Polarization effect on the ground motion of mountain topography under earthquake action
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摘要:
基于汶川MS8.0地震后在窦圌山坡顶和坡脚测点获得的9次余震记录，通过基线校正、滤波处理，得到各余震记录的傅里叶谱谱比及质点运动轨迹图，结果表明山体的自振频率具有多阶段性，其最大位移方位会出现在山体的横向或走向上，且山体存在偏振效应。将9次余震东西向和南北的水平向加速度时程以10°为单位进行分解得到324条新的时程曲线，基于分解合成后的时程记录，将坡顶与坡脚相同分解角度下的时程作比值，对其峰值加速度比和傅里叶谱谱比进行分析，结果表明二者最大值所在的方位均与山体最大位移所在的方位相同。结合9次余震坡脚测点的傅里叶谱分析可知，各输入地震动频率成分丰富的频段有所不同，低频段容易激发山体的低阶振型，导致山体在横向上发生偏振；高频段容易激发山体的高阶振型，导致山体在走向上发生偏振；当二者同时存在时，山体会同时产生低阶和高阶偏振效应。
Abstract:A large number of earthquake site investigation and theoretical studies have shown that local site conditions have a significant effect on seismic damage and ground motion characteristics, which is usually manifested as amplification or reduction of ground motion. The mountain topographic effect of strong ground motion plays a great role in the antiseismic defense of major projects in mountainous areas. Currently, there are three main ways to study the topographic effect: topographic effect observation array, analytical analysis and numerical simulation calculation. The strong motion observation data from the array can directly reflect the characteristics caused by the complex terrain, and analysis results are more intuitive, real and reliable.
Based on the nine aftershock records after the 2008 Wenchuan MS8.0 earthquake, the baseline-correction and filtration were carried out, and the Fourier spectral ratios and particle motion displacement trajectory diagrams were achieved.
The average spectral ratio curve of the two horizontal records of 9 aftershocks has good consistency with the spectral ratio curve of a single aftershock. The natural frequency of the mountain is not unique, and the maximum spectral ratio will appear in different frequency bands, indicating a clear multi-order nature of the mountain vibration. 1.0−4.0 Hz is the lower-order vibration mode of the mountain, and 9.0−15.0 Hz is the higher-order vibration mode. There are significant differences in the source, magnitude, epicenter distance, and propagation path of each aftershock, but the spectral ratio curves of each aftershock have good consistency, indicating that the natural frequency of the mountain is related to factors such as the geometric shape of the mountain itself.
The particle motion displacement trajectory diagrams show that under different earthquake input, the maximum displacement amplitude of the mountain vibration can appear in the transverse or longitudinal direction of the mountain.
There exists the obvious polarization effect in the mountain vibration. The EW and NS acceleration records of the nine aftershocks were decomposed in 10° increments to obtain 324 new time histories. The amplification coefficients of the peak ground acceleration and the Fourier spectral ratio were analyzed for each decomposition angle. The orientation of the maximum peak acceleration amplification coefficient is basically the same as that of the maximum displacement amplitude of the mountain vibration, and the peak acceleration amplification coefficients of each decomposition angle have obvious polarization effects. The frequency bands of the nine aftershocks with the largest Fourier spectral ratios at different decomposition angles are relatively close to each other, and all of them are distributed in the frequency bands of 0.8−2.8 Hz, 7.8−10.2 Hz, and 11.5−16.0 Hz.
However, the angular range in which the extreme values of the Fourier spectral ratios are located varies from one aftershock to another, with aftershocks 1, 3, 4, and 9. For the Fourier spectral ratio in the low frequency band of 0.8−2.8 Hz, the maximum amplitude appears in the range of 110°−160° i.e. transverse direction of the mountain; in the middle and high frequency bands of 7.8−10.2 Hz, the maximum amplitude appears in the range of 30°−60° i.e. longitudinal direction of the mountain.
The seismic energy of the aftershocks 2, 5, 6, 7, and 8 is mainly concentrated in the mid- and high-frequency bands, and the maximum value of the spectral ratio is concentrated in the range of 30°−60° i.e. longitudinal direction of the mountain, which is more easily to stimulate of higher-order vibration modes of the mountain in this angular range, and the phenomenon is also roughly similar to that of the particle motion displacement trajectory diagrams and the orientation of polarization of the peak ground acceleration.
