmethodsintimeforhyperbolicproblems.SIAMJ .Numer.Anal.,1986,23:12～26
[16] MoczaP ,KristekMJ,KristekovaM .3Ddisplacementfinitediffer enceandacombinedmemoryoptimisation.Bull.Seism.Soc.Am.,1999,89:69～79
[17] BiotMA .Theoryofelasticityandconsolidationforaporousaniso tropicsolid.J .Apply.Phys.,1955,26(2):182～185
[18] BiotMA .Theoryofdeformationofaporousviscoelasticanisotropicsolid.J .Appl.Phys.,1956,27(5):459～467
[19] BiotMA .Mechanicsofdeformationandacousticpropagationinpo rousmedia.J .Apply.Phys.,1962,3(4):1482～1498
[20] BiotMA .Generalizedtheoryofacousticpropagationinporousdissi pativemedia.J .Acoust.Soc.Am.,1962,34:1254～1264
[21] LevanderAR .Fourth orderfinite differenceP SVseismograms.Geophysics,1988,53(11):1425～1436
[22] WangX .Seismicwavesimulationinanisotropicmediawithhetero geneityusinghigh orderfinite differencemethod.In:Proceedingsofthe5 thSEGJInternationalSymposium:ImagingTechnology,Tokyo,Japan,2001.113～120
[2] SchmittDP .Acousticmultipoleloggingintransverselyisotropicporo elasticformations.J .Acoust.Soc.Am.,1989,86:2397～2421
[3] CarcioneJM ,QuirogaGoodeG .Fullfrequency rangetransientsolu tionforP wavesinafluid saturatedviscoacousticporousmedium.GeophysicalProspecting,1996,44:99～129
[4] CollinsMD ,LingvetchJF ,SiegmannW .Wavepropagationinporo acousticmedia.WaveMotion,1997,25(3):262～272
[5] DialloMS ,AppelE .Acousticwavepropagationinsaturatedporousmedia:reformulationoftheBiotSquirtflowtheory.J .ofAppliedGeophysics,2000,44(4):313～325
[6] ZhuX ,McMechanGA .NumericalsimulationofseismicresponsesofporoelasticreservoirsusingBiottheory.Geophysics,1990,56(3):328～339
[7] DaiN ,VafidisA ,KanasewichER .Wavepropagationinheteroge neous,porousmedia:Avelocity stress,finite differencemethod.Geophysics,1995,60(2):327～340
[8] AtallaN ,PannetonR ,DebergueP .AmixedDisplacement pressureformulationforBiot’sporoelasticequation.J.Acoust.Soc.Am.,1996,104:1444～1452
[9] PannetonR ,AtallaN .Anefficientfiniteelementschemeforsolvingthethreedimensionalporoelasticityprobleminacoustics.J .Acoust.Soc.Am.,1997,101:328～329
[10] 邵秀民,蓝志凌.流体饱和多孔介质波动方程的有限差分解.地球物理学报,2000,43(2):264～277SHAOXiumin,LANZhiling.Finiteelementmethodsfortheequationsofwavesinfluid saturatedporousmedia.ChineseJ.Geo phys.,2000,43(2):264～277
[11] KomatischD ,VilotteJP .Thespectralelementmethod:anefficienttooltosimulatetheseismicresponseof2Dand3Dgeologicalstruc tures.Bull.Seism.Soc.Am.,1998,88:368～392
[12] PauchezN ,SahraouiS .ConvergenceofporoelasticfiniteelementsbasedonBiotdisplacementformulation.J .Acoust.Soc.Am.,2001,109:33～40
[13] OzdenvarT ,McMechanA .Causesandreductionofnumericalarte factsinpseudo spectralwavefieldextrapolation.Geophys.J.Int.,1996,126:819～828
[14] OzdenvarT ,McMechanA .Algorithmsforstaggered gridcomputa tionsforporoelastic,elastic,acousticandscalarwaveequations.GeophysicalProspecting,1997,45(4):403～420
[15] TalEzerH .Spectralmethodsintimeforhyperbolicproblems.SIAMJ .Numer.Anal.,1986,23:12～26
[16] MoczaP ,KristekMJ,KristekovaM .3Ddisplacementfinitediffer enceandacombinedmemoryoptimisation.Bull.Seism.Soc.Am.,1999,89:69～79
[17] BiotMA .Theoryofelasticityandconsolidationforaporousaniso tropicsolid.J .Apply.Phys.,1955,26(2):182～185
[18] BiotMA .Theoryofdeformationofaporousviscoelasticanisotropicsolid.J .Appl.Phys.,1956,27(5):459～467
[19] BiotMA .Mechanicsofdeformationandacousticpropagationinpo rousmedia.J .Apply.Phys.,1962,3(4):1482～1498
[20] BiotMA .Generalizedtheoryofacousticpropagationinporousdissi pativemedia.J .Acoust.Soc.Am.,1962,34:1254～1264
[21] LevanderAR .Fourth orderfinite differenceP SVseismograms.Geophysics,1988,53(11):1425～1436
[22] WangX .Seismicwavesimulationinanisotropicmediawithhetero geneityusinghigh orderfinite differencemethod.In:Proceedingsofthe5 thSEGJInternationalSymposium:ImagingTechnology,Tokyo,Japan,2001.113～120
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