地震动的山体地形效应
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摘要
地震动的山体地形效应问题属于局部场地条件对地震动的影响范畴。汶川地震之后,记录到了大量主、余震山体地震动记录,结合“明灯一号”人工爆破山体地形地震动记录以及汶川地震震后现场与地形效应相关的震害调查资料,本文对地震动的山体地形效应进行了详细分析研究,取得了一些认识和结论。
通过对山体地形效应地震动记录的处理分析,得到了山体地震动的加速度、均方根加速度、90%持时以及频谱的基本特点。针对观测记录中相当数量山顶的地震动反应水平低于山底的异常现象,本文分析了山底水平自由地表覆盖土层、输入地震动频谱特性以及山体卓越频率特性对山底和山顶地震动反应的影响,发现当水平自由地表场点有覆盖土层时,在低水平地震动输入下,覆盖土层未进入强烈非线性状态,因此对地震动输入中不同频段范围的频率成分产生不同程度的放大作用,从而对水平自由地表覆盖土层地震动反应产生放大,而山体由于其振动特性的缘故,对高于其卓越频率的地震动频率成分产生明显的滤波作用,从而导致山体的地震动反应水平低于水平自由地表。
山体地震动反应水平与地震动输入中的频率成分有直接关系,当频率成分与山体卓越频率相近时则容易引起山体共振,从而对输入地震动产生放大效应;当频率成分高于山体卓越频率时,山体对地震动中的高频成分产生明显的滤波效应,从而对地震动产生抑制作用;山体对地震动中低于其卓越频率的频率成分没有明显的影响。
针对传统傅氏谱谱比在确定山体地形效应影响方面的缺点,通过对地震动反应谱谱比进行分析,本文基于能量谱的概念提出了均方根反应谱谱比的方法。结果表明,该方法消除了传统傅氏谱谱比方法基于某一频率点的放大幅值来确定山体地形效应的随机性和不合理性,可以作为一个合理的方法来确定山体地形对输入地震动中某一频段范围内地震动能量的放大效应。
山体地震动的偏振效应与山体的几何形状有很大关系,孤立的圆形山包很难发生偏振,而狭长的山梁则容易发生偏振。通过将地形效应观测台阵的两水平向加速度记录按照山体走向和横向进行分解,对山体走向、横向地震动的幅值、90%持时和频谱进行分析,得到了山体偏振效应的基本特点。对输入地震动频谱特性和山体走向、横向的振动特性进行分析发现,山体发生偏振效应与输入地震动中的频率成分有很大关系,山体的横向地震动反应水平并不总是大于走向。例如窦圌山，在大震作用下山体横向偏振大于走向,而在近场小震作用下,则是走向偏振大于横向,其原因是在大震作用下,输入地震动的中低频和中高频含量都很丰富,由于山体横向的卓越频率偏向中低频,因此大震容易引发山体横向共振,而近场小震中的高频含量非常丰富,中低频含量很少,因此不容易引起横向共振,而且山体横向会对小震高频成分产生滤波作用,从而导致山体横向地震动反应变弱,而山体走向的卓越频率偏向中高频,在小震作用下,山体走向更容易发生共振效应,从而对输入地震动产生放大效应。另外,山体振动的偏振效应与不同频率成分的地震动能量大小也有关系。
通过对陡坎、山梁两种典型地形进行二维数值模拟计算,讨论了P波和SV波垂直入射以及斜入射条件下不同坡度地形模型的地震动反应特征,并分析了地形模型自由地表覆盖土层对地震动反应的影响。结果表明,地形对自由地表的地震动反应影响明显。
对于陡坎模型,在水平方向上,斜坡坡脚对地震动反应有明显的抑制作用,坡角越大,抑制作用越强。斜坡上的地震动水平随着高程的增加而变大;陡坎地形顶部前缘对地震动有明显的放大作用,坡角越小,放大作用越明显,而随着与坡顶距离的变大,放大作用逐渐减弱,在远离陡坎斜坡的两侧,地震动反应逐渐接近水平自由地表反应。
对于山梁模型,在山体两侧斜坡上,决定其地震动反应水平大小的是入射波传播方向与斜坡坡面的夹角,夹角越大,山体在水平方向上的地震动反应水平越高,而在竖直方向上的地震动反应水平越低。通过对地震波斜入射条件下不同位置的地震动反应时程进行对比,发现由斜入射产生的水平自由地表行波效应明显。通过对在SV波垂直入射条件下,两种地形不同位置上覆土层对自由地表地震动反应的影响进行分析发现,水平自由地表覆盖土层的地震动反应水平有可能高于地形与其上覆土层综合作用下的地震动反应。上覆土层的地形斜坡地震动反应相对于无覆盖土层的岩石斜坡地震动反应并没有明显的放大,其原因是由于覆盖土层位于倾斜的斜坡,入射地震动的传播方向相对于土层为斜入射,在这种情况下,土层对入射的地震动放大系数与入射角度有很大关系,对于SV波,土层的放大系数随着入射角度的增加而变小,在临界入射角度处达到最小值。
Effects of topography on the ground motion are in the field of local site conditions affecting the ground motion. After Wenchuan earthquake, the main shock and many aftershocks are recorded. Combining the ground motion record of hill topography from“MingDeng NO.1”artifical explosion and the topography dependent earthquake damage data of Wenchuan earthquake, the hill topography effect on the ground motion is analysed and studied in this paper, and some understanding and conclusions are acquired.
