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浅壳与上地幔地震的水平加速度谱阻尼修正系数模型

苏开潍, 杨青松, 梁基冠

苏开潍, 杨青松, 梁基冠. 2019: 浅壳与上地幔地震的水平加速度谱阻尼修正系数模型. 地震学报, 41(6): 778-794. DOI: 10.11939/jass.20190052
引用本文: 苏开潍, 杨青松, 梁基冠. 2019: 浅壳与上地幔地震的水平加速度谱阻尼修正系数模型. 地震学报, 41(6): 778-794. DOI: 10.11939/jass.20190052
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Su Kaiwei, Yang Qingsong, Liang Jiguan. 2019: Damping correction factor for horizontal acceleration response spectrum of shallow crustal and upper-mantle earthquakes. Acta Seismologica Sinica, 41(6): 778-794. DOI: 10.11939/jass.20190052
Citation: Su Kaiwei, Yang Qingsong, Liang Jiguan. 2019: Damping correction factor for horizontal acceleration response spectrum of shallow crustal and upper-mantle earthquakes. Acta Seismologica Sinica, 41(6): 778-794. DOI: 10.11939/jass.20190052
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浅壳与上地幔地震的水平加速度谱阻尼修正系数模型

  • 中国成都 610000 西南交通大学土木工程学院

基金项目: 国家自然科学基金（51578470）资助
详细信息
    通讯作者:

    苏开潍: e-mail：sukaiweiim@gmail.com

  • 中图分类号: P315.9

Damping correction factor for horizontal acceleration response spectrum of shallow crustal and upper-mantle earthquakes

  • School of Civil Engineering，Southwest Jiaotong University，Chengdu 610000，China

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    摘要
  • 摘要: 对日本K-net和KiK-net台网中6 466条浅壳与上地幔地震动记录进行了统计分析，考虑四种场地类别分别建立了浅壳与上地幔地震的加速度谱阻尼修正系数模型，并利用随机效应模型将模型总残差分离为事件间残差、事件内残差（分为场地间残差和场地内残差），计算其相应的标准差，探究地震震源、路径、场地等因素对模型误差的影响。研究结果显示：所提出的模型能较好地拟合实际计算值，其随机误差整体随谱周期和阻尼比的增大而增大；震源效应导致的随机误差在谱周期小于2.0 s时小于其它效应；在大部分谱周期上，场地效应导致的随机误差小于路径效应及其它效应；事件间残差与震源和震源深度显著相关，场地内残差与震源距显著相关。
    Abstract: In this paper, 6 466 strong-motion records from 76 shallow crustal and 47 upper-mantle earthquakes in Japan were compiled to develop a damping correction factor （DCF） model. This study is aimed to provide a DCF that can be used to scale a design spectrum without known source and path parameters, therefore the models presented in this study did not include any terms for earthquake magnitude or source distance. Site effect on DCF was found to be significant, and a separate DCF model was constructed for the records from each of the four site classes. The total residuals were approximately separated into within- and between-event residuals, and the within-event residuals were further separated into within- and between-site components using a random effect model. Then the corresponding standard deviations were calculated to illustrate the variabilities associated with the source, path and site effects for the DCF model presented in this study. The results showed that the random errors tend to increase with spectral periods and damping ratios increasing, and the random errors associated with source effect are smaller than those associated with path and site effect at spectral periods less than 2.0 s. At most spectral periods, the random errors associated with site effect were smaller than those associated with path and other effects not explicitly modelled in this study. The between-event residuals are significantly correlated with magnitude and focal depth, while the within-site residuals were significantly correlated with source distance. Therefore, source and path parameters should be included for a model that can be used to scale a design spectrum from an earthquake with a known magnitude and source distance.
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  • 图  1   震级随震源距（a）和震源深度（b）的分布

    Figure  1.   The distribution of MW with respect to source distance （a） and focal depth （b）

    下载: 全尺寸图片 幻灯片

    图  2   阻尼比为1%和30%时场地类别间的显著性检验统计值| Z |与谱周期的关系

    （a） Ⅰ类与Ⅱ类；（b） Ⅰ类与Ⅲ类；（c） Ⅰ类与Ⅳ类；（d） Ⅱ类与Ⅲ类；（e） Ⅱ类与Ⅳ类；（f） Ⅲ类与Ⅳ类

    Figure  2.   Variation of | Z | values with spectral periods for each pair of site classes with damping ratios 1% and 30%