Considering the Fourier spectrum analysis of the nine aftershock records at the foot of the slope, we can obtain that the frequency content is different. The low frequency band is easy to stimulate the lower-order vibration mode of the mountain that leads to polarization in the transverse direction; the high-order vibration mode is easily stimulated by the high-frequency band that leads to polarization in the longitudinal direction of the mountain; the mountain can produce both low-order and high-order polarization effects when the low and high frequency exist at the same time. The maximum displacement amplitude of the mountain under the action of different earthquakes will appear in the transverse and longitudinal direction of the mountain, which is closely related to the spectral characteristics of the input earthquake. In the seismic design of large-scale structures such as bridges, tunnels and hydropower stations across mountain areas, the polarization effect of the mountain topography should be given priority consideration.
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Keywords:
- ground motion /
- mountain topography /
- polarization effect /
- spectral ratio /
- acceleration
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图 1 山体剖面及观测点高程示意图
Figure 1. Schematic diagram of hill profile and observation point elevation
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图 2 窦圌山强震台站和震中位置
Figure 2. The location of stations and epicenters of strong earthquakes on Douchuan mountain
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图 3 东西向和南北向地震动时程分解合成示意图
Figure 3. Schematic of the decomposition synthesis of the ground motion time history in the EW and NS directions
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图 4 9次余震东西向 （a） 和南北向 （b） 傅里叶谱谱比FSR云图
Figure 4. Fourier spectral ratio cloud maps at EW （a） and NS （b） directions for the nine aftershocks
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图 5 窦圌山9次余震东西向 （a） 和南北向 （b） 傅里叶谱谱比FSR及其平均值比较
Figure 5. Comparison of Fourier spectral ratios and its average values for the nine aftershocks at EW （a） and NS （b） directions
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图 6 窦圌山台阵记录到汶川地震9次余震坡脚、坡顶测点质点运动轨迹图
Figure 6. Particle motion trajectory diagrams at the foot and top of the slope for the nine aftershocks
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图 7 不同分解角度下9次余震坡顶/坡脚测点峰值加速度放大系数
Figure 7. PGA amplification coefficient at different decomposition angles for the nine aftershocks at the top/foot of the slope
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图 8 坡脚位置9次余震东西向和南北向傅里叶谱比较
Figure 8. Comparison of EW and NS direction Fourier spectra of the nine aftershocks at the foot of the slope
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9 9次余震不同分解角度下坡顶/坡脚测点傅里叶谱谱比FSR分布云图
9. Cloud plots of the FSR of the top and foot slope measure points at different decomposition angles of the nine aftershocks
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9 9次余震不同分解角度下坡顶/坡脚测点傅里叶谱谱比FSR分布云图
9. Cloud plots of the FSR of the top and foot slope measure points at different decomposition angles of the nine aftershocks
表 1 窦圌山观测台阵观测到的汶川MS8.0地震的9次余震信息
Table 1 Information of nine aftershocks of Douchuan mountain observation array
序号 MS 震中距/km 东经/° 北纬/° 方位角/° 序号 MS 震中距/km 东经/° 北纬/° 方位角/° 1 5.0 46.65 104.90 32.32 11 6 3.5 27.55 104.62 32.10 321 2 4.6 30.67 104.56 32.09 311 7 4.1 24.35 104.62 32.06 314 3 6.1 118.28 105.47 32.82 31 8 3.4 22.00 104.86 32.10 13 4 5.9 24.08 104.64 32.07 319 9 5.4 32.83 104.59 32.14 322 5 5.2 26.83 104.67 32.12 331 注：方位角为震中位置相对于山体坡顶测点的角度。 
