地表/井下加速度反应谱谱比的周期相关非线性特征

doi:10.3969/j.issn.0253-4967.2024.06.010

地震地质 ›› 2024, Vol. 46 ›› Issue (6): 1391-1407.DOI: 10.3969/j.issn.0253-4967.2024.06.010

地表/井下加速度反应谱谱比的周期相关非线性特征

王琳¹⁾(), 王玉石¹^,²⁾^,^*(), 李小军¹^,²⁾, 刘艳琼³⁾, 丁毅¹^,²⁾

¹⁾ 北京工业大学, 建筑工程学院, 北京 100124
²⁾ 中国地震局地球物理研究所, 北京 100081
³⁾ 中国地震台网中心, 北京 100045

收稿日期:2024-02-12 修回日期:2024-04-01 出版日期:2024-12-20 发布日期:2025-01-22
通讯作者: *王玉石, 男, 1982年生, 副研究员, 主要从事地震动场地效应研究, E-mail: wangyushi1982@126.com。
作者简介:
王琳, 女, 1996年生, 现为北京工业大学防灾减灾及防护工程专业在读硕士研究生, 主要从事强震动观测数据分析与应用研究, E-mail: doublelinya@163.com。
基金资助:
国家重点研发计划项目(2022YFC3003503); 国家自然科学基金(52192675); 中国地震局地震科技星火计划项目(XH22008B)

PERIOD-DEPENDENT NONLINEAR CHARACTERISTICS OF SURFACE/BOREHOLE SPECTRAL ACCELERATION RATIOS

WANG Lin¹⁾(), WANG Yu-shi¹^,²⁾^,^*(), LI Xiao-jun¹^,²⁾, LIU Yan-qiong³⁾, DING Yi¹^,²⁾

¹⁾ The College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China
²⁾ Institute of Geophysics, China Earthquake Administration, Beijing 100081, China
³⁾ China Earthquake Networks Center, Beijing 100045, China

Received:2024-02-12 Revised:2024-04-01 Online:2024-12-20 Published:2025-01-22

摘要/Abstract

摘要：

浅地表软弱覆盖土层会显著影响加速度反应谱等地震动特性表征参数, 且其影响程度随地震动强度增加呈现显著的非线性特征。文中基于日本KiK-net台网180个台站的166 700组强震动记录, 采用动态时间规整(DTW)算法对地表/井下反应谱谱比曲线的周期偏移进行修正, 定量分析了地表/井下反应谱谱比随地震动强度的周期偏移与幅值衰减特性, 发现相对周期偏移量与谱比幅值均与地震动强度在对数或半对数坐标系下呈线性关系, 且不同周期点的相对周期偏移与幅值衰减速率并不相同。统计获得了各台站及Ⅰ、 Ⅱ、 Ⅲ、 Ⅳ类场地上的周期偏移系数和幅值衰减系数, 发现其均随周期增加呈现先增大后减小的趋势, 表明在地震动能量丰富的加速度反应谱平台段, 地表/井下反应谱谱比曲线的周期偏移更为显著, 但幅值衰减则相对较慢。尽管地表/井下反应谱谱比与土层地表/基岩地表反应谱谱比之间存在差异, 统计得到的周期偏移系数和幅值衰减系数仍可在一定程度上反映地震动场地效应的非线性特征。

关键词: 地震动, 工程地质条件, 局部场地效应, 地表/井下反应谱谱比, 动态时间规整算法

Abstract:

Weak overburden layers at shallow surfaces would substantially affect the ground motion characteristic parameters of ground motion, such as spectral accelerations, and these influences regularly showed obvious nonlinearity with the increase of ground motion strength. Despite the differences between motions down the borehole and ground motions on bedrock, the surface/borehole spectral ratios could reflect the seismic site effect to some extent and overcome the shortcomings of the lack of reference bedrock stations in the standard spectral ratio method and the assumption of seismic point source in the generalized inversion method. In recent years, more and more scholars have studied the nonlinear dynamic characteristics of the soil body and its change trend based on the strong motion data by comparing the surface/borehole spectral acceleration ratios under different motion strengths. However, the research conclusions, especially the quantitative characterization of the nonlinear characteristics, still need to be improved due to the insufficient statistical sample size.

