利用伪谱法模拟横向非均匀全球模型中的SH波场
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摘要
基于傅里叶伪谱法(Fourier pseudospectral method,PSM),发展了模拟具有任意横向非均匀结构的全地球模型中SH波传播的算法.所采用的模型为通过地球大圆选取的一个二维全地球剖面,所求解的弹性波动方程定义在二维柱坐标系下.波动方程中空间微分的数值求解通过波数域的乘积运算实现,空间域与波数域之间的变换通过快速傅里叶变换(fast Fourier transformation,FFT)进行.由于PSM具有精度较高、计算速度较快的特点,所以对于非均匀结构可以近似为在垂直剖面方向上对称的模型,本算法能够较精确地计算较高频率的全球SH波场的理论地震图.和基于球坐标系二维全球模型的算法相比,本算法能够更方便地处理震源项.用该算法计算了PREM模型中全球SH波的传播,分析了各种震相的产生以及它们在各个界面上的反射、透射、绕射,并将其应用于包含核幔边界低速扰动结构的横向非均匀全球模型,讨论了他们对全球SH波传播的影响.
引文
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2Ni S D,Helmberger D V,Tromp J.Three-dimensional structure of the African superplume from waveform modeling.Geophys J Int,2005,161,doi:10.1111/j.1365-246X.2005.02508.x
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4Wang T,Chen L.Distinct velocity variations around the base of the upper mantle beneath northeast Asia.Phys Earth Planet Inter,2009,172,doi:10.1016/j.pepi.2008.09.021
5张瑞青,吴庆举,李永华,等.青藏高原羌塘西部上地幔SH波速度结构的研究.科学通报,2008,53:2335–2341
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14Nissen-Meyer T,Fournier A,Dahlen F A.A2-D spectral-element method for computing spherical-earth seismograms—I.Moment-tensor source.Geophys J Int,2007,168:1067–1093
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16Jahnke G,Thorne M S,Cochard A,et al.Global SH-wave propagation using a parallel axisymmetric spherical finite-difference scheme:Application to whole mantle scattering.Geophys J Int,2008,173:815–826,doi:10.1111/j.1365-246X.2008.03744.x
17Toyokuni G,Takenaka H,Wang Y,et al.Quasispherical approach for seismic wave modeling in a2D slice of a global Earth model with lateral heterogeneity.Geophys Res Lett,2005,32,doi:10.1029/2004GL022180
18Toyokuni G,Takenaka H.FDM computation of seismic wavefield for an axisymmetric earth with a moment tensor point source.Earth Planets Space,2006,58:e29–e32
19Fornberg B.The pseudospectral method:Comparisons with finite-differences for the elastic wave equations.Geophysics,1987,52:483–501
20Furumura T,Kennett B L N,Furumura M.Seismic wavefield calculation for laterally heterogeneous whole earth models using the pseudospectral method.Geophys J Int,1998,135:845–860
21Wang Y B,Takenaka H,Furumura T.Modelling seismic wave propagation in a two-dimensional cylindrical whole-earth model using the pseudospectral method.Geophys J Int,2001,145:689–708
22Kosloff D,Reshef M,Loewenthal D.Elastic wave calculation by the Fourier method.Bull Seismol Soc Amer,1984,74:875–891
23Fornberg B.The pseudospectral method:Accurate representation of interfaces for elastic wave calculations.Geophysics,1988,53:625–637
24Herrmann R B.SH-wave generation by dislocation source—A numerical study.Bull Seismol Soc Amer,1979,69:1–15
25Cerjan C,Kosloff D,Kosloff R,et al.A nonreflecting boundary condition for discrete acoustic and elastic wave equations.Geophysics,1985,50:705–708
26Daudt C R,Braile L W,Nowack R L,et al.A comparison of finite-difference and Fourier method calculations of synthetic seismograms.Bull Seismol Soc Amer,1989,79:1210–1230
27Graves R W.Simulating seismic wave propagation in3D elastic media using staggered-grid finite differences.Bull Seismol Soc Amer,1996,86:1091–1106
28Dziewonski A M,Anderson D L.Preliminary reference earth model.Phys Earth Planet Inter,1981,25:297–356
29Helmberger D V,Vidale J E.Modeling strong motions produced by earthquakes with two-dimensional numerical codes.Bull Seismol Soc Amer,1988,78:109–121
2Ni S D,Helmberger D V,Tromp J.Three-dimensional structure of the African superplume from waveform modeling.Geophys J Int,2005,161,doi:10.1111/j.1365-246X.2005.02508.x
3Wang Y,Wen L X,Weidner D,et al.SH velocity and compositional models near the660-km discontinuity beneath South America and northeast Asia.J Geophys Res,2006,111:B07305,doi:10.1029/2005JB003849.
