汶川震区地震动三维地形效应的谱元法模拟
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摘要
针对三维波动弹性动力方程推导了谱元法算法,并考虑三维真实地形及介质的衰减特性,基于并行计算环境采用谱元法和ASTER DEM模型对5.12汶川地震动的地形效应进行了模拟.模拟结果表明陡峻地形对地震波两个水平分量的影响要大于对竖向分量的.震中附近区域的PGA最大值为671cm/s2,高PGA区多分布于山顶及山脊区域.与平坦地形相比,PGA相对地形放大系数为-12%～110%,不同地点的z向速度分量波幅遵循峰顶、山脊得到放大或沟谷得到降低的模式.这说明与已有的二维概化模型计算结果相比,三维真实地形对地震动的影响比二维概化模型更为复杂.
The effects of topography on seismic ground motion of Wenchuan earthquake were simulated based upon elastodynamic equation for 3D wave propagation,the spectral-element method,ASTER DEM model and parallel computation environment and incorporated realistic 3D topography and attenuation of media.The simulated results show that topographic effects due to great rough terrain on two horizontal components of seismic wave are bigger than those on vertical component.The max PGA value in zone near epicentre is 671 cm/s2,while large PGA values are almost located near mountain tops and ridges.Compared with the model without topography,the relative topographic amplification factors of PGA in the zone near the epicentre are -12%～110%,while the z velocity component at different sites are in accordance with the pattern of amplification on mountain tops and ridges,and there is a decrease in valleys and brooks.It can be concluded that the effects of 3D realistic topography on seismic ground motion are more complex than those of the existing 2D generalized model.
The effects of topography on seismic ground motion of Wenchuan earthquake were simulated based upon elastodynamic equation for 3D wave propagation,the spectral-element method,ASTER DEM model and parallel computation environment and incorporated realistic 3D topography and attenuation of media.The simulated results show that topographic effects due to great rough terrain on two horizontal components of seismic wave are bigger than those on vertical component.The max PGA value in zone near epicentre is 671 cm/s2,while large PGA values are almost located near mountain tops and ridges.Compared with the model without topography,the relative topographic amplification factors of PGA in the zone near the epicentre are -12%～110%,while the z velocity component at different sites are in accordance with the pattern of amplification on mountain tops and ridges,and there is a decrease in valleys and brooks.It can be concluded that the effects of 3D realistic topography on seismic ground motion are more complex than those of the existing 2D generalized model.
引文
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[31]Komatitsch D,Tromp J.Introduction to thespectral element method for three-dimensional seis-mic wave propagation[J].Geophysical Journal Inter-national,1999,139(3):806-822.
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[34]Brocher T M.Key elements of regional seis-mic velocity models for long period ground motionsimulations[J].Journal of Seismology,2007,12(2):217-221.
[2]Meunier P,Hovius N,Haines J A.Topograph-ic site e-ects and the location of earthquake inducedlandslides[J].Earth and Planetary Science Letters,2008,275(3/4):221-232.
[3]Nguyen K,Gatmiri B.Evaluation of seismicground motion induced by topographic irregulari-ty[J].Soil Dynamics and Earthquake Engineering,2007,27(2):183-188.
[4]崔芳鹏,胡瑞林,殷跃平,等.纵横波时差耦合作用的斜坡崩滑效应离散元分析:以北川唐家山滑坡为例[J].岩石力学与工程学报,2010,29(2):319-327.
[5]石玉成.黄土场地的脉动特征及地震工程意义[J].兰州大学学报:自然科学版,2001,37(5):105-110.
[6]景立平,卓旭炀,王祥建.复杂场地对地震波传播的影响[J].地震工程与工程振动,2005,25(6):16-23.
[7]景立平,卓旭炀,王祥建.复杂介质对地震波传播的影响[J].岩土工程学报,2005,27(4):393-397.
[8]车伟,罗奇峰.复杂地形条件下地震波的传播研究[J].岩土工程学报,2008,30(9):1333-1337.
[9]Lay T,Wallace T C.Modern global seismolo-gy[M].San Diego:Academic Press,1995.
[10]Ashford S A,Sitar N.Analysis of topograph-ic amplification of inclined shear waves in a steepcoastal blu-[J].Bulletin of the Seismological Soci-ety of America,1997,87(3):692-700.
[11]Robertsson J O A,Holliger K.Modeling ofseismic wave propagation near the earth’s surface[J].Physics of the Earth and Planetary Interiors,1997,104(1/3):193-211.
[12]Bouckovalas G D,Papadimitriou A G.Nu-merical evaluation of slope topography e-ects onseismic ground motion[J].Soil Dynamics and Earth-quake Engineering,2005,25(7/10):547-558.
