各向异性介质弹性波传播的三维不规则网格有限差分方法
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摘要
提出一种新的三维空间不规则网格有限差分方法 ,模拟具有地形构造的非均匀各向异性介质中弹性波传播过程 .该方法通过具有二阶时间精度和四阶空间精度的不规则交错网格差分算子来近似一阶弹性波动方程 ,与多重网格不同 ,无需在精细网格和粗糙网格间进行插值 ,所有网格点上的计算在同一次空间迭代中完成 .针对具有复杂物性参数和复杂几何特征的地层结构 ,使用精细不规则网格处理粗糙界面、断层和空间界面等复杂几何构造 ,理论分析和数值算例表明 ,该方法不但节省了大量计算机内存和计算时间 ,而且具有令人满意的稳定性和精度 .
This paper presents a new 3D finite-difference (FD) method using spatially irregular grids to simulate elastic wave propagation in heterogeneous anisotropic media with topographic structures. The method approximates the first-order elastic wave equations by the finite difference operators on irregular grids with second-order time precise and fourth-order spatial precise. Unlike the multi-grid scheme, this method has no interpolation between the fine and coarse grids. All grids are computed at the same spatial iteration. Complicated geometrical structures like rough submarine interfaces, faults and nonplanar interfaces are treated with fine irregular grids. Theoretical analysis and numerical simulations show that this method saves considerable memory and computing time, at the same time, has satisfactory stability and accuracy. The proposed scheme is more efficient than conventional methods in simulating seismic wave propagation in complex topographic structures.
This paper presents a new 3D finite-difference (FD) method using spatially irregular grids to simulate elastic wave propagation in heterogeneous anisotropic media with topographic structures. The method approximates the first-order elastic wave equations by the finite difference operators on irregular grids with second-order time precise and fourth-order spatial precise. Unlike the multi-grid scheme, this method has no interpolation between the fine and coarse grids. All grids are computed at the same spatial iteration. Complicated geometrical structures like rough submarine interfaces, faults and nonplanar interfaces are treated with fine irregular grids. Theoretical analysis and numerical simulations show that this method saves considerable memory and computing time, at the same time, has satisfactory stability and accuracy. The proposed scheme is more efficient than conventional methods in simulating seismic wave propagation in complex topographic structures.
引文
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[20] AkiK ,RichardsPG .QuantitativeSeismology.W .H .FreemanandCompany,1980
[2] KellyKR ,WardRW ,TreitelS ,etal.Syntheticseismograms,afi nitedifferenceapproach.Geophysics,1976,41(1):2～27
[3] VirieuxJ .SH wavepropagationinheterogeneousmedia:velocity stressfinite differencemethod.Geophysics,1984,49(11):1933～1942
[4] VirieuxJ .P SVwavepropagationinheterogeneousmedia.velocity stressfinite differencemethod.Geophysics,1986,51(4):889～901
[5] LevanderAlanR .Fourth orderfinite differenceP SVseismograms.Geophysics,1988,53(11):1425～1436
[6] GravesRW .Simulatingseismicwavepropagationin3Delasticmediausingstaggered gridfinitedifferences.BulletinoftheSeismologicalSocietyofAmerica,1996,86(4):1091～1106
[7] DablainMA .Theapplicationofhigh orderdifferencingtothescalarwaveequation.Geophysics,1986,51(1):54～66
[8] ShortleyGH ,WellerR .NumericalsolutionofLaplace’sequation.J .Appl.Phys.,1938,9:334～348
[9] JastramC ,TessmerE .Elasticmodelingonagridwithverticallyvary ingspacing.Geophys.Prosp.,1994,42:357～370
[10] FalkJ,TessmerE ,GajevskiD .Tubewavemodelingbythefinite differ encesmethodwithvaryinggridspacing.Pageoph,1996,14:77～93
[11] TessmerE ,KosloffD ,BehleA .Elasticwavepropagationsimulationinthepresencesurfacetopography.Geophys.J .Internat.,1992,108:621～632
[12] HestholmSO ,RuudBO .2DFinite differenceelasticwavemodelingincludingsurfacetopography.Geophys.Prosp.,1994,42:371～390
[13] IvoOprsal,JiriZahradnik.Elasticfinite differencemethodforirregu largrids.Geophysics,1999,64(1):240～250
[14] PitarkaA .3Delasticfinite differencemodelingofseismicmotionus ingstaggeredgridswithnonuniformspacing.BulletinoftheSeis mologicalSocietyofAmerica,1999,89(1):54～68
[15] 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.地球物理学报,2000,43(3):411～419DongLG ,MaZT ,CaoJZ .Astaggeredgridhigh orderdifferencemethodofone orderelasticwaveequation.ChineseJ .Geophys.(inChinese),2000,43(3):411～419
[16] 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稳定性研究.地球物理学报,2000,43(6):856～864DongLG ,MaZT ,CaoJZ .Astudyonstabilityofthestaggeredgridhighorderdifferencemethodoffirstorderelasticwaveequation.ChineseJ.Geophys.(inChinese),2000,43(6):856～864
[17] 张剑锋.弹性波数值模拟的非规则网格差分法.地球物理学报,1998,41(增刊):357～366ZhangJF .Non orthogonalgridfinite differencemethodfornumericalsimulationofelasticwavepropagation.ChineseJ.Geophys.(ActaGeophysicaSinica),1998,41(Suppl.):357～366
[18] 孙卫涛.复杂介质弹性波场有限差分正演和全局优化方法研究[博士论文].北京:清华大学力学系,2003SunWT .Studiesontheelasticwavefieldincomplexmediawithfi nitedifferencemethodandglobaloptimization[Ph.D .thesis].Bei jing:TsinghuaUniv.,2003
[19] HigdonRL .Absorbingboundaryconditionsfordifferenceapproxima tionstothemulti dimensionalwaveequation.MathematicsofCompu tation,1986,47:437～459
[20] AkiK ,RichardsPG .QuantitativeSeismology.W .H .FreemanandCompany,1980
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