It was found that the surface/borehole spectral acceleration ratio curves at the same station exhibited high similarity under different motion strengths. However, these spectral acceleration ratios significantly decreased as motion strength increased and shifted towards longer periods at certain period ranges. The surface/borehole spectral acceleration ratios at different motion strengths corresponding to the same period point cannot adequately reflect their nonlinear characteristics. It is more reasonable to characterize these features by the corresponding relationships between the points on the surface/borehole spectral acceleration ratio curve shapes at different motion intensities. Although some scholars have proposed methods for correcting the dominant frequency offset, there remains a lack of effective methods for fixing the period shift of the surface/borehole spectral acceleration ratio across the wholeentire period range, as well as for the quantitative characterization of nonlinear characteristic parameters throughout the wholeentire period range. Dynamic Time Warping(DTW)algorithm is a nonlinear alignment method that combines time alignment and measurement matching. The core idea of the Dynamic Time Warping(DTW)algorithm is to find the optimal mapping between two-time series by calculating the distance between their respective discrete points and identifying the best path connecting them. This process enables point-to-point matching between the two-time series, and the DTW distance(sum of distances along the best path)can be utilized to assess their similarity.

In this study, we selected 166 700 strong-motion records from 180 stations in Japan's KiK-net network them. We grouped them by ground motion intensity to obtain the surface/borehole spectral acceleration ratios and their average values for each station under different intensity levels. A dynamic time warping algorithm was employed to effectively correct long-period shifts in the spectral acceleration ratio curves, which allowed for the precise extraction of both the period shift and amplitude attenuation values at various period points for each seismic station. Subsequently, a detailed statistical analysis was conducted to assess how these values varied about different levels of ground motion intensity. In addition, nonlinear characteristic parameter curves, dependent on both the period and seismic intensity changes, were derived for different site categories, accompanied by the establishment of corresponding empirical relationships. Furthermore, a novel method was proposed to predict the surface-to-borehole spectral ratio under conditions of strong seismic motion, utilizing the spectral acceleration ratio data obtained from weaker ground motion intensity scenarios. This approach is intended to offer more precise and detailed data support for adjusting nonlinear site effects in China's seismic design codes and seismic hazard zoning maps. Ultimately, the goal is to provide a more refined and comprehensive basis for enhancing the nonlinear site response adjustments in China's seismic design specifications and seismic motion parameter zoning maps.

The quantitative analysis of period offset characteristics of the surface/borehole spectral acceleration ratios indicated that the period offsets were more significant under larger motion strength. Meanwhile the period offsets at different periods were not consistent, and the relative period offsets at the same period exhibited linear relationships with motion strength under the double-logarithmic coordinates. The relative period offsets could be reliably expressed by the period offset coefficient defined empirically. The period offset coefficients obtained at each station and on each site class (Ⅰ, Ⅱ, Ⅲ, and Ⅳ) of Chinese standards were all related to the period, which showed a trend of initially increasing and subsequently decreasing with the increase of the period. Furthermore, the period offset coefficients increased with the thickness and softness of the overburden layers, which indicated more significant period offsets on sites of thick and soft overburden layers. The quantitative analysis of the amplitude decay characteristics of the surface/borehole spectral acceleration ratios indicated that the spectral ratio amplitude was lower under more considerable motion strength. Meanwhile, the amplitude rates at different periods were not consistent, and the spectral ratio amplitude at the same period exhibited fine linear relationships with motion strength under the semi-logarithmic coordinates. The amplitude decay rate could be reliably expressed by the amplitude decay coefficient defined empirically. The amplitude decay coefficients obtained at each station and on each site class (Ⅰ, Ⅱ, Ⅲ, and Ⅳ) of Chinese standards were all related to the period. They approximately conformed to a Gaussian function under the semi-logarithmic coordinates, indicating that the amplitude decay rates were lower in the middle period range(the platform segment of spectral accelerations)compared to the shorter or longer period ranges. Moreover, the amplitude decay coefficients (<0) decreased with the thickness and softness of the overburden layers, which indicated faster amplitude decay rates on sites of thick and soft overburden layers. Despite the differences between surface/borehole spectral acceleration ratios and soil surface/bedrock surface spectral acceleration ratios, the period offset coefficients and amplitude decay coefficients derived statistically could reflect the nonlinear characteristics of seismic site effects to some extent. According to the empirical relationships for relative period offsets and amplitude decay rates of surface/borehole spectral acceleration ratios on different site classes (Ⅰ, Ⅱ, Ⅲ and Ⅳ) of Chinese standards, the surface/borehole spectral acceleration ratios under stronger motions could be predicted reliably by surface/borehole spectral acceleration ratios under weaker motion.

