三维弹性波数值模拟中的吸收边界条件
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摘要
在地震波传播数值模拟的过程中 ,需要使用吸收边界条件从而达到衰减人为边界反射的目的 .本文基于傍轴近似法提出了计算三维弹性波方程的吸收边界条件公式 ,表示了各边界面、边棱和角点处波场所满足的单程波方程 ,并在三维弹性波数值模拟中进行了应用 .理论模型及三维盐丘地质模型波场切片快照试算结果表明 ,该吸收边界条件可以有效地吸收人为边界反射 ,适用于较大入射角情况 ,从而消除了边界有效波信息的干扰 .由于采用四阶近似方程 ,在保证计算精度的前提下 ,该方法具有节省计算工作量和易于实现的特点
The absorbing boundary conditions to avoid the artificial boundary reflections must be required in the numerical simulation of seismic wave propagation. In this paper, on the base of paraxial approximations, we present a set of absorbing boundary conditions of 3D elastic wave equations and apply to the 3D elastic wave numerical modeling in isotropic medium. The snapshots of the theoretical and salt model show that they reduce artificial reflections to a great extent and absorb energy over a wide range of incident angles. Since using forth order approximations, they save computer storage and are convenient to implement.
The absorbing boundary conditions to avoid the artificial boundary reflections must be required in the numerical simulation of seismic wave propagation. In this paper, on the base of paraxial approximations, we present a set of absorbing boundary conditions of 3D elastic wave equations and apply to the 3D elastic wave numerical modeling in isotropic medium. The snapshots of the theoretical and salt model show that they reduce artificial reflections to a great extent and absorb energy over a wide range of incident angles. Since using forth order approximations, they save computer storage and are convenient to implement.
引文
[1] 马在田,曹景忠,王家林等.计算地球物理学概论.上海:同济大学出版社,1997.10～71MaZT ,CaoJZ ,WangJL ,etal.ConspectusofComputationalGeo physics(inChinese).Shanghai:TongjiUniversitypress,1997.10～71
[2] CerjanC ,KosloffD ,KosloffR ,etal.Anonreflectingboundarycondi tionfordiscreteacousticandelasticwaveequations.Geophysics,1985,50:705～708
[3] KosloffD ,KosloffR .Absorbingboundariesforwavepropagationproblems.J.Comput.Phys.,1986,63:363～376
[4] BerengerJP .Aperfectlymatchedlayerfortheabsorptionofelectro magneticwaves.J .Comput.Phys.,1994,114:185～200
[5] ClaytonR ,EngquistB .Absorbingboundaryconditionsforacousticandelasticwaveequations.Bull.Seism.Soc.Am.,1977,67:1529～1540
[6] HigdonRL .Absorbingboundaryconditionsforelasticwaves.Geo physics,1991,56:231～241
[7] RandallCJ.Absorbingboundaryconditionfortheelasticwaveequa tion.Geophysics,1988,53:611～624
[8] Reynolds.Boundaryconditionsforthenumericalsolutionofwavepro pagationproblems.Geophysics,1978,43:1099
[9] 董良国.弹性波数值模拟中的吸收边界条件.石油地球物理勘探,1999,34(1):45～56DongLG .Absorptiveboundaryconditioninelastic wavenumericalmodeling.OilGeophysicalProspecting(inChinese),1999,34(1):45～56
[10] GravesRW .Simulatingseismicwavepropagationin3Delasticmediausingstaggered gridfinitedifferences.Bull.Seism.Soc.Am.,1996,88:881～897
[11] 董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法.地球物理学报,2000,43(3):411～419DongLG ,MaZT ,CaoJZ .Thestaggered gridhigh orderdifferencemethodofone orderelasticequation.ChineseJ .Geophys.(inChi nese),2000,43(3):411～419
[12] 董良国,马在田,曹景忠等.一阶弹性波方程交错网格高阶差分解法稳定性研究.地球物理学报,2000,43(6):856～864DongLG ,MaZT ,CaoJZ .etal.Thestabilitystudyofthestag gered gridhigh orderdifferencemethodofone orderelasticequation.ChineseJ.Geophys.(inChinese),2000,43(6):856～864
[2] CerjanC ,KosloffD ,KosloffR ,etal.Anonreflectingboundarycondi tionfordiscreteacousticandelasticwaveequations.Geophysics,1985,50:705～708
[3] KosloffD ,KosloffR .Absorbingboundariesforwavepropagationproblems.J.Comput.Phys.,1986,63:363～376
[4] BerengerJP .Aperfectlymatchedlayerfortheabsorptionofelectro magneticwaves.J .Comput.Phys.,1994,114:185～200
[5] ClaytonR ,EngquistB .Absorbingboundaryconditionsforacousticandelasticwaveequations.Bull.Seism.Soc.Am.,1977,67:1529～1540
[6] HigdonRL .Absorbingboundaryconditionsforelasticwaves.Geo physics,1991,56:231～241
[7] RandallCJ.Absorbingboundaryconditionfortheelasticwaveequa tion.Geophysics,1988,53:611～624
[8] Reynolds.Boundaryconditionsforthenumericalsolutionofwavepro pagationproblems.Geophysics,1978,43:1099
[9] 董良国.弹性波数值模拟中的吸收边界条件.石油地球物理勘探,1999,34(1):45～56DongLG .Absorptiveboundaryconditioninelastic wavenumericalmodeling.OilGeophysicalProspecting(inChinese),1999,34(1):45～56
[10] GravesRW .Simulatingseismicwavepropagationin3Delasticmediausingstaggered gridfinitedifferences.Bull.Seism.Soc.Am.,1996,88:881～897
[11] 董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法.地球物理学报,2000,43(3):411～419DongLG ,MaZT ,CaoJZ .Thestaggered gridhigh orderdifferencemethodofone orderelasticequation.ChineseJ .Geophys.(inChi nese),2000,43(3):411～419
[12] 董良国,马在田,曹景忠等.一阶弹性波方程交错网格高阶差分解法稳定性研究.地球物理学报,2000,43(6):856～864DongLG ,MaZT ,CaoJZ .etal.Thestabilitystudyofthestag gered gridhigh orderdifferencemethodofone orderelasticequation.ChineseJ.Geophys.(inChinese),2000,43(6):856～864
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