三维沉积盆地对地震动的放大效应——间接边界元法模拟
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摘要
基于一种高精度间接边界元法(IBEM),实现了沉积盆地三维地震响应的频域、时域精细求解,并以半空间中椭球形沉积盆地对平面P波和SV波的散射为例,着重探讨了入射角度、入射波型、入射频率、盆地长宽比和深宽比对沉积盆地地震动放大效应的影响规律.结果表明:盆地形状对地震波的放大效应和空间分布状态具有显著影响,且具体规律受控于入射波频段.1随着盆地深度增大,盆地边缘面波发育更为充分,在较宽频段内均会出现显著的地震动放大效应,且深盆地的放大区域集中于盆地中部.2圆形盆地对地震波的汇聚效应最为显著,而狭长盆地对地震波的汇聚作用相对较弱,高频情况下可在盆地内部形成多个聚焦区域.3不同波型入射下,盆地对地震动放大效应的机制有所差异:P波入射下,竖向位移放大主要是由于盆地边缘面波由四周向中部汇聚所致;SV波入射下,边缘面波汇聚效应相对较弱,而当盆地较深时,底部透射体波和边缘面波易形成同相干涉从而显著放大地震动.按盆地内外介质波速比为1/2,P波和SV波垂直入射下频域最大放大倍数分别为25和15,时域放大倍数约为4.0和3.7(雷克子波).4低频波入射下,位移从盆地中部向边缘逐渐减小,且浅层沉积盆地对地表位移幅值的放大作用不明显.5 P波和SV波的入射角度对盆地地震动放大幅值及空间分布特征也具有显著影响.
Based on the indirect boundary element method(IBEM)with high precision,this paper solves the seismic response of a three-dimensional sedimentary basins both in the frequency domain and time domain.Taking the scattering of plane P and SV waves around an semi-ellipsoidal three-dimensional sedimentary basin as an example,the amplification effects of incident angle,wave type,incident frequency,length-width ratio and depth-width ratio of the basin on the ground motion are investigated in detail.The numerical results show that the basin shape has a significant impact on the amplification effect of seismic waves and the spatial distribution characteristics,and the detail effect also strongly depends on the frequency band of incident wave.In particular,as the basin depth increases,edge-generated surface waves become dominant,significant ground motion amplification effect can be observed for a wider band,and amplification area is mainly located in the middle of basin.The seismic wave focusing effect within the circular basin seems most significant,while that within long-narrow basin seems relatively weak,and multiple wave-focused areas appear within the basin for incident high-frequency waves.The amplification mechanism of basin effect on ground motion is different for different types of waves:for incident P waves,significant amplification of vertical displacement in the middle of basin can be mainly attributed to the focusing of surface waves generated from the basin edge;as for SV wave incidence,the surface wave focusing effect is relatively weak,but when the basin is deep,constructive interference of transmitted body waves and edge surface waves tend to result in a considerable amplification effect.For the wave-velocity ratio 1/2between the alluvial basin and the bedrock,amplification factors of P and SV waves can reach up to 25,15,respectively in frequency domain,and to 4.0,3.7,respectively in time domain(Ricker waves).As for the low frequency waves,the displacement amplitude decreases from the basin center to basin edge,and the amplification is not obvious for the shallow basin.In addition,the angle of incidence also has significant impact on the amplitude and spatial distribution characteristics of ground motion.
