基于伪谱和有限差分混合方法的兰州盆地强地面运动二维数值模拟
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摘要
利用伪谱和有限差分混合方法对兰州盆地进行二维强地面运动模拟。假设3个不同的震源深度5、10、20km的同一地震下,以一个5层的二维剖面作为模型,以此来研究地震波传播过程并分析复杂的二维非均质路径效应,以及局部地下速度构造对强地面运动振幅加乘的影响,从而了解路径效应对强地面运动最大峰值位移的影响程度。研究结果显示:伪谱和有限差分混合方法模拟地震波场结合了有限差分法和伪谱法的优点,弥补了二者的不足,能较好地处理介质不连续面的计算,同时保证了和伪谱法相当的计算精度。通过地震波场模拟可知沉积盆地的强地面运动较基岩相比具有放大效应,震源深度的不同对兰州盆地垂直分量地面最大峰值位移影响较大,在震源深度为5km时最小,为0.06cm;震源深度10km时在水平剖面30～55km范围内峰值位移最大,达到0.14cm;但对水平分量的峰值位移影响较小。
In this study,we simulate two-dimensional(2D) numerical data related to a strong ground motion in the Lanzhou basin using a hybrid scheme based on the pseudospectral method(PSM) and the finite difference method(FDM).The simulation is based on a 10-km-deep focal point,and a 2D profile of five layers is used as a model for analyzing the site response and the peak displacement of the strong ground motion.The results show that the hybrid PSM/FDM method for the seismic wavefield simulation combines the advantages of PSM and FDM and compensates for the disadvantages of these methods.Therefore,the proposed method can better process the calculation of the discontinuous medium surface.The calculation accuracy of this method is similar to that of PSM.First,we simulate the theoretical seismograms and find that the peak ground displacement(PGD) of the vertical is obvious at the basin edge.Then,the wavefield snapshots of the profile at t= 3,6,9,12,15,18,21,24,27,and 30 s explain the propagation of the seismic wave,and it is ensured that the amplification of P waves and Sv waves is obvious in the inner basin.The results of the wavefield simulation reveal that the sedimentary basin can amplify a strong ground motion compared with the bedrock,and that the PGD of the vertical in the inner basin is 0.1 cm,which is larger by 0.03 cm than the PGD near the seismic source.Further,the PGD at the east edge of the basin is larger by 0.02 cm than that in the inner basin.However,the PGD of the horizontal in the inner basin is 0.025 cm,which is smaller by 0.2 cm than the PGD near the seismic source.Therefore,it is known that the PGD of the vertical is larger than that of the horizontal in the inner basin,and the results are opposite near a seismic source,which proves that the influence of a distant earthquake on a tall building is significant.Further,the wavefield simulation revealed a positive correlation between the site conditions and the PGD: if the site conditions are more complex,the PGD will be larger for the same earthquake.Otherwise,the influence of the surface wave of the vertical is more obvious than that of the horizontal at the basin edge,which provides the theoretical evidence for future quakeproof research.
In this study,we simulate two-dimensional(2D) numerical data related to a strong ground motion in the Lanzhou basin using a hybrid scheme based on the pseudospectral method(PSM) and the finite difference method(FDM).The simulation is based on a 10-km-deep focal point,and a 2D profile of five layers is used as a model for analyzing the site response and the peak displacement of the strong ground motion.The results show that the hybrid PSM/FDM method for the seismic wavefield simulation combines the advantages of PSM and FDM and compensates for the disadvantages of these methods.Therefore,the proposed method can better process the calculation of the discontinuous medium surface.The calculation accuracy of this method is similar to that of PSM.First,we simulate the theoretical seismograms and find that the peak ground displacement(PGD) of the vertical is obvious at the basin edge.Then,the wavefield snapshots of the profile at t= 3,6,9,12,15,18,21,24,27,and 30 s explain the propagation of the seismic wave,and it is ensured that the amplification of P waves and Sv waves is obvious in the inner basin.The results of the wavefield simulation reveal that the sedimentary basin can amplify a strong ground motion compared with the bedrock,and that the PGD of the vertical in the inner basin is 0.1 cm,which is larger by 0.03 cm than the PGD near the seismic source.Further,the PGD at the east edge of the basin is larger by 0.02 cm than that in the inner basin.However,the PGD of the horizontal in the inner basin is 0.025 cm,which is smaller by 0.2 cm than the PGD near the seismic source.Therefore,it is known that the PGD of the vertical is larger than that of the horizontal in the inner basin,and the results are opposite near a seismic source,which proves that the influence of a distant earthquake on a tall building is significant.Further,the wavefield simulation revealed a positive correlation between the site conditions and the PGD: if the site conditions are more complex,the PGD will be larger for the same earthquake.Otherwise,the influence of the surface wave of the vertical is more obvious than that of the horizontal at the basin edge,which provides the theoretical evidence for future quakeproof research.