    （a） Site classes Ⅰ and Ⅱ；（b） Site classes Ⅰ and Ⅲ；（c） Site classes Ⅰ and Ⅳ；（d） Site classes Ⅱ and Ⅲ；（e） Site classes Ⅱ and Ⅳ；（f） Site classes Ⅲ and Ⅳ

    下载: 全尺寸图片 幻灯片

    图  3   不同阻尼比ζ时阻尼修正系数对数lnBa的几何均值与谱周期的关系曲线

    Figure  3.   Mean value of lnBa with spectral periods with different damping ratio ζ

    （a） ζ＝3%；（b） ζ＝8%；（c） ζ＝15%；（d） ζ＝30%

    下载: 全尺寸图片 幻灯片

    图  4   阻尼修正系数DCF模型的水平分量几何均值及拟合曲线

    （a） Ⅰ类场地；（b） Ⅱ类场地；（c） Ⅲ类场地；（d） Ⅳ类场地

    Figure  4.   Fitting curves of DCF model to the geometric mean of the two horizontal components

    （a） Site class Ⅰ；（b） Site class Ⅱ；（c） Site class Ⅲ；（d） Site class Ⅳ

    下载: 全尺寸图片 幻灯片

    图  5   Ⅱ类场地下不同阻尼比ξ时DCF模型与规范模型的数值对比

    Figure  5.   Comparison of the predicted DCF from this study with designed specification for different damping ratios ξ for the class Ⅱ sites

    （a） ξ＝3%；（b） ξ＝10%；（c） ξ＝20%；（d） ξ＝30%

    下载: 全尺寸图片 幻灯片

    图  6   不同阻尼比ξ下标准差随谱周期的分布图

    Figure  6.   Distribution of standard deviations with spectral period

    （a） ξ＝3%；（b） ξ＝10%；（c） ξ＝20%；（d） ξ＝30%

    下载: 全尺寸图片 幻灯片

    图  7   Ⅱ 类场地下不同阻尼比ξ时标准差随谱周期的分布图

    Figure  7.   Distribution of standard deviations with different damping ratio ξ for the class Ⅱ site

    （a） ξ＝3%；（b） ξ＝10%；（c） ξ＝20%；（d） ξ＝30%

    下载: 全尺寸图片 幻灯片

    图  8   阻尼比为30%时四种场地类别的场地内标准差（a）和场地间标准差（b）的对比图

    Figure  8.   Comparison of standard deviations of between-site （a） and within-site （b） with damping ratio 30% for four-class sites

    下载: 全尺寸图片 幻灯片

    图  9   阻尼修正系数模型事件间及场地内残差分布图

    （a） 事件间残差与震级关系分布图（谱周期T＝0.08 s，阻尼比ξ＝7%）；（b） 事件间残差与震源深度关系的分布图（谱周期T＝0.08 s，ξ＝7%），（c） 场地内残差与震源距关系分布图（Ⅱ类场地，谱周期T＝0.08 s，ξ＝3%）；（d） 场地内残差与震源距关系分布图（Ⅱ类场地，谱周期T＝0.08 s，ξ＝20%）

    Figure  9.   The variation of between-event and within-site residuals of DCF model

    （a） Between-event residuals with moment magnitude （T＝0.08 s，ξ＝7%）； （b） Between-event residuals with focal depth （T＝0.08 s，ξ＝7%）； （c） Within-site residuals with source distance （site class Ⅱ ，T＝0.08 s，ξ＝3%）； （d） Within-site residuals with source distance （site class Ⅱ ，T＝0.08 s，ξ＝20%）

    下载: 全尺寸图片 幻灯片

    表  1   谱周期点数量

    Table  1   Number of spectral periods

    序号 周期/s 序号 周期/s 序号 周期/s 序号 周期/s 序号 周期/s
    2 0.01 10 0.09 18 0.25 26 0.80 34 3.50
    3 0.02 11 0.10 19 0.30 27 0.90 35 4.00
    4 0.03 12 0.12 20 0.35 28 1.00 36 4.50
    5 0.04 13 0.14 21 0.40 29 1.25 37 5.00
    6 0.05 14 0.15 22 0.45 30 1.50
    7 0.06 15 0.16 23 0.50 31 2.00
    8 0.07 16 0.18 24 0.60 32 2.50
    9 0.08 17 0.20 25 0.70 33 3.00
    下载: 导出CSV