Key words: ground motion, engineering geological condition, local site effect, surface/borehole spectral acceleration ratio, dynamic time warping algorithm

王琳, 王玉石, 李小军, 刘艳琼, 丁毅. 地表/井下加速度反应谱谱比的周期相关非线性特征[J]. 地震地质, 2024, 46(6): 1391-1407.

WANG Lin, WANG Yu-shi, LI Xiao-jun, LIU Yan-qiong, DING Yi. PERIOD-DEPENDENT NONLINEAR CHARACTERISTICS OF SURFACE/BOREHOLE SPECTRAL ACCELERATION RATIOS[J]. SEISMOLOGY AND GEOLOGY, 2024, 46(6): 1391-1407.

图/表 10

图1 所选取记录的震级、震中距和井下峰值加速度分布

Fig. 1 Distribution of magnitude, epicenter distance and borehole peak acceleration for selected records.

图2 典型台站(FKSH19)不同地震动强度下地表/井下反应谱谱比

Fig. 2 Surface/ borehole spectral acceleration ratios under different strong-motion strengths at Station FKSH19.

图3 地表/井下反应谱谱比的DTW算法规整路径示意图

Fig. 3 Schematic diagram of DTW algorithm regularization path for surface/borehole spectral acceleration ratios.

图4 典型台站(FKSH19)DTW算法最优映射及周期偏移修正结果

Fig. 4 Optimal mapping and period offset correction results of DTW algorithm regularization at Station FKSH19.

图5 典型台站(FKSH19)不同地震动强度、不同周期的相对周期偏移量

Fig. 5 Relative period offsets under different motion strengths and periods at Station FKSH19.

图6 Ⅰ、 Ⅱ、 Ⅲ、 Ⅳ类场地上周期相关的周期偏移系数α

Fig. 6 Period offset coefficient α related to period on site class Ⅰ, Ⅱ, Ⅲ and Ⅳ.

图7 典型台站(FKSH19)周期偏移修正后地表/井下反应谱谱比及归一化地表/井下反应谱谱比

Fig. 7 Surface/borehole spectral acceleration ratio after period offset correction and normalized surface/ borehole spectral acceleration ratio at Station FKSH19.

图8 典型台站(FKSH19)不同地震动强度、不同周期的归一化反应谱谱比

Fig. 8 Normalized surface/ borehole spectral acceleration ratio under different motion strengths and periods at Station FKSH19.

图9 Ⅰ、 Ⅱ、 Ⅲ、 Ⅳ类场地上周期相关的幅值衰减系数 β

Fig. 9 Amplitude decay coefficient β related to period on site class Ⅰ, Ⅱ, Ⅲ and Ⅳ.