By processing and analysing the hill topography effect data, the basic characteristics of acceleration , RMS acceleration , 90%duration and spectrum of the hill vibration are acquired. For considerable quantity of aftershocks, it is found that the ground motion intensity on the base of the hill is stronger than that on the hill crest, which is abnormal. In order to explain this phenomenon, the effect of overlying soil layer on the gorund surface around the base of the hill, the spectral characteristics of input earthquake motion and the predominant frequency of the hill, on the hill viberation is studied. When there exists soil layer on the horizontal ground surface around the base of the hill, and the input earthquake motion intensity is lower, the soil layer is not in the apparent nonlinear state, so the frequency contents of the input earthquake motion in different frequency bands are amplified differently; meanwhile the ground motion on the surface is amplified. However, the hill filters the high frequency components of the input earthquake motion beyond its predominant frequency because of its vibration characteristics, which leads its seismic response lower than that of the ground surface.
The seismic response of the hill depends on the frequency components of the input earthquake motion. When the frequency components are close to the predominant frequency of the hill, the resonance response happens, and the input earthquake motion is amplified. When the frequency components are higher than the predominant frequency of the hill, the higher frequency of input earthquake motion is filtered, and the response of the hill is inhibited. However, there is almost no effect on the frequency components lower than the predominant frequency of the hill.
There exists disadvantage while using the traditional Fourier spectrum ratio method to confirm the hill topography effect. By analysing the response spectrum ratio of the record data, the RMS response spectrum ratio method is put forward. It is proved that the randomicity and inconsequence of the Fourier spectrum ratio method caused by using the amplification amplitude at some frequency point to confirm the hill topography effect are eliminated. TheRMS response spectrum ratio method is reasonable in confirming the amplification effect on the energy of some frequency band in the input earthquake motion.
The polarization effect of the hill seismic response is much relevant to its geometry. The isolated round hill is hard to polarize, but it is easy for the narrow and long mountain ridge. The two horizontal component acceleration record data are decomposed along the strike and transverse direction of the mountain ridge, and the characteristics of acceleration, RMS acceleration, 90%duration and spectrum of the mountain ridge vibration in these two directions are acquired. By analysing the spectrum characteristics of the input earthquake motion and the mountain ridge vibration characteristics in the strike and transverse directions, it is found that the polarization effect of the mountain ridge is quite relevant to the frequency component of the input earthquake motion, and the seismic response intensity in the transverse direction is not alwayes stronger than that in the srtike direction. Set Douchuan Mountain as an example, the seicmic response in the transverse direction is greater than that in the strike direction under the large earthquake input, however, the comparison result is converse under the small earthquake input. It is because that the frequency components are abundant in both the low-intermediate and intermediate-high frequency bands for large earthquakes, and the predominant frequency in the transverse direction belongs to the low-intermediate frequency band, so the resonance happens in this direction. However, for small earthquakes the frequency component is abundant in the high frequency band, and there is almost no low frequency component, which is hard to cause the transverse polarization, but the strike polarization, because the predominant frequency in the strike direciton of the mountain ridge belongs to the high frequency band. Further more, the polarization of the mountain ridge vibration is relavent to the energy content in different frequency bands.
By simulating the two types of typical topography, scarp and mountain ridge, in two dimensions, the seismic response characteristics of different slop topography models are disscussed under the vertical and oblique incidence of P and SV waves, and the effect of overlying soil layer of rock topography models is analysed. It is proved that the topography effect on the seismic response of ground surface is obvious.
