Strong ground motion simulation for the 2013 MS7.0 Lushan, China, earthquake
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摘要: 运用经验格林函数法模拟2013年4月20日芦山MS7.0地震的近场强地面运动. 在拟合过程中， 首先参考前人远场反演结果给出的滑动量分布特征和主震波形的包络线特征， 确定强震动生成区的大致范围和数量； 然后利用Somerville等提出的地震矩与凹凸体面积的经验关系式确定强震动生成区细小划分的初值， 继而利用遗传优化算法确定以上二者的最优值及其它震源参数. 将数值模拟波形与实际地震观测记录在时间域和频率域分别进行比较， 结果显示， 在所选取的30个观测台站中， 多数台站的数值模拟结果与实际观测结果符合得很好， 特别是大于1 Hz的高频部分. 断层面上有两个强震动生成区， 其位置与前人反演的滑动量集中分布区相一致， 而且强震动生成区规模比Somerville等获得的标度率估计值要小.Abstract: The near source strong ground motions of the 2013 MS7.0 Lushan, China, earthquake were simulated using empirical Green’s function (EGF) method. At first, we estimated the amount and location of strong motion gene-ration areas (SMGAs) based on the characteristics of both slip distributions from far-field seismic inversion and the envelopes of recorded acceleration from the main shock, and determined the amount of subfaults on SMGAs referring to the scaling law of asperity area versus seismic moment introduced by Somerville et al. Then, we implemented the genetic algorithm searching for the optimized value of above two and other source parameters. Based on the source models, we synthetized the waveforms for the 30 selected stations near the source region. The comparison of the synthetic waveforms with the observed records indicated that they agreed very well with each other, especially for the part of high-frequency larger than 1 Hz. We found that there were two obvious SMGAs on the fault, which take the position that the asperities from far-field seismic inversion take. The combined SMGAs we obtained were smaller than those predicted by extension of the scaling law by Somerville et al.
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图 1 经验格林函数法示意图
（a）经验格林函数法主要参数；（b）校正函数F(t), 图中tr为上升时间
Figure 1. Schematic diagram of empirical Green’s function method
(a) The parameters of empirical Green’s function method; (b) The correcting function F(t)， where tr is rising time
图 2 主震、 余震和台站空间分布图
震源附近的矩形框是断层面在地表的投影
Figure 2. Locations of the main shock (asterisk) and the aftershock (dot) used as empirical Green’s function（EGF）
The triangles indicate the locations of strong ground motion stations used for simulation by EGF. The rectangle near the hypocenter represents the surface projection of fault
图 3 051BXD(a)和051CDZ(b)台站记录到的余震加速度时程(上)及其傅里叶谱与噪声谱(下)
Figure 3. Acceleration time histories (upper) of the aftershock recorded by the station 051BXD (a) and 051CDZ (b) as well as their Fourier spectra (dashed lines) and noise spectra (solid lines) (lower)
图 4 芦山地震断层面上的滑动量分布
(a) 王卫民等(2013)远震反演结果； (b) 张勇等(2013)远震反演结果； (c) 赵翠萍等(2013)远震反演结果； (d) 金明培等(2014) GPS与近场强震联合反演结果
Figure 4. Slip distributions on the fault for the Lushan earthquake
Figs.(a)-(c) give the teleseismic inversion results from Wang et al (2013), Zhang et al (2013) and Zhao et al (2013), respectively; and Fig.(d) gives the joint inversion result of GPS and near filed strong motion from Jin et al (2014)
图 5 051LSF台站记录的芦山主震加速度时程.