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表 2 9次余震坡顶/坡脚测点各分解角度峰值加速度PGA放大系数
Table 2 PGA amplification factor for the decomposition angles of the nine aftershocks at the top/foot of the slope measurement points
分解角度/° PGA放大系数 余震1 余震2 余震3 余震4 余震5 余震6 余震7 余震8 余震9 10 0.765 0.767 1.048 0.881 1.148 1.620 0.704 0.721 1.051 20 0.722 0.697 1.016 0.901 1.159 1.744 0.820 0.745 0.904 30 0.671 0.761 0.910 0.907 1.170 1.747 0.912 0.777 0.796 40 0.697 0.836 0.801 0.841 1.176 1.394 0.984 0.822 0.709 50 0.711 0.913 0.825 0.783 1.041 1.072 0.895 0.851 0.624 60 0.773 1.015 0.852 0.864 0.903 0.832 0.836 0.843 0.521 70 0.888 1.163 0.843 0.948 0.770 0.629 0.791 0.828 0.459 80 0.998 1.278 0.791 1.053 0.695 0.592 0.784 0.893 0.451 90 1.095 1.375 0.739 1.172 0.754 0.579 0.844 1.020 0.453 100 1.196 1.418 0.723 1.334 0.747 0.579 0.901 1.098 0.456 110 1.154 1.446 0.786 1.323 0.712 0.580 0.851 1.120 0.465 120 1.045 1.471 0.860 1.262 0.680 0.580 0.792 1.141 0.484 130 0.981 1.554 0.937 1.239 0.644 0.582 0.737 1.165 0.549 140 0.930 1.375 1.049 1.268 0.668 0.680 0.683 1.191 0.687 150 0.893 1.228 1.079 1.331 0.717 0.895 0.627 1.081 0.852 160 0.863 1.091 1.075 1.320 0.772 1.188 0.621 0.898 0.879 170 0.834 0.976 1.064 1.206 0.812 1.372 0.638 0.743 0.919 180 0.801 0.870 1.057 0.964 1.017 1.493 0.659 0.682 1.114
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巴振宁,吴孟桃,梁建文. 2019. 坡体几何参数与弹性模量对岩质斜坡地震动力响应的影响:IBEM求解[J]. 岩石力学与工程学报,38(8):1578–1592. Ba Z N,Wu M T,Liang J W. 2019. Influence of geometric parameters and elastic modulus on seismic dynamic response of rock slopes by IBEM[J]. Chinese Journal of Rock Mechanics and Engineering,38(8):1578–1592 (in Chinese).
薄景山,李琪,齐文浩,王玉婷,赵鑫龙,张毅毅. 2021. 场地条件对地震动和震害影响的研究进展与建议[J]. 吉林大学学报(地球科学版),51(5):1295–1305. Bo J S,Li Q,Qi W H,Wang Y T,Zhao X L,Zhang Y Y. 2021. Research progress and discussion of site condition effect on ground motion and earthquake damage[J]. Journal of Jilin University (Earth Science Edition),51(5):1295–1305 (in Chinese).
胡聿贤,孙平善,章在墉,田启文. 1980. 场地条件对震害和地震动的影响[J]. 地震工程与工程振动,试刊(1):34–41. Hu Y X,Sun P S,Zhang Z Y,Tian Q W. 1980. Effects of site conditions on earthquake damage and ground motion[J]. Earthquake Engineering and Engineering Dynamics,T(1):34–41 (in Chinese).
李小军,廖振鹏,关慧敏. 1995. 粘弹性场地地形对地震动影响分析的显式有限元-有限差分方法[J]. 地震学报,17(3):362–369. Li X J,Liao Z P,Guan H M. 1995. An explicit finite element-finite difference method for the analysis of viscoelastic field topography on ground motion[J]. Acta Seismologica Sinica, 17 (3):362−369 (in Chinese).
梁建文,张彦帅,Lee V W. 2006. 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,28(3):238–249. doi: 10.3321/j.issn:0253-3782.2006.03.003 Liang J W,Zhang Y S,Lee V W. 2006. Surface motion of a semi-cylindrical hill for incident plane SV waves:Analytical solution[J]. Acta Seismologica Sinica,28(3):238–249 (in Chinese).
刘晶波. 1996. 局部不规则地形对地震地面运动的影响[J]. 地震学报,18(2):239–245. Liu J B. 1996. The influence of local irregular terrain on seismic ground motion[J]. Acta Seismologica Sinica,18(2):239–245 (in Chinese).
荣棉水,李小军,吕悦军,尤红兵. 2009. 粘弹性浅圆弧形山谷地形对地震动谱特性的影响[J]. 地震研究,32(1):40–45. doi: 10.3969/j.issn.1000-0666.2009.01.008 Rong M S,Li X J,Lü Y J,You H B. 2009. Effect of viscoelastic local canyon on the spectrum property of ground motion[J]. Journal of Seismological Research,32(1):40–45 (in Chinese).