As to the scarp model, the seismic response is inhibited seriously on the foot of the slop in the horizontal direction, and the larger slop, the greater inhibition. The ground motion intensity on the slop becomes stronger with the increasing elevation. The amplification of seicmic response in the front of the scarp crest is obvious, and the smaller slop, the greater amplification. However, the seismic response amplification becomes weaker as the distance away from the slop crest increases, and in the two sides far away from the slop, the seismic response level is close to the ground motion of the horizontal ground surface.
As to the mountain ridge, the intensity of seismic response is dependent on the angle between the propagation direction of incidence wave and the slop surface, and the larger angle, the stronger intensity in the horizontal direction and the weaker intensity in the vertical direction. By comparing the seismic response history at different positions under the oblique incidence, the travelling wave effect of the ground surface is obvious.
The effect of soil layer on the seismic response at ground surface of two types of topography is analysed, and the results show that the intensity of seismic response at the soil layer covered on the horizontal ground surface may be stronger than that on the soil layer covered on the slop. There dosen’t exist obvious amplification between the seismic response on the slop with and without soil layer. It is because that the vertical incidence becomes oblique incidence relative to the soil layer covered on the slop, and the seismic response amplification of soil layer depends on the incidence angle. As to the SV wave, the amplification coefficient of soil layer decreases with the increasing incidence angle, and finally decreases to the minimum at the critical angle.
通过对山体地形效应地震动记录的处理分析,得到了山体地震动的加速度、均方根加速度、90%持时以及频谱的基本特点。针对观测记录中相当数量山顶的地震动反应水平低于山底的异常现象,本文分析了山底水平自由地表覆盖土层、输入地震动频谱特性以及山体卓越频率特性对山底和山顶地震动反应的影响,发现当水平自由地表场点有覆盖土层时,在低水平地震动输入下,覆盖土层未进入强烈非线性状态,因此对地震动输入中不同频段范围的频率成分产生不同程度的放大作用,从而对水平自由地表覆盖土层地震动反应产生放大,而山体由于其振动特性的缘故,对高于其卓越频率的地震动频率成分产生明显的滤波作用,从而导致山体的地震动反应水平低于水平自由地表。
山体地震动反应水平与地震动输入中的频率成分有直接关系,当频率成分与山体卓越频率相近时则容易引起山体共振,从而对输入地震动产生放大效应;当频率成分高于山体卓越频率时,山体对地震动中的高频成分产生明显的滤波效应,从而对地震动产生抑制作用;山体对地震动中低于其卓越频率的频率成分没有明显的影响。
针对传统傅氏谱谱比在确定山体地形效应影响方面的缺点,通过对地震动反应谱谱比进行分析,本文基于能量谱的概念提出了均方根反应谱谱比的方法。结果表明,该方法消除了传统傅氏谱谱比方法基于某一频率点的放大幅值来确定山体地形效应的随机性和不合理性,可以作为一个合理的方法来确定山体地形对输入地震动中某一频段范围内地震动能量的放大效应。
山体地震动的偏振效应与山体的几何形状有很大关系,孤立的圆形山包很难发生偏振,而狭长的山梁则容易发生偏振。通过将地形效应观测台阵的两水平向加速度记录按照山体走向和横向进行分解,对山体走向、横向地震动的幅值、90%持时和频谱进行分析,得到了山体偏振效应的基本特点。对输入地震动频谱特性和山体走向、横向的振动特性进行分析发现,山体发生偏振效应与输入地震动中的频率成分有很大关系,山体的横向地震动反应水平并不总是大于走向。例如窦圌山，在大震作用下山体横向偏振大于走向,而在近场小震作用下,则是走向偏振大于横向,其原因是在大震作用下,输入地震动的中低频和中高频含量都很丰富,由于山体横向的卓越频率偏向中低频,因此大震容易引发山体横向共振,而近场小震中的高频含量非常丰富,中低频含量很少,因此不容易引起横向共振,而且山体横向会对小震高频成分产生滤波作用,从而导致山体横向地震动反应变弱,而山体走向的卓越频率偏向中高频,在小震作用下,山体走向更容易发生共振效应,从而对输入地震动产生放大效应。另外,山体振动的偏振效应与不同频率成分的地震动能量大小也有关系。
通过对陡坎、山梁两种典型地形进行二维数值模拟计算,讨论了P波和SV波垂直入射以及斜入射条件下不同坡度地形模型的地震动反应特征,并分析了地形模型自由地表覆盖土层对地震动反应的影响。结果表明,地形对自由地表的地震动反应影响明显。
对于陡坎模型,在水平方向上,斜坡坡脚对地震动反应有明显的抑制作用,坡角越大,抑制作用越强。斜坡上的地震动水平随着高程的增加而变大;陡坎地形顶部前缘对地震动有明显的放大作用,坡角越小,放大作用越明显,而随着与坡顶距离的变大,放大作用逐渐减弱,在远离陡坎斜坡的两侧,地震动反应逐渐接近水平自由地表反应。
对于山梁模型,在山体两侧斜坡上,决定其地震动反应水平大小的是入射波传播方向与斜坡坡面的夹角,夹角越大,山体在水平方向上的地震动反应水平越高,而在竖直方向上的地震动反应水平越低。通过对地震波斜入射条件下不同位置的地震动反应时程进行对比,发现由斜入射产生的水平自由地表行波效应明显。通过对在SV波垂直入射条件下,两种地形不同位置上覆土层对自由地表地震动反应的影响进行分析发现,水平自由地表覆盖土层的地震动反应水平有可能高于地形与其上覆土层综合作用下的地震动反应。上覆土层的地形斜坡地震动反应相对于无覆盖土层的岩石斜坡地震动反应并没有明显的放大,其原因是由于覆盖土层位于倾斜的斜坡,入射地震动的传播方向相对于土层为斜入射,在这种情况下,土层对入射的地震动放大系数与入射角度有很大关系,对于SV波,土层的放大系数随着入射角度的增加而变小,在临界入射角度处达到最小值。
Effects of topography on the ground motion are in the field of local site conditions affecting the ground motion. After Wenchuan earthquake, the main shock and many aftershocks are recorded. Combining the ground motion record of hill topography from“MingDeng NO.1”artifical explosion and the topography dependent earthquake damage data of Wenchuan earthquake, the hill topography effect on the ground motion is analysed and studied in this paper, and some understanding and conclusions are acquired.