4Wang T,Chen L.Distinct velocity variations around the base of the upper mantle beneath northeast Asia.Phys Earth Planet Inter,2009,172,doi:10.1016/j.pepi.2008.09.021
5张瑞青,吴庆举,李永华,等.青藏高原羌塘西部上地幔SH波速度结构的研究.科学通报,2008,53:2335–2341
6Cummins P R,Takeuchi N,Geller R J.Computation of complete synthetic seismograms for laterally heterogeneous models using the Direct Solution Method.Geophys J Int,1997,130:1–16
7Takeuchi N,Geller R J,Cummins P R.Complete synthetic seismograms for3-D heterogeneous Earth models computed using modified DSM operators and their applicability to inversion for Earth structure.Phys Earth Planet Inter,2000,119:25–36
8Komatitsch D,Tromp J.Spectral-element simulations of global seismic wave propagation—I.Validation.Geophys J Int,2002,149:390–412
9Komatitsch D,Tromp J.Spectral-element simulations of global seismic wave propagation—II.Three-dimensional models,oceans,rotation and self-gravitation.Geophys J Int,2002,150:303–318
10严珍珍,张怀,杨长春,等.汶川大地震地震波传播的谱元法数值模拟研究.中国科学D辑:地球科学,2009,39:393–402
11Igel H,Weber M.SH-wave propagation in the whole mantle using high-order finite differences.Geophys Res Lett,1995,22:731–734
12Igel H,Weber M.P-SV wave propagation in the Earth's mantle using finite differences:Application to heterogeneous lowermost mantle structure.Geophys Res Lett,1996,23:415–418
13Igel H,Gudmundsson O.Frequency-dependent effects on travel times and waveforms of long-period S and SS waves.Phys Earth Planet Inter,1997,104:229–246
14Nissen-Meyer T,Fournier A,Dahlen F A.A2-D spectral-element method for computing spherical-earth seismograms—I.Moment-tensor source.Geophys J Int,2007,168:1067–1093
15Thorne M S,Lay T,Garnero E J,et al.Seismic imaging of the laterally varying D″region beneath the Cocos Plate.Geophys J Int,2007,170:635–648,doi:10.1111/j.1365-246X.2006.03279.x
16Jahnke G,Thorne M S,Cochard A,et al.Global SH-wave propagation using a parallel axisymmetric spherical finite-difference scheme:Application to whole mantle scattering.Geophys J Int,2008,173:815–826,doi:10.1111/j.1365-246X.2008.03744.x
17Toyokuni G,Takenaka H,Wang Y,et al.Quasispherical approach for seismic wave modeling in a2D slice of a global Earth model with lateral heterogeneity.Geophys Res Lett,2005,32,doi:10.1029/2004GL022180
18Toyokuni G,Takenaka H.FDM computation of seismic wavefield for an axisymmetric earth with a moment tensor point source.Earth Planets Space,2006,58:e29–e32
19Fornberg B.The pseudospectral method:Comparisons with finite-differences for the elastic wave equations.Geophysics,1987,52:483–501
20Furumura T,Kennett B L N,Furumura M.Seismic wavefield calculation for laterally heterogeneous whole earth models using the pseudospectral method.Geophys J Int,1998,135:845–860
21Wang Y B,Takenaka H,Furumura T.Modelling seismic wave propagation in a two-dimensional cylindrical whole-earth model using the pseudospectral method.Geophys J Int,2001,145:689–708
22Kosloff D,Reshef M,Loewenthal D.Elastic wave calculation by the Fourier method.Bull Seismol Soc Amer,1984,74:875–891
23Fornberg B.The pseudospectral method:Accurate representation of interfaces for elastic wave calculations.Geophysics,1988,53:625–637
24Herrmann R B.SH-wave generation by dislocation source—A numerical study.Bull Seismol Soc Amer,1979,69:1–15
25Cerjan C,Kosloff D,Kosloff R,et al.A nonreflecting boundary condition for discrete acoustic and elastic wave equations.Geophysics,1985,50:705–708
26Daudt C R,Braile L W,Nowack R L,et al.A comparison of finite-difference and Fourier method calculations of synthetic seismograms.Bull Seismol Soc Amer,1989,79:1210–1230
27Graves R W.Simulating seismic wave propagation in3D elastic media using staggered-grid finite differences.Bull Seismol Soc Amer,1996,86:1091–1106
28Dziewonski A M,Anderson D L.Preliminary reference earth model.Phys Earth Planet Inter,1981,25:297–356
29Helmberger D V,Vidale J E.Modeling strong motions produced by earthquakes with two-dimensional numerical codes.Bull Seismol Soc Amer,1988,78:109–121
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