    表  2   阻尼比数量

    Table  2   Number of damping ratios

    序号阻尼比序号阻尼比序号阻尼比
    11% 6 6%1115%
    22% 7 7%1220%
    33% 8 8%1325%
    44% 9 9%1430%
    55%1010%
    下载: 导出CSV

    表  3   场地类别分类标准

    Table  3   Site class definitions used in this study

    场地类别土质类别场地特征周期Tg/s平均剪切波速v30/（km·s−1）记录条数
    Ⅰ岩土Tg＜0.2v30＞6003 007
    Ⅱ硬土0.2≤Tg＜0.4300＜v30≤6001 828
    Ⅲ中硬土0.4≤Tg＜0.6200＜v30≤300 578
    Ⅳ软土Tg＞0.6v30＜2001 053
    下载: 导出CSV

    表  4   四类场地类别下阻尼修正系数模型的回归系数

    Table  4   Regressive parameters for damping correction factor model for site classes Ⅰ to Ⅳ

    谱周期/s　　　Ⅰ类场地　　　Ⅱ类场地　　　
    a　　　b　　　c　　　a　　　b　　　c　　　
    　0.03−0.507 8%　　　0.080 0%　　　−0.189 8%　　　−0.550 0%　　　0.100 0%　　　−0.049 9%　　　
    　0.04−7.950 5%　　　1.218 2%　　　−0.170 9%　　　−4.200 9%　　　0.911 5%　　　−0.059 7%　　　
    　0.05−15.022 4%　　　1.272 6%　　　−0.088 0%　　　−8.216 0%　　　1.228 8%　　　−0.039 6%　　　
    　0.06−21.022 3%　　　0.843 4%　　　0.012 5%　　　−12.559 9%　　　1.209 6%　　　−0.000 2%　　　
    　0.07−25.837 4%　　　0.285 8%　　　0.119 0%　　　−16.909 3%　　　1.025 3%　　　0.051 3%　　　
    　0.08−29.366 4%　　　−0.255 8%　　　0.226 0%　　　−21.501 6%　　　0.758 2%　　　0.110 5%　　　
    　0.09−31.472 6%　　　−0.700 0%　　　0.331 0%　　　−24.952 4%　　　0.451 1%　　　0.174 5%　　　
    　0.10−32.970 3%　　　−0.992 1%　　　0.432 8%　　　−27.541 0%　　　0.127 5%　　　0.241 2%　　　
    　0.12−34.812 4%　　　−1.326 8%　　　0.625 1%　　　−31.029 6%　　　−0.521 6%　　　0.378 0%　　　
    　0.14−35.739 9%　　　−1.505 6%　　　0.801 9%　　　−33.120 8%　　　−1.137 0%　　　0.514 8%　　　
    　0.15−35.996 1%　　　−1.556 0%　　　0.884 9%　　　−33.832 9%　　　−1.426 2%　　　0.582 1%　　　
    　0.16−36.157 1%　　　−1.587 1%　　　0.964 3%　　　−34.385 3%　　　−1.674 3%　　　0.648 5%　　　
    　0.18−36.275 6%　　　−1.605 1%　　　1.113 7%　　　−35.133 3%　　　−1.835 7%　　　0.777 7%　　　
    　0.20−36.214 3%　　　−1.580 3%　　　1.251 4%　　　−35.545 6%　　　−1.910 6%　　　0.901 8%　　　
    　0.25−35.668 4%　　　−1.406 8%　　　1.553 4%　　　−35.741 6%　　　−1.867 6%　　　1.189 2%　　　
    　0.30−34.908 3%　　　−1.151 5%　　　1.807 0%　　　−35.345 2%　　　−1.646 4%　　　1.445 5%　　　
    　0.35−34.112 2%　　　−0.862 3%　　　2.023 6%　　　−34.703 7%　　　−1.342 0%　　　1.674 2%　　　
    　0.40−33.341 7%　　　−0.561 2%　　　2.211 1%　　　−33.964 9%　　　−0.999 6%　　　1.879 1%　　　