Based on the indirect boundary element method(IBEM)with high precision,this paper solves the seismic response of a three-dimensional sedimentary basins both in the frequency domain and time domain.Taking the scattering of plane P and SV waves around an semi-ellipsoidal three-dimensional sedimentary basin as an example,the amplification effects of incident angle,wave type,incident frequency,length-width ratio and depth-width ratio of the basin on the ground motion are investigated in detail.The numerical results show that the basin shape has a significant impact on the amplification effect of seismic waves and the spatial distribution characteristics,and the detail effect also strongly depends on the frequency band of incident wave.In particular,as the basin depth increases,edge-generated surface waves become dominant,significant ground motion amplification effect can be observed for a wider band,and amplification area is mainly located in the middle of basin.The seismic wave focusing effect within the circular basin seems most significant,while that within long-narrow basin seems relatively weak,and multiple wave-focused areas appear within the basin for incident high-frequency waves.The amplification mechanism of basin effect on ground motion is different for different types of waves:for incident P waves,significant amplification of vertical displacement in the middle of basin can be mainly attributed to the focusing of surface waves generated from the basin edge;as for SV wave incidence,the surface wave focusing effect is relatively weak,but when the basin is deep,constructive interference of transmitted body waves and edge surface waves tend to result in a considerable amplification effect.For the wave-velocity ratio 1/2between the alluvial basin and the bedrock,amplification factors of P and SV waves can reach up to 25,15,respectively in frequency domain,and to 4.0,3.7,respectively in time domain(Ricker waves).As for the low frequency waves,the displacement amplitude decreases from the basin center to basin edge,and the amplification is not obvious for the shallow basin.In addition,the angle of incidence also has significant impact on the amplitude and spatial distribution characteristics of ground motion.
引文
陈学良,高孟潭,李铁飞.2011.Rayleigh面波作用下盆地场地响应特性研究[J].土木建筑与环境工程,33(S2):29--33.Chen X L,Gao M T,Li T F.2011.Study on response characteristics of basin site under the action of Rayleigh surface wave[J].Journal of Civil,Architectural&Environmental Engineering,33(S2):29--33(in Chinese).
高孟潭,俞言祥,张晓梅,吴健,胡平,丁彦慧.2002.北京地区地震动的三维有限差分模拟[J].中国地震,18(4):356--364.Gao M T,Yu Y X,Zhang X M,Wu J,Hu P,Ding Y H.2002.Three-dimensional finite-difference simulations of ground motions in the Beijing area[J].Earthquake Research in China,18(4):356--364(in Chinese).
景立平,卓旭炀,王祥建.2005.复杂场地对地震波传播的影响[J].地震工程与工程振动,25(6):16--23.Jing L P,Zhuo X Y,Wang X J.2005.Effect of complex site on seismic wave propagation[J].Earthquake Engineering and Engineering Vibration,25(6):16--23(in Chinese).
李铁飞,陈学良,高孟潭.2013.盆地场地效应的三维数值模拟研究进展及沉积环境对盆地场地的影响[J].世界地震工程,29(3):128--138.Li T F,Chen X L,Gao M T.2013.Research progress of basin site effect based on 3Dnumerical simulation and influence of sedimentary environment on basin site[J].World Earthquake Engineering,29(3):128--138(in Chinese).
梁建文,张郁山,顾晓鲁.2003.圆弧形层状凹陷地形对平面SH波的散射[J].振动工程学报,16(2):158--165.Liang J W,Zhang Y S,Gu X L.2003.Scattering of plane SH waves by a circular-arc layered canyon[J].Journal of Vibration Engineering,16(2):158--165(in Chinese).
梁建文,巴振宁.2007.弹性层状半空间中沉积谷地对入射平面SH波的放大作用[J].地震工程与工程振动,27(3):1--9.Liang J W,Ba Z N.2007.Surface motion of an alluvial valley in layered half-space for incident plane SH waves[J].Journal of Earthquake Engineering and Engineering Vibration,27(3):1--9(in Chinese).
刘启方,李雪强,孙平善.2013a.施甸盆地三维速度结构模型研究[J].地震工程与工程振动,33(3):88--94.Liu Q F,Li X Q,Sun P S.2013a.Study on the 3-D velocity model of Shidian basin[J].Journal of Earthquake Engineering and Engineering Vibration,33(3):88--94(in Chinese).
刘启方,于彦彦,章旭斌.2013b.施甸盆地三维地震动研究[J].地震工程与工程振动,33(4):54--60.Liu Q F,Yu Y Y,Zhang X B.2013b.Three-dimensional ground motion simulation for Shidian basin[J].Journal of Earthquake Engineering and Engineering Vibration,33(4):54--60(in Chinese).
