切比雪夫伪谱法模拟地震波场
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摘要
介绍了切比雪夫伪谱法以及快速傅立叶算法在其中的应用,并用切比雪夫伪谱法模拟二维有限区域弹性介质地震波场。分别计算了兰姆问题,均匀介质中心爆破源问题,介质内部的速度异常体问题以及各种分界面情况下地震首波传播问题。
The pseudospectral methods,especial Fourier method and Chebyshev method are introduced first.Then the first order 2-D elastodynamic seismic wavefield equation based on velocity-stress by the Chebyshev pseudospectral method is solved,and in the compatation the Lame problem,the problem of demolition source in center of homogeneous media,the velocity anomaly intermedia,and the more important problem,headwave propagation in multi-layered media are simulated.At last,we try to get a similar pseudospectral method to Chebyshev method.
The pseudospectral methods,especial Fourier method and Chebyshev method are introduced first.Then the first order 2-D elastodynamic seismic wavefield equation based on velocity-stress by the Chebyshev pseudospectral method is solved,and in the compatation the Lame problem,the problem of demolition source in center of homogeneous media,the velocity anomaly intermedia,and the more important problem,headwave propagation in multi-layered media are simulated.At last,we try to get a similar pseudospectral method to Chebyshev method.
引文
[1]Bengt Fornberg.The pseudospectral method:Comparisonswith finite differences for the elastic equation[J].Geophys-ics,1987,52(4):483-501.
[2]Dean C Witte,Paul G Richard.The pseudospectral method forsimulating wave propagation[M].North-Holland:ElsevierScience Publishers B.V.,IMACS,1990,1:1-18.
[3]Dan Kosloff,Mouse Reshef,Dan Loewenthal.Elastc wavecalculations by the Fourier method[J].Bulletin of the Seismo-logical Society of America,1984,74(3):875-891.
[4]D Kosloff,DKessler,A Q Filho,et al..Solution of the equa-tions of dynamics elasticity by a Chebyshev spectral method[J].Geophysics,1990,55(6):734-748.
[5]Dan Kosloff,Hillel Tal-Ezer.A modified Chebyshevpseudospectral method with an O(N-1)time step restriction[J].Journal of computational physics,1993,104:457-469.
[6]Yanbin Wang,H Takenaka,T Furumura.Modelling seismicwave propagation in a 2-D cylindrical whole earth model u-sing the pseudospectral method[J].Geophys.J.Int.,2001,145:689-708.
[7]Heiner Igel.Wave propagation in three-dimensional sphericalsections by the Chebyshev spectral method[J].Geophys.J.Int,1999,136:559-566.
[8]Jeffrey M Augenbaum.The pseudospectral method for limited-area elastic wave calculations[A]∥Computational methodsin geosciences[C].Philadelphia,PA.:SIAM,1992:1-15.
[9]A Solomonoff,E Turkel.Global properties of pseudospectralmethods[J].J.Comp.Phys.,1989,81:239-276.
[2]Dean C Witte,Paul G Richard.The pseudospectral method forsimulating wave propagation[M].North-Holland:ElsevierScience Publishers B.V.,IMACS,1990,1:1-18.
[3]Dan Kosloff,Mouse Reshef,Dan Loewenthal.Elastc wavecalculations by the Fourier method[J].Bulletin of the Seismo-logical Society of America,1984,74(3):875-891.
[4]D Kosloff,DKessler,A Q Filho,et al..Solution of the equa-tions of dynamics elasticity by a Chebyshev spectral method[J].Geophysics,1990,55(6):734-748.
[5]Dan Kosloff,Hillel Tal-Ezer.A modified Chebyshevpseudospectral method with an O(N-1)time step restriction[J].Journal of computational physics,1993,104:457-469.
[6]Yanbin Wang,H Takenaka,T Furumura.Modelling seismicwave propagation in a 2-D cylindrical whole earth model u-sing the pseudospectral method[J].Geophys.J.Int.,2001,145:689-708.
[7]Heiner Igel.Wave propagation in three-dimensional sphericalsections by the Chebyshev spectral method[J].Geophys.J.Int,1999,136:559-566.
[8]Jeffrey M Augenbaum.The pseudospectral method for limited-area elastic wave calculations[A]∥Computational methodsin geosciences[C].Philadelphia,PA.:SIAM,1992:1-15.
[9]A Solomonoff,E Turkel.Global properties of pseudospectralmethods[J].J.Comp.Phys.,1989,81:239-276.
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