    　0.45−32.616 5%　　　−0.259 4%　　　2.375 1%　　　−33.196 7%　　　−0.642 4%　　　2.063 3%　　　
    　0.50−31.940 0%　　　0.037 6%　　　2.519 9%　　　−32.430 9%　　　−0.282 9%　　　2.229 6%　　　
    　0.60−30.721 0%　　　0.607 2%　　　2.763 9%　　　−30.958 6%　　　0.418 8%　　　2.517 3%　　　
    　0.70−29.647 9%　　　1.138 9%　　　2.961 2%　　　−29.589 9%　　　1.080 3%　　　2.756 2%　　　
    　0.80−28.683 6%　　　1.632 6%　　　3.123 4%　　　−28.322 5%　　　1.695 7%　　　2.956 2%　　　
    　0.90−27.799 0%　　　2.091 1%　　　3.258 3%　　　−27.143 3%　　　2.265 6%　　　3.124 9%　　　
    　1.00−26.972 5%　　　2.517 6%　　　3.371 6%　　　−26.038 2%　　　2.793 1%　　　3.267 6%　　　
    　1.25−25.066 9%　　　3.465 2%　　　3.584 4%　　　−23.522 0%　　　3.950 7%　　　3.536 5%　　　
    　1.50−23.283 9%　　　4.275 7%　　　3.726 0%　　　−21.250 5%　　　4.920 1%　　　3.712 5%　　　
    　2.00−19.830 8%　　　5.600 9%　　　3.878 3%　　　−17.126 9%　　　6.450 0%　　　3.883 8%　　　
    　2.50−16.370 2%　　　6.650 6%　　　3.925 7%　　　−13.301 8%　　　7.601 0%　　　3.902 4%　　　
    　3.00−12.845 6%　　　7.511 4%　　　3.911 4%　　　−9.628 3%　　　8.494 9%　　　3.826 4%　　　
    　3.50−9.251 3%　　　8.235 0%　　　3.857 8%　　　−6.041 0%　　　9.204 9%　　　3.687 7%　　　
    　4.00−5.596 0%　　　8.854 9%　　　3.778 0%　　　−2.508 1%　　　9.777 7%　　　3.505 7%　　　
    　4.50−1.891 5%　　　9.393 8%　　　3.679 9%　　　0.986 4%　　　10.245 0%　　　3.292 7%　　　
    　5.001.850 8%　　　9.867 6%　　　3.569 0%　　　4.450 9%　　　10.629 1%　　　3.057 1%　　　
    谱周期/s　　　Ⅲ类场地　　　Ⅳ类场地　　　
    a　　　b　　　c　　　a　　　b　　　c　　　
    　0.03−0.267 5%　　　0.080 0%　　　−0.004 7%　　　−0.054 3%　　　0.100 0%　　　−0.059 8%　　　
    　0.04−2.468 6%　　　0.935 0%　　　−0.004 5%　　　−1.320 6%　　　0.678 3%　　　−0.105 8%　　　
    　0.05−6.151 3%　　　1.248 6%　　　0.010 4%　　　−3.806 6%　　　0.939 3%　　　−0.058 7%　　　
    　0.06−10.524 5%　　　1.229 7%　　　0.037 4%　　　−7.517 3%　　　0.957 4%　　　−0.007 1%　　　
    　0.07−14.976 8%　　　1.068 1%　　　0.072 7%　　　−11.806 0%　　　0.864 5%　　　0.046 1%　　　
    　0.08−19.139 5%　　　0.847 7%　　　0.113 6%　　　−16.158 0%　　　0.720 7%　　　0.099 3%　　　
    　0.09−22.600 0%　　　0.608 0%　　　0.158 2%　　　−20.231 6%　　　0.555 6%　　　0.151 8%　　　
    　0.10−25.140 8%　　　0.368 6%　　　0.205 3%　　　−23.500 0%　　　0.384 4%　　　0.203 1%　　　
    　0.12−28.559 5%　　　−0.075 5%　　　0.303 1%　　　−27.563 9%　　　0.052 6%　　　0.301 8%　　　