孙崇绍,闵祥仪,周民都. 2011. 陇南山区局部地形对地震动强度的影响[J]. 西北地震学报,33(4):331–335. Sun C S,Min X Y,Zhou M D. 2011. Influence of local topography on ground motion in mountain region of southern Gansu Province[J]. Northwestern Seismological Journal,33(4):331–335 (in Chinese).
唐晖,李小军,李亚琦. 2012. 自贡西山公园山脊地形场地效应分析[J]. 振动与冲击,31(8):74–79. doi: 10.3969/j.issn.1000-3835.2012.08.015 Tang H,Li X J,Li Y Q. 2012. Site effect of topograghy on ground motions of Xishan park of Zigong city[J]. Journal of Vibration and Shock,31(8):74–79 (in Chinese).
王海云,谢礼立. 2010. 自贡市西山公园地形对地震动的影响[J]. 地球物理学报,53(7):1631–1638. doi: 10.3969/j.issn.0001-5733.2010.07.014 Wang H Y,Xie L L. 2010. Effects of topography on ground motion in the Xishan park,Zigong city[J]. Chinese Journal of Geophysics,53(7):1631–1638 (in Chinese).
王铭锋,郑傲,章文波. 2017. 局部山体地形对强地面运动的影响研究[J]. 地球物理学报,60(12):4655–4670. doi: 10.6038/cjg20171210 Wang M F,Zheng A,Zhang W B. 2017. Effect of local mountain topography on strong ground motion[J]. Chinese Journal of Geophysics,60(12):4655–4670 (in Chinese).
王伟. 2011. 地震动的山体地形效应[D]. 哈尔滨:中国地震局工程力学研究所:105−110. Wang W. 2011. Effect of Hill Topography on Ground Motion[D]. Harbin:Institute of Engineering Mechanics,China Earthquake Administration:105−110 (in Chinese).
王伟,刘必灯,刘欣,杨明亮,周正华. 2015. 基于汶川MS8.0地震强震动记录的山体地形效应分析[J]. 地震学报,37(3):452–462. doi: 10.11939/j.issn:0253-3782.2015.03.008 Wang W,Liu B D,Liu X,Yang M L,Zhou Z H. 2015. Analysis on the hill topography effect based on the strong ground motion records of Wenchuan MS8.0 earthquake[J]. Acta Seismologica Sinica,37(3):452–462 (in Chinese).
王伟,刘必灯,刘培玄,王振宇,刘欣. 2016. 基于台阵记录的局部场地条件地震动效应分析[J]. 地震学报,38(2):307–317. doi: 10.11939/jass.2016.02.014 Wang W,Liu B D,Liu P X,Wang Z Y,Liu X. 2016. Analyses on the effect of the local site conditions on the strong motion based on the array records[J]. Acta Seismologica Sinica,38(2):307–317 (in Chinese).
姚凯,卢大伟,刘旭宙,周民都,闵祥仪. 2009. 利用汶川余震流动观测资料探讨地形对峰值加速度的影响[J]. 西北地震学报,31(1):46–50. Yao K,Lu D W,Liu X Z,Zhou M D,Min X Y. 2009. Using observational data from the aftershocks of Wenchuan great earthquake to study the influence of geography on peak ground acceleration[J]. Northwestern Seismological Journal,31(1):46–50 (in Chinese).
袁晓铭,廖振鹏. 1996. 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,16(2):1–13. Yuan X M,Liao Z P. 1996. Scattering of plane SH waves by a cylindrical hill of circular-arc cross-section[J]. Earthquake Engi neering and Engineering Vibration,16(2):1–13 (in Chinese).
章文波,谢礼立,郭明珠. 2001. 利用强震记录分析场地的地震反应[J]. 地震学报,23(6):604–614. doi: 10.3321/j.issn:0253-3782.2001.06.006 Zhang W B,Xie L L,Guo M Z. 2001. Estimation on site-amplification from different methods using strong motion data obtained in Tangshan,China[J]. Acta Seismologica Sinica,23(6):604–614 (in Chinese).
章小龙,李小军,周正华,陈国兴,彭小波. 2017. 三维复杂山谷地形SV波垂直输入地震反应分析[J]. 地球物理学报,60(7):2779–2790. doi: 10.6038/cjg20170723 Zhang X L,Li X J,Zhou Z H,Chen G X,Peng X B. 2017. The seismic response analysis of three-dimensional canyon complex topography under incident SV seismic waves[J]. Chinese Journal of Geophysics,60(7):2779–2790 (in Chinese).