By processing and analysing the hill topography effect data, the basic characteristics of acceleration , RMS acceleration , 90%duration and spectrum of the hill vibration are acquired. For considerable quantity of aftershocks, it is found that the ground motion intensity on the base of the hill is stronger than that on the hill crest, which is abnormal. In order to explain this phenomenon, the effect of overlying soil layer on the gorund surface around the base of the hill, the spectral characteristics of input earthquake motion and the predominant frequency of the hill, on the hill viberation is studied. When there exists soil layer on the horizontal ground surface around the base of the hill, and the input earthquake motion intensity is lower, the soil layer is not in the apparent nonlinear state, so the frequency contents of the input earthquake motion in different frequency bands are amplified differently; meanwhile the ground motion on the surface is amplified. However, the hill filters the high frequency components of the input earthquake motion beyond its predominant frequency because of its vibration characteristics, which leads its seismic response lower than that of the ground surface.
The seismic response of the hill depends on the frequency components of the input earthquake motion. When the frequency components are close to the predominant frequency of the hill, the resonance response happens, and the input earthquake motion is amplified. When the frequency components are higher than the predominant frequency of the hill, the higher frequency of input earthquake motion is filtered, and the response of the hill is inhibited. However, there is almost no effect on the frequency components lower than the predominant frequency of the hill.
There exists disadvantage while using the traditional Fourier spectrum ratio method to confirm the hill topography effect. By analysing the response spectrum ratio of the record data, the RMS response spectrum ratio method is put forward. It is proved that the randomicity and inconsequence of the Fourier spectrum ratio method caused by using the amplification amplitude at some frequency point to confirm the hill topography effect are eliminated. TheRMS response spectrum ratio method is reasonable in confirming the amplification effect on the energy of some frequency band in the input earthquake motion.
The polarization effect of the hill seismic response is much relevant to its geometry. The isolated round hill is hard to polarize, but it is easy for the narrow and long mountain ridge. The two horizontal component acceleration record data are decomposed along the strike and transverse direction of the mountain ridge, and the characteristics of acceleration, RMS acceleration, 90%duration and spectrum of the mountain ridge vibration in these two directions are acquired. By analysing the spectrum characteristics of the input earthquake motion and the mountain ridge vibration characteristics in the strike and transverse directions, it is found that the polarization effect of the mountain ridge is quite relevant to the frequency component of the input earthquake motion, and the seismic response intensity in the transverse direction is not alwayes stronger than that in the srtike direction. Set Douchuan Mountain as an example, the seicmic response in the transverse direction is greater than that in the strike direction under the large earthquake input, however, the comparison result is converse under the small earthquake input. It is because that the frequency components are abundant in both the low-intermediate and intermediate-high frequency bands for large earthquakes, and the predominant frequency in the transverse direction belongs to the low-intermediate frequency band, so the resonance happens in this direction. However, for small earthquakes the frequency component is abundant in the high frequency band, and there is almost no low frequency component, which is hard to cause the transverse polarization, but the strike polarization, because the predominant frequency in the strike direciton of the mountain ridge belongs to the high frequency band. Further more, the polarization of the mountain ridge vibration is relavent to the energy content in different frequency bands.