    　0.14−30.831 7%　　　−0.455 2%　　　0.402 5%　　　−30.112 2%　　　−0.246 4%　　　0.395 1%　　　
    　0.15−31.683 1%　　　−0.620 1%　　　0.451 9%　　　−31.053 7%　　　−0.381 4%　　　0.439 7%　　　
    　0.16−32.393 3%　　　−0.769 2%　　　0.500 9%　　　−31.834 3%　　　−0.506 7%　　　0.483 0%　　　
    　0.18−33.488 5%　　　−1.023 8%　　　0.597 2%　　　−33.032 2%　　　−0.729 7%　　　0.566 1%　　　
    　0.20−34.264 2%　　　−1.227 1%　　　0.690 8%　　　−33.882 4%　　　−0.919 0%　　　0.644 7%　　　
    　0.25−35.342 3%　　　−1.558 9%　　　0.911 0%　　　−35.110 2%　　　−1.271 0%　　　0.824 5%　　　
    下载: 导出CSV
    续表 4　
    谱周期/s　　　Ⅲ类场地　　　Ⅳ类场地　　　
    a　　　b　　　c　　　a　　　b　　　c　　　
    　0.30−35.726 5%　　　−1.708 4%　　　1.111 7%　　　−35.653 5%　　　−1.490 8%　　　0.984 5%　　　
    　0.35−35.751 4%　　　−1.736 2%　　　1.294 4%　　　−35.866 3%　　　−1.617 1%　　　1.128 7%　　　
    　0.40−35.576 2%　　　−1.681 3%　　　1.461 1%　　　−35.906 1%　　　−1.675 7%　　　1.260 0%　　　
    　0.45−35.284 2%　　　−1.569 3%　　　1.613 7%　　　−35.849 7%　　　−1.684 7%　　　1.380 5%　　　
    　0.50−34.921 9%　　　−1.417 5%　　　1.753 9%　　　−35.737 5%　　　−1.656 5%　　　1.492 0%　　　
    　0.60−34.086 0%　　　−1.039 1%　　　2.002 5%　　　−35.424 0%　　　−1.522 6%　　　1.692 8%　　　
    　0.70−33.185 1%　　　−0.606 3%　　　2.216 3%　　　−35.051 8%　　　−1.321 2%　　　1.870 0%　　　
    　0.80−32.266 7%　　　−0.151 1%　　　2.401 8%　　　−34.650 6%　　　−1.079 5%　　　2.028 5%　　　
    　0.90−31.351 5%　　　0.308 9%　　　2.564 2%　　　−34.231 2%　　　−0.813 7%　　　2.172 0%　　　
    　1.00−30.448 5%　　　0.763 8%　　　2.707 2%　　　−33.797 4%　　　−0.533 9%　　　2.303 2%　　　
    　1.25−28.262 2%　　　1.846 2%　　　2.998 0%　　　−32.656 1%　　　0.188 2%　　　2.588 8%　　　
    　1.50−26.178 2%　　　2.828 2%　　　3.217 3%　　　−31.435 4%　　　0.905 7%　　　2.829 1%　　　
    　2.00−22.262 8%　　　4.486 3%　　　3.512 5%　　　−28.768 5%　　　2.255 8%　　　3.218 4%　　　
    　2.50−18.599 1%　　　5.791 8%　　　3.682 8%　　　−25.840 9%　　　3.467 9%　　　3.526 7%　　　
    　3.00−15.118 3%　　　6.816 0%　　　3.772 8%　　　−22.706 4%　　　4.548 9%　　　3.781 1%　　　
    　3.50−11.777 9%　　　7.616 6%　　　3.807 6%　　　−19.411 9%　　　5.515 0%　　　3.996 9%　　　
    　4.00−8.550 7%　　　8.237 1%　　　3.802 6%　　　−15.994 6%　　　6.382 3%　　　4.183 7%　　　
    　4.50−5.418 1%　　　8.710 7%　　　3.768 1%　　　−12.483 9%　　　7.164 7%　　　4.348 0%　　　
    　5.00−2.366 9%　　　9.062 7%　　　3.711 1%　　　−8.902 1%　　　7.873 7%　　　4.494 2%　　　
    下载: 导出CSV