表1 Ⅰ、 Ⅱ、 Ⅲ、 Ⅳ类场地非线性特征参数与周期回归系数

Table1 Regression coefficients between nonlinear characteristic parameters and periodicity for site Class Ⅰ, Ⅱ, Ⅲ and Ⅳ

非线性特征参数	回归系数	场地类别
非线性特征参数	回归系数	Ⅰ	Ⅱ	Ⅲ	Ⅳ
周期偏移系数 $α$	a	0.196	0.276	0.243	0.555
	b	0.06	0.07	0.09	0.13
	c	1.10	1.09	1.21	2.15
	d	0	0	0	-0.258
幅值衰减系数 $β$	$a 1$	0.069	0.124	0.141	0.102
	$b 1$	0.35	0.42	0.9	0.58
	$c 1$	0.593	0.581	0.176	1.08
	$a 2$	0.008	0.027	0.012	0.0075
	$b 2$	0.132	0.240	0.220	0.242

表1 Ⅰ、 Ⅱ、 Ⅲ、 Ⅳ类场地非线性特征参数与周期回归系数

Table1 Regression coefficients between nonlinear characteristic parameters and periodicity for site Class Ⅰ, Ⅱ, Ⅲ and Ⅳ

非线性特征参数	回归系数	场地类别
非线性特征参数	回归系数	Ⅰ	Ⅱ	Ⅲ	Ⅳ
周期偏移系数 $α$	a	0.196	0.276	0.243	0.555
	b	0.06	0.07	0.09	0.13
	c	1.10	1.09	1.21	2.15
	d	0	0	0	-0.258
幅值衰减系数 $β$	$a 1$	0.069	0.124	0.141	0.102
	$b 1$	0.35	0.42	0.9	0.58
	$c 1$	0.593	0.581	0.176	1.08
	$a 2$	0.008	0.027	0.012	0.0075
	$b 2$	0.132	0.240	0.220	0.242