By simulating the two types of typical topography, scarp and mountain ridge, in two dimensions, the seismic response characteristics of different slop topography models are disscussed under the vertical and oblique incidence of P and SV waves, and the effect of overlying soil layer of rock topography models is analysed. It is proved that the topography effect on the seismic response of ground surface is obvious.
As to the scarp model, the seismic response is inhibited seriously on the foot of the slop in the horizontal direction, and the larger slop, the greater inhibition. The ground motion intensity on the slop becomes stronger with the increasing elevation. The amplification of seicmic response in the front of the scarp crest is obvious, and the smaller slop, the greater amplification. However, the seismic response amplification becomes weaker as the distance away from the slop crest increases, and in the two sides far away from the slop, the seismic response level is close to the ground motion of the horizontal ground surface.
As to the mountain ridge, the intensity of seismic response is dependent on the angle between the propagation direction of incidence wave and the slop surface, and the larger angle, the stronger intensity in the horizontal direction and the weaker intensity in the vertical direction. By comparing the seismic response history at different positions under the oblique incidence, the travelling wave effect of the ground surface is obvious.
The effect of soil layer on the seismic response at ground surface of two types of topography is analysed, and the results show that the intensity of seismic response at the soil layer covered on the horizontal ground surface may be stronger than that on the soil layer covered on the slop. There dosen’t exist obvious amplification between the seismic response on the slop with and without soil layer. It is because that the vertical incidence becomes oblique incidence relative to the soil layer covered on the slop, and the seismic response amplification of soil layer depends on the incidence angle. As to the SV wave, the amplification coefficient of soil layer decreases with the increasing incidence angle, and finally decreases to the minimum at the critical angle.
引文
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[10]粱建文,严林隽,Vincent W.Lee.圆弧形凹陷地形表面覆盖层对入射平面SV波的影响[J].地震学报, 2001,23(6):622- 636.
[11]廖振鹏.近场波动问题的有限元解法[J].地震工程与工程振动,1984, 4(2):1-14.
[12]潘旦光,楼梦麟,董聪. P、SV波作用下层状土层随机波动分析[J].工程力学,2006, 23(2):66-71.
[13]王海云,谢礼立.自贡市西山公园地形对地震动的影响[J].地球物理学报,2010,53(7):1631-1638.
[14]王艳,刘晶波.地震波斜入射时软土层对地震地面位移峰值的影响[J].防灾减灾工程学报,2007, 27(s1):28-32.
[15]网易新闻中心汶川5.12大地震,http://news.qq.com/a/20080904/001668.htm
[16]杨彩红.圆弧状凹陷地形对平面P波的散射:高频解答[J].中国地震,2009,25(6):234-245.
[17]袁晓铭,廖振鹏.任意圆弧形凸起地形对平面SH波的散射[J].地震工程与工程振动学报,1996,16(2):1-13.
[18]钟慧,张郁山.圆弧状凹陷地形对平面sV波散射问题的宽频带解析解[J].中国地震,2010,26(2):142-155.
[19]Aki, K. and K. L. Larner. Surface motion in a layered medium having an irregular interface due to incident plane SH waves [J]. J. Geophys. Res., 1970, 75(5): 933-954.
[20]Ashford, S. A., and N. Sitar. Analysis of topographic amplificationof inclined shear waves in a steep coastal bluff [J]. Bull. Seism. Soc. Am., 1997, 87(5): 692–700.
[21]Ashford, S. A., N. Sitar, J. Lysmer, and N. Deng. Topographic effects on the seismic response of steep slopes [J]. Bull. Seism. Soc. Am., 1997, 87(3): 701–709.
[22]Assimaki, D., and G. Gazetas. Soil and topographic amplification on canyon banks and the Athens 1999 earthquake [J]. J. Earthquake Eng.,2004, 8(1): 1–44.
[23] Bard, P.-Y.. Diffracted waves and displacement field over two-dimensional elevated topographies [J]. Geophys. J. R. Astr. Soc., 1982, 71(3): 111-120.