引文
[1]Komatitsch D,Vilotte J P.The Spectral Element Method:AnEfficient Tool to Simulate the Seismic Response of 2Dand 3DGeological Structures[J].Bull.Seis.Soc.Amer.,1998,88(2):368-392.
[2]Mikhailenko B G.Seismic Modeling by the Spectral-finiteDifference Method[J].Phys.Earth Planet Interi.,2000,119(1-2):133-147.
[3]Furumura T,Koketsu K,Wen K L.Parallel PSM/FDM Hy-brid Simulation of Ground Motions from the 1999Chi-Chi,Taiwan,Earthquake[J].Pure Appl.Geophys.,2002,159(9):2133-2146.
[4]马德堂,朱光明.有限元法与伪谱法混合求解弹性波动方程[J].地球科学与环境学报,2004,26(1):61-64.MA De-tang,ZHU Guang-ming.Hybrid Method CombiningFinite Difference and Pseudospectral Method for Solving the E-lastic Wave Equation[J].Journal of Earth Science and Environ-mental,2004,26(1):61-64.
[5]严九鹏,王彦宾.重叠区域伪谱法计算非均匀地球介质地震波传播[J].地震学报,2008,30(1):47-58.YAN Jiu-peng,WANG Yan-bin.Modeling Seismic WavePropagation in Heterogeneous Medium Using Overlap DomainPseudospectral Method[J].Acta Seismologica Sinica,2008,30(1):47-58.
[6]魏星,王彦宾,陈晓非.模拟地震波场的伪谱和高阶有限差分混合方法[J].地震学报,2010,32(4):392-400.WEI Xing,WANG Yan-bin.Hybrid PSM/FDM Method forSeismic Wavefield Simulation[J].Acta Seismologica Sinca,2010,32(4):392-400.
[7]Fornberg B.A Practical Guide to Pseudospectral Method[M].Cambridge,UK:Cambridge University Press,1996:15-34.
[8]Virieux J.P-SV Wave Propagation in Heterogeneous Media:Velocity-stress Finite-difference Method[J].Geophysics,1986,51(4):889-901.
[9]Witte D C,Richards P G.The Pseudospectral Method for Sim-ulating Wave Propagation[A]∥Lee D,Cakmak R,Vichn-evetsky R,eds.Computational Acoustics:Proceedings of the2nd IMA CS Symposium on Computational Acoustics.NewYork:North-Holland,1990:1-18.
[10]Ozdenvar T,McMechan G A.Causes and Reduction of Nu-merical Artifacts in Pseudo-spectral Wavefield Extrapolation[J].Geophys.J.Int.,1996,126(3):819-828.
[11]Zhao Z,Xu J,Horiuchi S.Differentiation Operation in theWave Equation for the Pseudospectral Method with A Stag-gered Mesh[J].Earth Planets and Space,2003,53:327-332.
[12]Cerjan C,Kosloff D,Kosloff R,et al.A NonreflectingBoundary Condition for Discrete Acoustic and Elastic WaveEquation[J].Geophysics,1985,50(4):705-708.
[13]Mittet R.Free-surface Boundary Conditions for Elastic Stag-gered-grid Modeling Schemes[J].Geophysics,2002,67(5):1616-1623.
[14]Wang Y B,Takenaka H.A Multidomain Approach of theFourier Pseudospectral Method Using Discontinuous Grid forElastic Wave Modeling[J].Earth Planets and Space,2001,53:149-158.
[15]Wang Y B,Takenaka H,Furumura T.Modeling SeismicWave Propagation in A Two-dimensional Cylindrical WholeEarth Model Using the Pseudospectral Method[J].Geo-phys.J.Int.,2001,145(3):689-708.
[16]Daudt C R,Brail L W,Nowack R L,et al.A Comparison ofFinite-difference and Fourier Method Calculations of Synthet-ic Seismograms[J].Bull.Seis.Soc.Amer.,1989,79(4):1210-1230.
[17]Kosloff D.Baysal E.Forward Modeling by A Fourier Meth-od[J].Geophysics,1982,47(10):1402-1412.
[18]Furumura T,Kennett B L N.On the Nature of Regional Seis-mic Phases-Ⅲ.The Influence of Crustal Heterogeneity onthe Wavefield for Subduction Earthquakes:the 1985 Mi-choacan and 1995Copala,Guerrero,Mexico earthquakes[J].Geophys.J.Int.,1998,135(3):1060-1084.
