An estimation model of high frequency attenuation coefficient of ground motion for local site
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摘要:
采用随机有限断层法进行地震动模拟时，选用合理的参数描述特定局部场地近地表高频衰减特征，对评价地震动模拟结果的正确与否具有重要的实践意义。 在工程场址地震动参数预测中，如何快速确定参数的取值，是实际应用中亟需解决的问题。首先对场地高频衰减系数κ0与平均剪切波速vS30的相关性进行了分析；然后，基于国内外学者计算得到的546个κ0系数，采用一定时窗内的κ0均方根值，讨论其随平均剪切波速vS30增加的变化趋势。 结果表明，虽然κ0具有明显的区域差异性，但其均方根值随着vS30的增大呈现出逐渐减小的趋势。 为了得到合理的κ0估计模型，分别采用线性函数、多项式函数、对数线性函数和双对数线性函数对κ0均方根值与vS30的关系进行初步拟合，结果表明，对数线性函数能够较好地描述κ0与vS30之间的关系。 最后，基于筛选得到的477个数据，采用最小二乘法对模型参数进行拟合，建立了适合工程应用的κ0-vS30模型。对模型适用性的分析表明，本研究所构建的κ0估计模型能够合理估计地震动的高频衰减影响。
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关键词:
- 地震动模拟 /
- 高频衰减系数κ0 /
- 平均剪切波速vS30 /
- 最小二乘法
Abstract:When using the stochastic finite fault method for ground motion simulation, how to select reasonable parameters to describe the near-surface high-frequency attenuation characteristics of a specific local site has important practical significance for evaluating the correctness of ground motion simulation results. In the prediction of ground motion parameters of engineering sites, how to quickly determine the value of parameters is an urgent problem to be solved in practical applications. Firstly, we analyzed the correlation between the high-frequency attenuation coefficient κ0 of the site and the average shear wave velocity vS30. Then, based on the 546 κ0 coefficients calculated by domestic and foreign scholars, the root mean square value of κ0 in a certain time window was used to discuss its variation trend with the increase of the average shear wave velocity vS30.The results showed that although κ0 had obvious regional differences, its root mean square value showed a decreasing trend with the increase of vS30. In order to obtain a reasonable κ0 estimation model, the linear function, polynomial function, logarithmic linear function and log-log linear function were used to preliminarily fit the relationship between the root mean square value of κ0 and vS30. The results show that the logarithmic linear function can better describe the relationship between κ0 and vS30. Finally, based on the 477 data obtained from the screening, the model parameters were fitted by the least square method, and a practical model of κ0-vS30 suitable for engineering applications was obtained. The analysis of the applicability of the model shows that the κ0 estimation model constructed in this study can reasonably estimate the high-frequency attenuation of ground motion when predicting engineering site ground motion parameters.
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图 1 本文研究采用的κ0值随平均剪切波速 vS30的分布
Figure 1. The distribution of κ0 value used in this study with mean shear wave velocity vS30
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图 5 对数线性函数拟合以及与其它模型对比
Figure 5. Log-linear function fitting and comparison with other models
表 1 本文研究采用的κ0数目、来源及相应的vS分布范围
Table 1 The number and source of κ0 used in this study and the corresponding distribution range of vS
序号 数据个数 vS30/（m·s−1） 地区 数据来源 1 60 106.8—904.2 日本 Cabas等（2017） 2 16 213.2—744.1 日本 Cabas等（2017） 3 50 507.7—1 433.4 日本 van Houtte等（2011） 4 27 1 106.8— 2 394.0 日本 van Houtte等（2011） 5 4 515.7—1 301.3 日本 Laurendeau等（2013） 6 14 170.6—1 428.1 法国 Drouet等（2010） 7 24 192.1—747.1 瑞士 Edwards等（2015） 8 8 1 174.0—1 810.5 瑞士 Edwards等（2011） 9 16 380.1—1 811.5 瑞士 Edwards等（2011） 10 54 160.1—942.8 中国台湾 Huang等（2017） 11 4 233.1—684.8 中国台湾 Lai等（2016） 12 10 167.5—496.4 中国台湾 Lai等（2016） 13 29 191.8—746.9 土耳其 Bora等（2017） 14 16 142.6—1 029.6 意大利 Bora等（2017） 15 5 1 054.7—1 392.5 克罗地亚 Stanko等（2017） 16 4 854.1—953.3 克罗地亚 Stanko等（2017） 17 11 516.6—715.5 中国台湾 van Houtte等（2011） 18 38 299.6—652.9 中国 傅磊和李小军（2017） 19 10 435.7—1 518.3 新西兰 van Houtte等（2018） 20 9 401.0—661.8 亚利桑那 Kishida等（2014） 21 6 550.9—1 000.3 加利福尼亚 van Houtte等（2011） 22 117 170.9—1 531.2 中国台湾 Chang等（2019） 23 7 263.3—660.3 中国 郑旭等（2019） 24 7 531.2—912.1 日本 朱百慧（2016） 
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表 2 κ0值在不同 vS30范围的分组统计
Table 2 Group statistics of κ0 values in different vS30 ranges
vS30/（m·s−1） κ0值 数量 最小值 最大值 标准差 均值 100—200 37 0.019 6 0.076 7 0.014 85 0.054 48 200—300 65 0.022 2 0.072 6 0.014 58 0.051 33 300—400 95 0.009 2 0.077 2 0.015 38 0.043 41 400—500 95 0.008 8 0.087 5 0.016 06 0.040 43 500—600 73 0.003 8 0.067 4 0.015 16 0.035 60 600—700 46 0.003 8 0.080 9 0.015 17 0.029 28 700—800 24 0.013 0 0.071 1 0.014 11 0.033 48 800—900 19 0.004 9 0.073 9 0.017 84 0.034 12 900—1000 16 0.014 3 0.052 8 0.010 99 0.027 61 1 000—1 100 7 0.015 3 0.027 0 0.003 93 0.022 73 1 100—1 200 7 0.006 0 0.025 8 0.007 52 0.015 47 1 200—1 300 10 0.013 6 0.026 0 0.004 61 0.019 67 1 300—1 400 6 0.010 1 0.031 5 0.009 06 0.020 13 1 400—1 500 9 0.009 6 0.026 3 0.006 15 0.015 72 1 500—1 800 16 0.006 9 0.027 1 0.006 75 0.016 06 1 800—2 100 11 0.002 9 0.029 3 0.009 36 0.013 71 2 100—2 400 10 0.002 9 0.025 0 0.009 30 0.011 93
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表 3 κrms与 vS30的经验关系
Table 3 The empirical relationship between кrms and vS30
拟合函数 模型参数 a b SSE R2 c 线性函数：κrms＝avS30＋b −1.557×10−5 4.478×10−2 3.61×10−3 7.734×10−1 多项式函数：κrms＝${av^2_{{\rm{S}}30}} $＋bvS30＋c 1.284×10−8 −4.741×10−5 6.559×10−4 9.587×10−1 5.886×10−5 对数线性函数：κrms ＝algvS30＋b −3.439×10−2 1.286×10−1 1.466×10−3 9.07 8×10−1 双对数线性函数：lgκrms＝algvS30＋b −4.488×10−1 −2.72×10−1 2.245×10−3 8.587×10−1 注：表中a，b和c为模型拟合参数，SSE 表示和方差，R2为拟合优度。
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