[24]Bard, P.-Y. and B. E. Tucker. Underground and ridge site effects: A comparison of observation and theory [J]. Bull.Seism. Soc. Am., 1985, 75(4): 905-922.
[25]Bard, P.-Y. and J. C. Gariel. The seismic response of two-dimensional sedimentary deposits with large vertical velocity gradients [J]. Bull.Seism. Soc. Am., 1986, 76(2): 343-366.
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[65] Shuo Ma, Ralph J. Archuleta, and Morgan T. Page. Effects of Large-Scale Surface Topography on Ground Motions, as Demonstrated by a Study of the San Gabriel Mountains, Los Angeles, California [J]. Bull. Seism. Soc. Am, 2007, 97(6): 2066–2079.
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[72]Wong, H. L., and P. C. Jennings. Effect of canyon topography on strong ground motion [J]. Bull. Seism. Soc. Am., 1975, 72 (1): 1167–1183.
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[2]胡静.用契合方法求平面SH波对半圆形突起地形的散射[J].中国民航学院学报,2002,20(4):16-19.
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[6]李伟华,赵成刚.圆弧形凹陷饱和土场地对平面P波散射问题的解析解[J].地球物理学报, 2003,46(4):539-546.
[7]梁建文,张彦帅,Vincent W Lee.平面SV波入射下半圆凸起地形地表运动解析解[J].地震学报, 2006,28(3):238-249.
[8]梁建文,罗昊,Vincent W Lee.任意圆弧形凸起地形中隧洞对入射平面SH波的影响[J].地震学报,2004,26(5):495-508.
[9]梁建文,李方杰,顾晓鲁. Rayleigh波在浅圆凹陷地形附近的散射:高频解答[J].地震工程与工程振动学报, 2005,25(5):9-15.
[10]粱建文,严林隽,Vincent W.Lee.圆弧形凹陷地形表面覆盖层对入射平面SV波的影响[J].地震学报, 2001,23(6):622- 636.
[11]廖振鹏.近场波动问题的有限元解法[J].地震工程与工程振动,1984, 4(2):1-14.
[12]潘旦光,楼梦麟,董聪. P、SV波作用下层状土层随机波动分析[J].工程力学,2006, 23(2):66-71.
[13]王海云,谢礼立.自贡市西山公园地形对地震动的影响[J].地球物理学报,2010,53(7):1631-1638.
[14]王艳,刘晶波.地震波斜入射时软土层对地震地面位移峰值的影响[J].防灾减灾工程学报,2007, 27(s1):28-32.
[15]网易新闻中心汶川5.12大地震,http://news.qq.com/a/20080904/001668.htm
[16]杨彩红.圆弧状凹陷地形对平面P波的散射:高频解答[J].中国地震,2009,25(6):234-245.
[17]袁晓铭,廖振鹏.任意圆弧形凸起地形对平面SH波的散射[J].地震工程与工程振动学报,1996,16(2):1-13.
[18]钟慧,张郁山.圆弧状凹陷地形对平面sV波散射问题的宽频带解析解[J].中国地震,2010,26(2):142-155.
[19]Aki, K. and K. L. Larner. Surface motion in a layered medium having an irregular interface due to incident plane SH waves [J]. J. Geophys. Res., 1970, 75(5): 933-954.
[20]Ashford, S. A., and N. Sitar. Analysis of topographic amplificationof inclined shear waves in a steep coastal bluff [J]. Bull. Seism. Soc. Am., 1997, 87(5): 692–700.
[21]Ashford, S. A., N. Sitar, J. Lysmer, and N. Deng. Topographic effects on the seismic response of steep slopes [J]. Bull. Seism. Soc. Am., 1997, 87(3): 701–709.
[22]Assimaki, D., and G. Gazetas. Soil and topographic amplification on canyon banks and the Athens 1999 earthquake [J]. J. Earthquake Eng.,2004, 8(1): 1–44.
[23] Bard, P.-Y.. Diffracted waves and displacement field over two-dimensional elevated topographies [J]. Geophys. J. R. Astr. Soc., 1982, 71(3): 111-120.
[24]Bard, P.-Y. and B. E. Tucker. Underground and ridge site effects: A comparison of observation and theory [J]. Bull.Seism. Soc. Am., 1985, 75(4): 905-922.
[25]Bard, P.-Y. and J. C. Gariel. The seismic response of two-dimensional sedimentary deposits with large vertical velocity gradients [J]. Bull.Seism. Soc. Am., 1986, 76(2): 343-366.