周港圣,周游,周正华,魏来,魏鑫,沈欣茹,陈珍. 2022. 山脊地形效应的强震动观测研究[J]. 地震工程学报,44(5):1110–1116. Zhou G S,Zhou Y,Zhou Z H,Wei L,Wei X,Shen X R,Chen Z. 2022. Topographic effect of ridge terrains based on strong motion observation data[J]. China Earthquake Engineering Journal,44(5):1110–1116 (in Chinese).
周红,高孟潭,俞言祥. 2010. SH波地形效应特征的研究[J]. 地球物理学进展,25(3):775–782. doi: 10.3969/j.issn.1004-2903.2010.03.005 Zhou H,Gao M T,Yu Y X. 2010. A study of topographical effect on SH waves[J]. Progress in Geophysics,25(3):775–782 (in Chinese).
周正华,王玉石,王伟,王宇欢,刘泉,杨程. 2009. 汶川MS8.0地震中的山脊地形效应:自贡西山公园典型事例[C]//纪念汶川地震一周年地震工程与减轻地震灾害研讨会论文集. 成都:中国建筑学会,中国地震学会:58−64. Zhou Z H,Wang Y S,Wang W,Wang Y H,Liu Q,Yang C. 2009. Ridge topography effect in Wenchuan MS8.0 earthquake:Typical examples of Xishan park in Zigong[C]//Collection of Seminar on Earthquake Engineering and Earthquake Disaster Reduction to Commemorate the First Anniversary of Wenchuan Earthquake. Chengdu:Architectural Society of China,China Earthquake Society:58−64 (in Chinese).
Bard P Y,Tucker B E. 1985. Underground and ridge site effects:A comparison of observation and theory[J]. Bull Seismol Soc Am,75(4):905–922. doi: 10.1785/BSSA0750040905
Bonamassa O,Vidale J E. 1991. Directional site resonances observed from aftershocks of the 18 October 1989 Loma Prieta earthquake[J]. Bull Seismol Soc Am,81(5):1945–1957.
Bouchon M. 1973. Effect of topography on surface motion[J]. Bull Seismol Soc Am,63(2):615–632. doi: 10.1785/BSSA0630020615
Bouchon M,Barker J S. 1996. Seismic response of a hill:The example of Tarzana,California[J]. Bull Seismol Soc Am,86(1A):66–72. doi: 10.1785/BSSA08601A0066
Çelebi M. 1987. Topographical and geological amplifications determined from strong-motion and aftershock records of the 3 March 1985 Chile earthquake[J]. Bull Seismol Soc Am,77(4):1147–1167. doi: 10.1785/BSSA0770041147
Çelebi M. 1991. Topographical and geological amplification:Case studies and engineering implications[J]. Struct Saf,10(1/2/3):199–217.
Geli L,Bard P Y,Jullien B. 1988. The effect of topography on earthquake ground motion:A review and new results[J]. Bull Seismol Soc Am,78(1):42–63. doi: 10.1785/BSSA0780010042
Kurita T,Annaka T,Takahashi S,Shimada M,Suehiro T. 2005. Effect of irregular topography on strong ground motion amplification[J]. J Japan Assoc Earthq Eng,5(3):1–11.
Pedersen H,Le Brun B,Hatzfeld D,Campillo M,Bard P Y. 1994. Ground-motion amplitude across ridges[J]. Bull Seismol Soc Am,84(6):1786–1800. doi: 10.1785/BSSA0840061786
Tessmer E,Kosloff D. 1994. 3-D elastic modeling with surface topography by a Chebychev spectral method[J]. Geophysics,59(3):464–473. doi: 10.1190/1.1443608
Vidale J E,Bonamassa O,Houston H. 1991. Directional site resonances observed from the 1 October 1987 Whittier Narrows,California,earthquake and the 4 October aftershock[J]. Earthq Spectra,7(1):107–125. doi: 10.1193/1.1585616
Vincenzo D G. 2017. Instantaneous polarization analysis of ambient noise recordings in site response investigations[J]. Geophys J Int,210(1):443–464.
Wong H L,Trifunac M D. 1974. Scattering of plane SH waves by a semi-elliptical canyon[J]. Earthq Eng Struct Dyn,3(2):157–169. doi: 10.1002/eqe.4290030205
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