[19]Herrmann R B.SH-wave Generation by Dislocation SourceA Numerical Study[J].Bull.Seis.Soc.Amer.,1979,69(1):1-15.
[2]Mikhailenko B G.Seismic Modeling by the Spectral-finiteDifference Method[J].Phys.Earth Planet Interi.,2000,119(1-2):133-147.
[3]Furumura T,Koketsu K,Wen K L.Parallel PSM/FDM Hy-brid Simulation of Ground Motions from the 1999Chi-Chi,Taiwan,Earthquake[J].Pure Appl.Geophys.,2002,159(9):2133-2146.
[4]马德堂,朱光明.有限元法与伪谱法混合求解弹性波动方程[J].地球科学与环境学报,2004,26(1):61-64.MA De-tang,ZHU Guang-ming.Hybrid Method CombiningFinite Difference and Pseudospectral Method for Solving the E-lastic Wave Equation[J].Journal of Earth Science and Environ-mental,2004,26(1):61-64.
[5]严九鹏,王彦宾.重叠区域伪谱法计算非均匀地球介质地震波传播[J].地震学报,2008,30(1):47-58.YAN Jiu-peng,WANG Yan-bin.Modeling Seismic WavePropagation in Heterogeneous Medium Using Overlap DomainPseudospectral Method[J].Acta Seismologica Sinica,2008,30(1):47-58.
[6]魏星,王彦宾,陈晓非.模拟地震波场的伪谱和高阶有限差分混合方法[J].地震学报,2010,32(4):392-400.WEI Xing,WANG Yan-bin.Hybrid PSM/FDM Method forSeismic Wavefield Simulation[J].Acta Seismologica Sinca,2010,32(4):392-400.
[7]Fornberg B.A Practical Guide to Pseudospectral Method[M].Cambridge,UK:Cambridge University Press,1996:15-34.
[8]Virieux J.P-SV Wave Propagation in Heterogeneous Media:Velocity-stress Finite-difference Method[J].Geophysics,1986,51(4):889-901.
[9]Witte D C,Richards P G.The Pseudospectral Method for Sim-ulating Wave Propagation[A]∥Lee D,Cakmak R,Vichn-evetsky R,eds.Computational Acoustics:Proceedings of the2nd IMA CS Symposium on Computational Acoustics.NewYork:North-Holland,1990:1-18.
[10]Ozdenvar T,McMechan G A.Causes and Reduction of Nu-merical Artifacts in Pseudo-spectral Wavefield Extrapolation[J].Geophys.J.Int.,1996,126(3):819-828.
[11]Zhao Z,Xu J,Horiuchi S.Differentiation Operation in theWave Equation for the Pseudospectral Method with A Stag-gered Mesh[J].Earth Planets and Space,2003,53:327-332.
[12]Cerjan C,Kosloff D,Kosloff R,et al.A NonreflectingBoundary Condition for Discrete Acoustic and Elastic WaveEquation[J].Geophysics,1985,50(4):705-708.
[13]Mittet R.Free-surface Boundary Conditions for Elastic Stag-gered-grid Modeling Schemes[J].Geophysics,2002,67(5):1616-1623.
[14]Wang Y B,Takenaka H.A Multidomain Approach of theFourier Pseudospectral Method Using Discontinuous Grid forElastic Wave Modeling[J].Earth Planets and Space,2001,53:149-158.
[15]Wang Y B,Takenaka H,Furumura T.Modeling SeismicWave Propagation in A Two-dimensional Cylindrical WholeEarth Model Using the Pseudospectral Method[J].Geo-phys.J.Int.,2001,145(3):689-708.
[16]Daudt C R,Brail L W,Nowack R L,et al.A Comparison ofFinite-difference and Fourier Method Calculations of Synthet-ic Seismograms[J].Bull.Seis.Soc.Amer.,1989,79(4):1210-1230.
[17]Kosloff D.Baysal E.Forward Modeling by A Fourier Meth-od[J].Geophysics,1982,47(10):1402-1412.
[18]Furumura T,Kennett B L N.On the Nature of Regional Seis-mic Phases-Ⅲ.The Influence of Crustal Heterogeneity onthe Wavefield for Subduction Earthquakes:the 1985 Mi-choacan and 1995Copala,Guerrero,Mexico earthquakes[J].Geophys.J.Int.,1998,135(3):1060-1084.
[19]Herrmann R B.SH-wave Generation by Dislocation SourceA Numerical Study[J].Bull.Seis.Soc.Amer.,1979,69(1):1-15.
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