图中数字为记录到的加速度峰值
Figure 5. Acceleration time histories of the Lushan main shock recorded by the station 051LSF
The numbers are the recorded values of peak ground acceleration
图 6 基于王卫民等（2013）的反演结果构建的强震动震源模型
Figure 6. Strong motion source model based on the inversion result from Wang et al (2013) The star indicates the hypocenter of the main shock. The black and red rectangles represent the SMGA1 and SMGA2， respectively
图 7 强震动生成区面积（a）和上升时间（b）与地震矩的标度关系
The gray solid lines indicate the empirical scaling relationship from Somerville et al (1999), the black solid lines represent 3 stage scaling relationships proposed by Irikura and Miyake (2011), and the star indicates the value obtained in this study
Figure 7. The empirical relationship between the strong motion generation area (a), the rising time (b) and seismic moment
图 8 各台站加速度时程（a）和加速度傅里叶谱（b）的观测记录(黑色)与最优模型的拟合结果（灰色）对比（Ⅰ）
The numbers in acceleration time histories indicate the values of peak ground acceleration
Figure 8. Comparison of acceleration time histories (a) and Fourier spectra (b) between the observed waveforms (black lines) and synthetic ones (gray lines) for the best model of different stations
图 8 各台站加速度时程（a）和加速度傅里叶谱（b）的观测记录(黑色)与最优模型的拟合结果（灰色）对比（Ⅱ）
The numbers in acceleration time histories indicate the values of peak ground acceleration
Figure 8. Comparison of acceleration time histories (a) and Fourier spectra (b) between the observed waveforms (black lines) and synthetic ones (gray lines) for the best model of different stations
图 8 各台站加速度时程（a）和加速度傅里叶谱（b）的观测记录(黑色)与最优模型的拟合结果（灰色）对比（Ⅲ）
The numbers in acceleration time histories indicate the values of peak ground acceleration
Figure 8. Comparison of acceleration time histories (a) and Fourier spectra (b) between the observed waveforms (black lines) and synthetic ones (gray lines) for the best model of different stations
图 9 051QLY(a)和051YAM(b)台站记录到的余震加速度时程(上)及其傅里叶谱与噪声谱（下）
Figure 9. Acceleration time histories (upper) of the aftershock recorded by the stations 051QLY (a) and 051YAM (b) as well as their Fourier spectra (dashed lines) and noise spectra (solid lines) (lower)
表 1 主震和作为经验格林函数的余震的震源位置和震源机制
Table 1. Focal mechanisms and locations of the main shock and the aftershock used as EGF in this study
地震类型 发震时间 北纬/° 东经/° 深度/km MW 地震矩/（N·m） 走向/° 倾角/° 滑动角/° 年-月-日 时:分 主震 2013-04-20 00:02 30.22 103.12 21.9 6.6 1.02×1019 212 42 100 余震 2013-04-20 20:53 30.28 103.31 30.3 4.8 2.15×1016 177 42 74 注：引自哈佛大学全球质心矩张量目录. 
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表 2 强震动台站位置信息
Table 2. Locations of the 30 strong motion stations used in this study
台站代码 台站名称 台站位置 场地条件 台站代码 台站名称 台站位置 场地条件 东经/° 北纬/° 东经/° 北纬/° 051BXD 宝兴地办 102.8 30.4 基岩 051LSF 芦山飞仙 102.9 30.0 土层 051BXM 宝兴明礼 102.7 30.4 土层 051MNA 冕宁惠安 102.2 28.6 土层 051BXY 宝兴盐井 102.9 30.5 土层 051MNC 冕宁曹古 102.2 28.6 土层 051BXZ 宝兴民治 102.9 30.5 基岩 051MNH 冕宁回龙 102.1 28.5 土层 051CDZ 成都中和 104.1 30.6 基岩 051MNJ 冕宁地办 102.2 28.5 土层 051DJZ 都江紫平 103.6 31.0 土层 051MNL 冕宁泸沽 102.2 28.3 土层 051HYQ 汉源清溪 102.6 29.6 土层 051MNT 冕宁专业 102.2 28.5 土层 051HYT 洪雅科技 103.4 29.9 土层 051MNW 冕宁拖乌 102.3 28.8 土层 051HYW 汉源乌斯 102.9 29.2 土层 051PJD 蒲江大兴 103.4 30.3 土层 051HYY 汉源宜东 102.4 29.6 土层 051QLY 邛崃油榨 103.3 30.4 土层 051KDT 康定专业 102.0 30.0 土层 051TQL 天全两路 102.4 29.9 土层 051LBH 雷波黄琅 103.8 28.4 土层 051XDM 喜德冕山 102.3 28.4 土层 051LDG 泸定甘谷 102.2 29.8 土层 051YAD 雅安专业 103.0 30.0 土层 051LDJ 泸定加郡 102.2 29.7 土层 051YAL 荥经石龙 102.8 29.9 土层 051LDL 泸定冷碛 102.2 29.8 土层 051YAM 名山科技 103.1 30.1 土层 注： 引自国家强震动台网中心．
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表 3 最优模型参数和遗传算法搜索范围
Table 3. The optimal parameters of determined model and their search scopes for genetic algorithm
搜索参数 强震生成区1 强震生成区2 VR/（km·-1） N1 w1/km 初始破裂点 tr1/s R1/km C1 N2 w2/km 初始破裂点 tr2/s R2/km C2 最小值 5 0.1 (1, 1) 0.1 -30 0.1 1 0.1 (1, 1) 0.1 -50 0.1 2.1 最大值 15 6.0 (8, 8) 10.0 30 5.0 10 6.0 (4, 4) 10.0 50 5.0 3.6 最优值 8 1.0 (4, 4) 2.0 12 1.6 4 1.0 (2, 2) 2.0 14 0.7 2.8 注：N为子断层细小划分的数目，w为子断层宽， tr为上升时间， R为震中距， VR为破裂速度.
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