[26] B. E. TUCKER , J. L. KING , D. HATZFELD and I. L. NERSESOV. Obeservations of Hard-Rock Site Effects [J]. Bull. Seism. Soc. Am, 1984, 74 (1): 121-136.
[27] Blume, J. A. Response of highrise buildings to ground motion from underground nuclear detonations [J]. Bulletinof the Seismological Society of America, 1969, 59 (6): 2343-2370.
[28] Blume, J. A. Highrise building characteristics and responses determined from nuclear seismology [J]. Bulletinof the Seismological Society of America, 1972, 62 (2): 519-540.
[29] Boore, D. M.. A note on the effect of simple topography on seismic SH waves [J]. Bull. Seism. Soc. Am, 1972, 62(1):275-284.
[30]Boore, D. M., S. C. Harmsen, and S. T. Harding. Wave scattering from a step change in surface topography [J]. Bull. Seism. Soc. Am, 1981, 71(1): 117–125.
[31]Bouchon, M.. Effect of topography on surface motion [J]. Bull. Seism. Soc. Am, 1973, 63(2): 615-632.
[32]Bouchon, M., C. A. Schultz, and M. N. Toksoz. Effect of 3D topography on seismic motion [J]. J. Geophys. Res., 1995, 10(B3): 5835–5846.
[33]Celebi , M.. Topographical and geological amplifications determined from strong-motion and aftershock records of the 3 March 1985 Chile earthquake [J]. Bull. Seism. Soc. Am., 1987, 77(4): 1147–1157.
[34]Davis, L. L. and L. R. West. Observed effects of topography on ground motion [J]. Bull. Seism. Soc. Am, 1973, 63(1): 283-298.
[35] Dominic Assimaki, George Gazetas, and Eduardo Kausel. Effects of Local Soil Conditions on the Topographic Aggravation of Seismic Motion: Parametric Investigation and Recorded Field Evidence from the 1999 Athens Earthquake [J]. Bull. Seism. Soc. Am, 2005, 95(3): 1059–1089.
[36] Edward H. Field and Klaus H. Jacob. A comparison and test of various site-response estimation techniques, including three that are not reference-site dependent [J]. Bulletinof the Seismological Society of America, 1995, 85 (4): 1127-1143.
[37] FRANCISCO J. SANCHEZ-SESMA. An Index for Measuring the Effects of Topography on Seismic Ground Motion Intensity [J]. Earthquake Engineering and Structural Dynamics, 1986, 14 (5): 719-731.
[38]Gazetas, G., P. V. Kallou, and P. N. Psarropoulos. Topography and soil effects in the MS 5.9 Parnitha (Athens) earthquake: the case of Ada`mes [J]. Nat. Hazards, 2002, 27 (1-2): 133–169.
[39] Geli, L., P.-Y. Bard, and B. Jullien. The effect of topography on earthquakeground motion: a review and new results [J]. Bull. Seism. Soc.Am., 1988, 78 (1): 42-63.
[40]Gianella, V. P. and E. Callaghan. The earthquake of December 20, 1932, at Cedar Mountain, Nevada, and its bearing on the genesis of Basin Range structure [J]. the Journal of Geology, 1934, 42 (1): 1-22.
[41]Gilbert, F. and L. Knopoff. Seismic scattering from topographic irregularities [J]. the Journal of Geophysical Research, 1960, 65 (1): 3437-3444.
[42]Griffiths, D. W. and G. A. Bollinger. The effect of Appalachian Mountain topography on seismicwaves [J]. Bull. Seism. Soc. Am., 1979, 69 (4): 1081-1105.
[43]Hudson, J. A.. Bollinger. Scattered surface waves from a surface obstacle [J]. Geophys. J. R. Astr. Soc., 1967, 13 (4): 1081-1105.
[44]Hudson, J. A., and D. M. Boore. Comments on scattered surface waves from a surface obstacle [J]. Geophys. J. R. Astr. Soc., 1980, 60 (1): 123–127.
[45]Kawase, H., and K. Aki. Topography effect at the critical SV wave incidence: possible explanation of damage pattern by to the Whittier-Narrows, California Earthquake of 1 October 1987 [J]. Bull. Seism. Soc.Am., 1990, 80 (1): 1–22.
[46] LAWRENCE L. DAVIS, LEWIS R. WEST. Observed Efftcts of Topography on Ground Motion [J]. Bull. Seism. Soc. Am, 1973, 63 (1): 283-298.
[47]Lebrun, B., D. Hatzfeld, P.-Y. Bard, and M. Bouchon. Experimental study of the ground motion on a large scale topography hill at Kitherion (Greece) [J]. J. Seism., 1999, 3 (1): 1–15.