参考文献 35

[1]	陈棋福, 刘澜波, 王伟君, 等. 2008. 利用地脉动探测北京城区的地震动场地响应[J]. 科学通报, 53(18): 2229—2235.
	CHEN Qi-fu, LIU Lan-bo, WANG Wei-jun, et al. 2008. The seismic motion site response in Beijing urban area associated with microtremor survey method[J]. Chinese Science Bulletin, 53(18): 2229—2235(in Chinese).
[2]	丁毅, 王玉石, 王宁, 等. 2021. 地表/井下反应谱比值非线性统计特征与影响因素研究[J]. 震灾防御技术, 16(2): 362—370.
	DING Yi, WANG Yu-shi, WANG Ning, et al. 2021. Study on nonlinear statistical characteristics of surface/downhole response spectrum ratio and influencing factors[J]. Technology for Earthquake Disaster Prevention, 16(2): 362—370(in Chinese).
[3]	何浩祥, 解鑫, 王文涛. 2018. 基于动态时间归整距的地震动特性分析及合成精度评价[J]. 振动与冲击, 37(12): 207—215.
	HE Hao-xiang, XIE Xin, WANG Wen-tao. 2018. Ground motion characteristics analysis and synthesis accuracy evaluation based on dynamic time warping distance[J]. Journal of Vibration and Shock, 37(12): 207—215(in Chinese).
[4]	李小军, 彭青. 2001a. 不同类别场地地震动参数的计算分析[J]. 地震工程与工程振动, 21(1): 29—36.
	LI Xiao-jun, PENG Qing. 2001a. Calculation and analysis of earthquake ground motion parameters for different site categories[J]. Earthquake Engineering and Engineering Dynamics, 21(1): 29—36(in Chinese).
[5]	李小军, 彭青, 刘文忠. 2001b. 设计地震动参数确定中的场地影响考虑[J]. 世界地震工程, 17(4): 34—41.
	LI Xiao-jun, PENG Qing, LIU Wen-zhong. 2001b. Consideration of site effects for determination of design earthquake ground motion parameters[J]. World Earthquake Engineering, 17(4): 34—41(in Chinese).
[6]	刘浩, 朱敬洲, 徐龙军, 等. 2019. 动态时间规整算法在时程反应分析选取地震动中的应用[J]. 地震工程与工程振动, 39(5): 223—233.
	LIU Hao, ZHU Jing-zhou, XU Long-jun, et al. 2019. Application of dynamic time warping algorithm in selecting ground motion for time history response analysis[J]. Earthquake Engineering and Engineering Dynamics, 39(5): 223—233(in Chinese).
[7]	任叶飞. 2014. 基于强震动记录的汶川地震场地效应研究[D]. 哈尔滨: 中国地震局工程力学研究所.
	REN Ye-fei. 2014. Study on site effect in the Wenchuan earthquake using strong-motion recordings[D]. Institute of Engineering Mechanics, China Earthquake Administration, Harbin(in Chinese).
[8]	宋海锋, 张敏杰, 曾小清, 等. 2022. 基于线路数据信息的列车定位方法研究[J]. 同济大学学报(自然科学版), 50(1): 13—21.
	SONG Hai-feng, ZHANG Min-jie, ZENG Xiao-qing, et al. 2022. Train location method based on line data information[J]. Journal of Tongji University(Natural Science), 50(1): 13—21(in Chinese).
[9]	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.
	WANG Hai-yun, XIE Li-li. 2010. Effects of topography on ground motion in the Xishan park, Zigong city[J]. Chinese Journal of Geophysics, 53(7): 1631—1638(in Chinese).
[10]	王玉石, 李小军, 兰日清, 等. 2016. 强震动作用下土体非线性动力特征研究发展与展望[J]. 震灾防御技术, 11(3): 480—492.
	WANG Yu-shi, LI Xiao-jun, LAN Ri-qing, et al. 2016. Development and prospect of study on soil nonlinear dynamic characteristics under strong-motion[J]. Technology for Earthquake Disaster Prevention, 11(3): 480—492(in Chinese).
[11]	张立宝. 2018. 基于钻井台阵数据的场地非线性效应研究[D]. 北京: 中国地震局地球物理研究所.
	ZHANG Li-bao. 2018. Study on nonlinearity of site effects on ground motion based on vertical borehole array data[D]. Institute of Geophysics, China Earthquake Administration, Beijing(in Chinese).
[12]	中华人民共和国住房和城乡建设部. 2016. 建筑抗震设计规范(2016年版)(GB 50011-2010)[S]. 北京: 中国建筑工业出版社.
	Ministry of Housing and Urban-Rural Development of the People's Republic of China. 2016. Code for Seismic Design of Buildings(2016 ed.)(GB 50011-2010)[S]. China Architecture & Building Press, Beijing(in Chinese).
[13]	Aguirre J, Irikura K. 1997. Nonlinearity, liquefaction, and velocity variation of soft soil layers in Port Island, Kobe, during the Hyogo-ken Nanbu earthquake[J]. Bulletin of the Seismological Society of America, 87(5): 1244—1258.
[14]	Aki K. 1993. Local site effects on weak and strong ground motion[J]. Tectonophysics, 218(1): 93—111.
[15]	Andrews D J. 1986. Objective determination of source parameters and similarity of earthquakes of different size[J]. Earthquake Source Mechanics, 37: 259—267.
[16]	Beresnev I A, Atkinson G M. 1998. Stochastic finite-fault modeling of ground motions from the 1994 Northridge, California, earthquake. I. Validation on rock sites[J]. Bulletin of the Seismological Society of America, 88(6): 1392—1401.