王海云.2011.渭河盆地中土层场地对地震动的放大作用[J].地球物理学报,54(1):137--150.Wang H Y.2011.Amplification effects of soil sites on ground motion in the Weihe basin[J].Chinese Journal of Geophysics,54(1):137--150(in Chinese).
王建龙,陈学良,高孟潭,李宗超,鄢兆伦,李铁飞.2014.地震动峰值放大与盆地深度关系的初步数值模拟[J].地震工程与工程振动,34(S):167--172.Wang J L,Chen X L,Gao M T,Li Z C,Yan Z L,Li T F.2014.Preliminary numerical simulation of the dependence of the peak ground motion amplification on the basin depth[J].Earthquake Engineering and Engineering Dynamics,34(S):167--172(in Chinese).
张冬丽,徐锡伟,赵伯明,陈桂华,解廷伟.2007.强地面运动数值模拟中三维物理模型的建立方法:以昆明盆地为例[J].地震学报,29(2):187--196.Zhang D L,Xu X W,Zhao B M,Chen G H,Xie T W.2007.3-D physical model in strong ground motion numerical simulation:A case study of Kunming basin[J].Acta Seismologica Sinica,29(2):187--196(in Chinese).
赵成刚,韩铮.2007.半球形饱和土沉积谷场地对入射平面Rayleigh波的三维散射问题的解析解[J].地球物理学报,50(3):905--914.Zhao C G,Han Z.2007.Three-dimensional scattering and diffraction of plane Rayleigh-waves by a hemispherical alluvial valley with saturated soil deposit[J].Chinese Journal of Geophysics,50(3):905--914(in Chinese).
Anderson J G,Bodin P,Brune J N,Prince J,Singh S K,Quaas R,Onate M.1986.Strong ground motion from the Michoacan,Mexico,earthquake[J].Science,233(4768):1043--1049.
Bouchon M.1973.Effect of topography on surface motion[J].Bull Seismol Soc Am,63(2):615--632.
Chaillat S,Bonnet M,Semblat J F.2009.A new fast multi-domain BEM to model seismic wave propagation and amplification in 3-D geological structures[J].Geophys J Int,177(2):509--531.
Chen G X,Jin D D,Zhu J,Shi J,Li X J.2015.Nonlinear analysis on seismic site response of Fuzhou basin,China[J].Bull Seismol Soc Am,105(2A):928--949.
Kamalian M,Gatmiri B,Sohrabi-Bidar A,Khalaj A.2007.Amplification pattern of 2Dsemi-sine-shaped valleys subjected to vertically propagating incident waves[J].Int J Numer Meth Biomed Eng,23(9):871--887.
Kawase H,Aki K.1989.A study on the response of a soft basin for incident S,P,and Rayleigh waves with special reference to the long duration observed in Mexico city[J].Bull Seismol Soc Am,79(5):1361--1382.
Lee S J,Chen H W,Liu Q,Komatitsch D,Huang B S,Tromp J.2008.Three-dimensional simulations of seismic wave propagation in the Taipei basin with realistic topography based upon the spectral element method[J].Bull Seismol Soc Am,98(1):253--264.
Lee V W.1984.Three-dimensional diffraction of plane P,SV&SH waves by a hemispherical alluvial valley[J].Soil Dyn Earthquake Eng,3(3):133--144.
Luzón F,Sánchez-Sesma F J,Pérez-Ruiz J A,Ramírez-Guzmán L,Pech A.2009.In-plane seismic response of inhomogeneous alluvial valleys with vertical gradients of velocities and constant Poisson ratio[J].Soil Dyn Earthquake Eng,29(6):994--1004.
Mossessian T K,Dravinski M.1990.Amplification of elastic waves by a three dimensional valley.Part 1:Steady state response[J].Earthquake Eng Struct Dyn,19(5):667--680.
Olsen K B.2000.Site amplification in the Los Angeles basin from three dimensional modeling of ground motion[J].Bull Seismol Soc Am,90(6B):S77--S94.
Sánchez-Sesma F J,Luzón F.1995.Seismic response of three-dimensional alluvial valleys for incident P,S,and Rayleigh waves[J].Bull Seismol Soc Am,85(1):269--284.