[48] Lee, W. H. K., R. A. White, D. H. Harlow, J. A. Rogers, and P. Spudich. Digital seismograms of selected aftershocks of the Northridge earthquake recorded by a dense seismic array on February 11, 1994 at Cedar Hill Nursery in Tarzana, California, U.S. Geol. Surv. Open-File Rep., 1994,94-234
[49] M. CELEBI. Topographical and geological amplifications determined from strong-motion and aftershock records of the 3 March 1985 Chile earthquake [J]. Bull. Seism. Soc. Am, 1987, 77 (4): 1147-1167.
[50] M. CELEBI. Topographical and geological amplification: case studies and engineering implications[J]. Structural Safety, 1991, 10 (1-3): 199-217.
[51] Michel Bouchon and Jeffrey S. Barker. Seismic Response of a Hill: The Example of Tarzana, California [J]. Bull. Seism. Soc. Am, 1996, 86(1): 66-72.
[52] Ohtsuki, A., and K. Effect of topography and subsurface inhomogeneities on seismic SV waves [J]. Earthquake Eng. Struct. Dyn., 1983, 11(4): 441–462.
[53] Paolucci R. Numerical evaluation of the effect of cross-coupling of different components of ground motion in site response analyses. [J]. Bulletinof the Seismological Society of America, 1999, 89 (4): 1786-1800.
[54] Pedersen H, Le Brun B, Hatzfeld D, Campillo M, Bard P-Y. Ground motion amplitude across ridges [J]. Bulletinof the Seismological Society of America, 1994, 84 (6): 1786-1800.
[55] P.-Y. Bard. Effects of surface geology on ground motion: recent results and remaining issues. In Proc. of the 10th European Conf. on Earthquake Engineering, Vienna, 1994, 305-323.
[56] R. D. BORCHERDT. Effects of local geology on ground motion near San Francisco Bay[J]. Bulletin of the Seismological Society of America, 1970, 60 (1): 29-61.
[57] Roberto Paolucci. Amplication of earthquake ground motion by steep topographic irregularities [J]. Earthquake Engng Struct. Dyn., 2002, 31(10): 1831–1853.
[58]Rogers, A. M., L. J. Katz, and T. J. Benett. Topographic effect on ground motion for incident P waves: a model study [J]. Bull. Seism. Soc. Am., 1974, 64(2): 437-456.
[59] Sanchez-Sesma, I. Herrera, and J. Aviles. A boundary method for elastic wave diffraction: application to scattering SH waves by surface irregularities [J]. Bull. Seism. Soc. Am, 1982, 72(2): 473-490.
[60]Sanchez-Sesma, F.. Diffraction of elastic waves by three-dimensional surface irregularities [J]. Bull. Seism. Soc. Am, 1983, 73(6A): 1621-1636.
[61]Sanchez-Se′sma, F. J., and M. Campillo. Diffraction of P, SV and Rayleigh waves by topographic features. A boundary integral formulation [J]. Bull. Seism. Soc. Am, 1991, 81(6): 2234–3353.
[62] Shiann-Jong Lee, Dimitri Komatitsch, Bor-Shouh Huang, and Jeroen Tromp. Effects of Topography on Seismic-Wave Propagation: An Example from Northern Taiwan [J]. Bull. Seism. Soc. Am, 2009, 99(1): 314–325.
[63] Shakal, A., M. Huang, and T. Cao. The Whittier Narrows, California, earthquake of October 1, 1987: CSM1P strong motion data . Earthquake Spectra4, 1988: 75-100.
[64] Shakal, A., M. Huang, R. Darragh, T. Cao, R. Sherburne, P. Malhotra, C. Cramer, R. Sydnor, V. Graizer, G. Maldonado, C. Peterson, and J. Wampole. CSMIP Strong motion records from the Northridge, California, earthquake of 17 January 1994. Report OSMS 94-07, Calif. Div. Mines Geol., Sacramento, California,1994.
[65] Shuo Ma, Ralph J. Archuleta, and Morgan T. Page. Effects of Large-Scale Surface Topography on Ground Motions, as Demonstrated by a Study of the San Gabriel Mountains, Los Angeles, California [J]. Bull. Seism. Soc. Am, 2007, 97(6): 2066–2079.
[66] Smith, W. D.. The application of finite element analysis to elastic body wave propagation problems [J]. Geophys. Z R. Astr. Soc., 1975, 42(2): 747-768.
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