[17]	Beresnev I A, Wen K. 1996. Nonlinear soil response—A reality?[J]. Bulletin of the Seismological Society of America, 86(6): 1964—1978.
[18]	Bernardie S, Foerster E, Modaressi H. 2006. Non-linear site response simulations in Chang-Hwa region during the 1999 Chi-Chi earthquake, Taiwan[J]. Soil Dynamics and Earthquake Engineering, 26(11): 1038—1048.
[19]	Borcherdt R D. 1970. Effects of local geology on ground motion near San Francisco Bay[J]. Bulletin of the Seismological Society of America, 60(1): 29—61.
[20]	Castro-Cruz D, Régnier J, Bertrand E, et al. 2020. A new parameter to empirically describe and predict the non-linear seismic response of sites derived from the analysis of Kik-net database[J]. Soil Dynamics and Earthquake Engineering, 128:105833.
[21]	Forestier G, Lalys F, Riffaud L, et al. 2012. Classification of surgical processes using dynamic time warping[J]. Journal of Biomedical Informatics, 45(2): 255—264. DOI PMID
[22]	Gardezi S J S, Faye I, Sanchez Bornot J M, et al. 2018. Mammogram classification using dynamic time warping[J]. Multimedia Tools and Applications, 77(3): 3941—3962.
[23]	Gollmer K, Posten C. 1996. Supervision of bioprocesses using a dynamic time warping algorithm[J]. Control Engineering Practice, 4(9): 1287—1295.
[24]	Huang H, Shieh C, Chiu H C. 2001. Linear and nonlinear behaviors of soft soil layers using Lotung downhole array in Taiwan[J]. Terrestrial, Atmospheric and Oceanic Sciences, 12(3): 503—524.
[25]	Huang S, Lu H. 2020. Classification of temporal data using dynamic time warping and compressed learning[J]. Biomedical Signal Processing and Control, 57:101781.
[26]	Joswig M, Schulte-Theis H. 1993. Master-event correlations of weak local earthquakes by dynamic waveform matching[J]. Geophysical Journal International, 113(3): 562—574.
[27]	Moya A, Irikura K. 2003. Estimation of site effects and Q factor using a reference event[J]. Bulletin of the Seismological Society of America, 93(4): 1730—1745.
[28]	Piyush Shanker A, Rajagopalan A N. 2007. Off-line signature verification using DTW[J]. Pattern Recognition Letters, 28(12): 1407—1414.
[29]	Régnier J, Cadet H, Bard P Y. 2016. Empirical quantification of the impact of nonlinear soil behavior on site response[J]. Bulletin of the Seismological Society of America, 106(4): 1710—1719.
[30]	Ren Y, Wen R, Yamanaka H, et al. 2013. Site effects by generalized inversion technique using strong motion recordings of the 2008 Wenchuan earthquake[J]. Earthquake Engineering and Engineering Vibration, 12(2): 165—184.
[31]	Sakoe H, Chiba S. 1978. Dynamic programming algorithm optimization for spoken word recognition[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 26(1): 43—49.
[32]	Steidl J H, Tumarkin A G, Archuleta R J. 1996. What is a reference site?[J]. Bulletin of the Seismological Society of America, 86(6): 1733—1748.
[33]	Wang H, Ren Y, Wen R. 2018. Source parameters, path attenuation and site effects from strong-motion recordings of the Wenchuan aftershocks(2008—2013)using a non-parametric generalized inversion technique[J]. Geophysical Journal International, 212(2): 872—890.
[34]	Wen K L, Lin C M, Chiang H J, et al. 2008. Effect of surface geology on ground motions: The case of station TAP056-Chutzuhu site[J]. Terrestrial, Atmospheric and Oceanic Sciences, 19(5): 451—462.
[35]	Wu C, Peng Z, Ben-Zion Y. 2010. Refined thresholds for non-linear ground motion and temporal changes of site response associated with medium-size earthquakes[J]. Geophysical Journal International, 182(3): 1567—1576.

地表/井下加速度反应谱谱比的周期相关非线性特征

PERIOD-DEPENDENT NONLINEAR CHARACTERISTICS OF SURFACE/BOREHOLE SPECTRAL ACCELERATION RATIOS

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[11]	夏晨, 赵伯明. 应用动力学拐角频率对经验格林函数法的改进[J]. 地震地质, 2015, 37(2): 529-540.
[12]	陈鲲, 俞言祥, 高孟潭, 亢川川. 中国西部地区利用烈度数据估计地震动参数的方法[J]. 地震地质, 2014, 36(4): 1043-1052.
[13]	范文, 邓龙胜, 邵辉成, 刘佳, 贺龙鹏, 文毅. 不同转换方法在关中平原区地震动衰减关系研究中的应用[J]. 地震地质, 2012, 34(1): 129-137.
[14]	陈晓利, 马文涛, 杨清源. 基于GIS的水库诱发地震成因分析[J]. 地震地质, 2010, 32(4): 656-665.
[15]	潘波, 许建东, 刘启方. 1679年三河-平谷8级地震近断层强地震动的有限元模拟[J]. 地震地质, 2009, 31(1): 69-83.