Sánchez-Sesma F J,Palencia V J,Luzón F.2002.Estimation of local site effects during earthquakes:An overview[J].ISET J Earthq Techn,39(3):167--193.
Trifunac M D.1971.Surface motion of a semi-cylindrical alluvial valley for incident plane SH waves[J].Bull Seismol Soc Am,61(6):1755--1770.
Yuan XM,Liao Z P.1995.Scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross-section[J].Earthquake Eng Struct Dyn,24(10):1303--1313.
Zhao C B,Valliappan S.1993.Incident P and SV wave scattering effects under different canyon topographic and geological conditions[J].Int J Numer Anal Meth Geomech,17(2):73--94.
高孟潭,俞言祥,张晓梅,吴健,胡平,丁彦慧.2002.北京地区地震动的三维有限差分模拟[J].中国地震,18(4):356--364.Gao M T,Yu Y X,Zhang X M,Wu J,Hu P,Ding Y H.2002.Three-dimensional finite-difference simulations of ground motions in the Beijing area[J].Earthquake Research in China,18(4):356--364(in Chinese).
景立平,卓旭炀,王祥建.2005.复杂场地对地震波传播的影响[J].地震工程与工程振动,25(6):16--23.Jing L P,Zhuo X Y,Wang X J.2005.Effect of complex site on seismic wave propagation[J].Earthquake Engineering and Engineering Vibration,25(6):16--23(in Chinese).
李铁飞,陈学良,高孟潭.2013.盆地场地效应的三维数值模拟研究进展及沉积环境对盆地场地的影响[J].世界地震工程,29(3):128--138.Li T F,Chen X L,Gao M T.2013.Research progress of basin site effect based on 3Dnumerical simulation and influence of sedimentary environment on basin site[J].World Earthquake Engineering,29(3):128--138(in Chinese).
梁建文,张郁山,顾晓鲁.2003.圆弧形层状凹陷地形对平面SH波的散射[J].振动工程学报,16(2):158--165.Liang J W,Zhang Y S,Gu X L.2003.Scattering of plane SH waves by a circular-arc layered canyon[J].Journal of Vibration Engineering,16(2):158--165(in Chinese).
梁建文,巴振宁.2007.弹性层状半空间中沉积谷地对入射平面SH波的放大作用[J].地震工程与工程振动,27(3):1--9.Liang J W,Ba Z N.2007.Surface motion of an alluvial valley in layered half-space for incident plane SH waves[J].Journal of Earthquake Engineering and Engineering Vibration,27(3):1--9(in Chinese).
刘启方,李雪强,孙平善.2013a.施甸盆地三维速度结构模型研究[J].地震工程与工程振动,33(3):88--94.Liu Q F,Li X Q,Sun P S.2013a.Study on the 3-D velocity model of Shidian basin[J].Journal of Earthquake Engineering and Engineering Vibration,33(3):88--94(in Chinese).
刘启方,于彦彦,章旭斌.2013b.施甸盆地三维地震动研究[J].地震工程与工程振动,33(4):54--60.Liu Q F,Yu Y Y,Zhang X B.2013b.Three-dimensional ground motion simulation for Shidian basin[J].Journal of Earthquake Engineering and Engineering Vibration,33(4):54--60(in Chinese).
王海云.2011.渭河盆地中土层场地对地震动的放大作用[J].地球物理学报,54(1):137--150.Wang H Y.2011.Amplification effects of soil sites on ground motion in the Weihe basin[J].Chinese Journal of Geophysics,54(1):137--150(in Chinese).
王建龙,陈学良,高孟潭,李宗超,鄢兆伦,李铁飞.2014.地震动峰值放大与盆地深度关系的初步数值模拟[J].地震工程与工程振动,34(S):167--172.Wang J L,Chen X L,Gao M T,Li Z C,Yan Z L,Li T F.2014.Preliminary numerical simulation of the dependence of the peak ground motion amplification on the basin depth[J].Earthquake Engineering and Engineering Dynamics,34(S):167--172(in Chinese).