[13]Bourdeau C,Havenith H.Site e-ects modellingapplied to the slope a-ected by the Suusamyr earth-quake(Kyrgyzstan,1992)[J].Engineering Geology,2008,97(3/4):126-145.
[14]Sun C,Chung C.Assessment of sitee-ects ofa shallow and wide basin using geotechnicalinformation-based spatial characterization[J].SoilDynamics and Earthquake Engineering,2008,28(12):1 028-1 044.
[15]Aki K,Richards P G.Quantitative seismolo-gy[M].2nd ed.Sausalito:University Science Books,2002.
[16]Gatmiri B,Arson C.Seismic site e-ects by anoptimized 2D BE/FE methodⅡ:quantificationof site e-ects in two-dimensional sedimentary val-leys[J].Soil Dynamics and Earthquake Engineering,2008,28(8):646-661.
[17]Dineva P S,Manolis G D.Scattering of seismicwaves by cracks in multi-layered geological regionsⅠ:mechanical model[J].Soil Dynamics and Earth-quake Engineering,2001,21(7):615-625.
[18]Kamalian M,Jafari M K,Sohrabi-bidar A,et al.Time-domain two-dimensional site responseanalysis of non-homogeneous topographic structuresby a hybrid BE/FE method[J].Soil Dynamics andEarthquake Engineering,2006,26(8):753-765.
[19]Gatmiri B,Arson C,Nguyen K.Seismic sitee-ects by an optimized 2D BE/FE methodⅠ:theo-ry,numerical optimization and application to topo-graphical irregularities[J].Soil Dynamics and Earth-quake Engineering,2008,28(8):632-645.
[20]Kreiss H,Oliger J.Comparison of accu-rate methods for the integration of hyperbolicequations[J].Tellus,1972,24(3):199-215.
[21]Yan Jiu-peng,Wang Yan-bin.Modeling seis-mic wave propagation in heterogeneous mediumusing overlap domain pseudospectral method[J].Acta Seismologica Sinica,2008,21(1):46-57.
[22]郭桂红,石双虎,剡慧君,等.基于二维三分量伪谱法模拟数据的EDA介质中横波分裂研究[J].地球物理学报,2008,51(2):469-478.
[23]Patera A T.A spectral element method for-uiddynamics:laminar-ow in a channel expansion[J].Journal of Computational Physics,1984,54(3):468-488.
[24]Seriani G.A parallel spectral element methodfor acoustic wave modeling[J].Journal of Computa-tional Acoustics,1997,5(1):53-69.
[25]Maday Y,Patera A T.Spectral element meth-ods for the incompressible Navier-Stokes equa-tions[M]//State-of-the-art surveys on computationalmechanics.New York:American Society of Mechan-ical Engineers,1989:71-143.
[26]Komatitsch D,Vilotte J.The spectral elementmethod:an e-cient tool to simulate the seismic re-sponse of 2D and 3D geological structures[J].Bul-letin of the Seismological Society of America,1998,88(2):368-392.
[27]Komatitsch D,Liu Q,Tromp J,et al.Simulations of ground motion in the Los Angelesbasin based upon the spectral-element method[J].Bulletin of the Seismological Society of America,2004,94(1):187-206.
[28]Lee S,Chan Y,Komatitsch D,et al.E-ects ofrealistic surface topography on seismic ground mo-tion in the Yangminshan region of Taiwan basedupon the spectral-element method and Lidartem[J].Bulletin of the Seismological Society of America,2009,99(2A):681-693.
[29]Komatitsch D,Ritsema J,Tromp J.Thespectral-element method,Beowulf computing,andglobal seismology[J].Science,2002,298(5 599):1 737-1 742.
[30]Yan Zhen-zhen,Zhang Huai,Yang Chang-chun,et al.Spectral element analysis on the character-istics of seismic wave propagation triggered byWenchuan Ms 8.0 earthquake[J].Science in ChinaSeries D:Earth Sciences,2009,52(6):764-773.
[31]Komatitsch D,Tromp J.Introduction to thespectral element method for three-dimensional seis-mic wave propagation[J].Geophysical Journal Inter-national,1999,139(3):806-822.
[32]Udías A.Principles of seismology[M].New York:Cambridge University Press,2000.
[33]叶其孝,沈永欢.实用数学手册[M].第2版.北京:科学出版社,2008.
[34]Brocher T M.Key elements of regional seis-mic velocity models for long period ground motionsimulations[J].Journal of Seismology,2007,12(2):217-221.
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