张冬丽,徐锡伟,赵伯明,陈桂华,解廷伟.2007.强地面运动数值模拟中三维物理模型的建立方法:以昆明盆地为例[J].地震学报,29(2):187--196.Zhang D L,Xu X W,Zhao B M,Chen G H,Xie T W.2007.3-D physical model in strong ground motion numerical simulation:A case study of Kunming basin[J].Acta Seismologica Sinica,29(2):187--196(in Chinese).
赵成刚,韩铮.2007.半球形饱和土沉积谷场地对入射平面Rayleigh波的三维散射问题的解析解[J].地球物理学报,50(3):905--914.Zhao C G,Han Z.2007.Three-dimensional scattering and diffraction of plane Rayleigh-waves by a hemispherical alluvial valley with saturated soil deposit[J].Chinese Journal of Geophysics,50(3):905--914(in Chinese).
Anderson J G,Bodin P,Brune J N,Prince J,Singh S K,Quaas R,Onate M.1986.Strong ground motion from the Michoacan,Mexico,earthquake[J].Science,233(4768):1043--1049.
Bouchon M.1973.Effect of topography on surface motion[J].Bull Seismol Soc Am,63(2):615--632.
Chaillat S,Bonnet M,Semblat J F.2009.A new fast multi-domain BEM to model seismic wave propagation and amplification in 3-D geological structures[J].Geophys J Int,177(2):509--531.
Chen G X,Jin D D,Zhu J,Shi J,Li X J.2015.Nonlinear analysis on seismic site response of Fuzhou basin,China[J].Bull Seismol Soc Am,105(2A):928--949.
Kamalian M,Gatmiri B,Sohrabi-Bidar A,Khalaj A.2007.Amplification pattern of 2Dsemi-sine-shaped valleys subjected to vertically propagating incident waves[J].Int J Numer Meth Biomed Eng,23(9):871--887.
Kawase H,Aki K.1989.A study on the response of a soft basin for incident S,P,and Rayleigh waves with special reference to the long duration observed in Mexico city[J].Bull Seismol Soc Am,79(5):1361--1382.
Lee S J,Chen H W,Liu Q,Komatitsch D,Huang B S,Tromp J.2008.Three-dimensional simulations of seismic wave propagation in the Taipei basin with realistic topography based upon the spectral element method[J].Bull Seismol Soc Am,98(1):253--264.
Lee V W.1984.Three-dimensional diffraction of plane P,SV&SH waves by a hemispherical alluvial valley[J].Soil Dyn Earthquake Eng,3(3):133--144.
Luzón F,Sánchez-Sesma F J,Pérez-Ruiz J A,Ramírez-Guzmán L,Pech A.2009.In-plane seismic response of inhomogeneous alluvial valleys with vertical gradients of velocities and constant Poisson ratio[J].Soil Dyn Earthquake Eng,29(6):994--1004.
Mossessian T K,Dravinski M.1990.Amplification of elastic waves by a three dimensional valley.Part 1:Steady state response[J].Earthquake Eng Struct Dyn,19(5):667--680.
Olsen K B.2000.Site amplification in the Los Angeles basin from three dimensional modeling of ground motion[J].Bull Seismol Soc Am,90(6B):S77--S94.
Sánchez-Sesma F J,Luzón F.1995.Seismic response of three-dimensional alluvial valleys for incident P,S,and Rayleigh waves[J].Bull Seismol Soc Am,85(1):269--284.
Sánchez-Sesma F J,Palencia V J,Luzón F.2002.Estimation of local site effects during earthquakes:An overview[J].ISET J Earthq Techn,39(3):167--193.
Trifunac M D.1971.Surface motion of a semi-cylindrical alluvial valley for incident plane SH waves[J].Bull Seismol Soc Am,61(6):1755--1770.
Yuan XM,Liao Z P.1995.Scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross-section[J].Earthquake Eng Struct Dyn,24(10):1303--1313.
Zhao C B,Valliappan S.1993.Incident P and SV wave scattering effects under different canyon topographic and geological conditions[J].Int J Numer Anal Meth Geomech,17(2):73--94.
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