    表  5   阻尼修正系数模型的总标准差

    Table  5   Total standard deviations of DCF model

    谱周期
    /s    		总标准差
    ξ＝1%ξ＝2%ξ＝3%ξ＝4%ξ＝6%ξ＝7%ξ＝8%ξ＝9%ξ＝10%ξ＝15%ξ＝20%ξ＝25%ξ＝30%
    0.030.014 50.006 90.004 10.002 00.001 90.003 70.005 50.007 20.008 90.015 90.021 60.026 40.030 5
    0.040.153 70.086 60.047 60.020 50.015 90.028 80.039 50.048 70.056 70.085 10.103 30.116 50.126 5
    0.050.177 50.103 10.058 10.025 60.020 70.037 70.052 00.064 40.075 20.114 30.139 70.158 20.172 3
    0.060.193 40.116 90.067 10.029 80.024 90.044 70.061 90.077 00.090 30.139 80.172 40.196 30.214 6
    0.070.199 30.123 30.073 90.032 50.026 70.050 10.071 80.087 20.102 70.160 30.198 80.226 60.247 8
    0.080.197 40.123 60.072 70.032 90.028 60.051 00.073 40.089 10.105 10.165 80.206 90.237 00.259 6
    0.090.187 50.119 20.071 00.032 40.028 10.050 50.070 60.088 50.104 60.165 80.207 80.238 50.261 5
    0.100.184 60.117 60.070 10.033 20.028 10.050 20.070 20.088 00.103 90.165 20.207 30.238 00.261 2
    0.120.174 90.112 10.067 00.030 80.026 10.049 60.067 80.087 00.100 40.159 20.199 00.227 80.249 5
    0.140.169 00.107 60.064 10.029 40.024 90.047 00.064 10.080 10.096 60.148 40.185 30.212 40.232 9
    0.150.164 80.105 90.062 00.029 10.024 90.044 60.062 10.079 70.093 90.143 30.179 50.206 00.226 5
    0.160.166 80.105 40.062 70.030 00.024 20.044 50.061 90.081 40.095 90.142 00.177 50.204 00.224 6
    0.180.160 50.102 00.060 40.028 10.023 20.042 40.059 00.074 70.086 50.136 40.171 10.197 50.218 3
    0.200.159 40.103 10.060 60.028 00.023 60.043 20.060 20.074 20.088 20.137 00.171 80.198 80.220 6
    0.250.161 40.102 90.060 90.028 10.023 50.043 00.059 70.073 40.087 40.136 00.172 50.202 10.227 3
    0.300.158 80.102 20.060 70.027 70.023 20.042 60.059 50.073 70.086 50.137 60.176 50.209 10.237 8
    0.350.158 00.102 60.061 60.028 20.023 40.043 40.059 70.074 60.089 50.141 50.182 80.218 20.250 4
    0.400.161 50.104 10.062 10.028 30.024 10.044 20.061 60.076 90.090 70.146 40.191 10.230 30.266 1
    0.450.160 90.104 40.062 50.028 60.024 10.044 30.061 80.077 20.091 60.149 30.196 80.238 90.278 0
    0.500.160 10.104 90.062 90.028 70.024 20.044 70.062 50.078 30.092 70.152 60.203 30.248 70.290 2
    0.600.165 70.107 50.064 50.029 60.025 10.046 40.065 10.082 00.097 50.164 10.219 70.269 30.314 4
    0.700.167 30.108 00.064 50.029 60.025 30.047 00.066 50.084 20.100 70.171 50.232 10.285 90.334 4
    0.800.170 70.111 00.066 90.030 80.026 40.049 30.069 80.088 80.106 50.183 30.248 60.305 90.356 7
    0.900.169 50.110 30.066 30.030 60.026 90.050 50.072 00.092 00.111 00.193 90.265 40.326 80.380 5
    1.000.171 20.112 80.068 70.032 10.028 20.053 30.076 10.097 30.117 20.205 30.280 00.344 00.399 2
    1.250.176 50.118 50.072 50.034 00.030 80.057 90.083 20.106 90.129 30.229 90.313 20.383 30.442 8
    1.500.189 80.128 50.079 20.037 20.033 60.064 20.092 80.119 80.145 50.257 90.350 00.424 80.487 0
    2.000.202 50.140 90.088 30.042 10.038 70.074 60.108 10.139 60.169 20.299 20.398 80.479 10.542 6
    2.500.218 10.154 50.097 60.047 10.043 80.084 20.122 30.158 10.191 20.331 60.438 50.521 10.584 2
    3.000.232 30.166 00.105 90.051 00.047 50.091 50.132 30.170 40.206 30.354 10.465 80.549 30.610 4
    3.500.240 90.175 10.112 90.054 60.051 20.098 80.143 00.184 50.222 60.379 70.492 70.574 60.636 0
    4.000.253 40.185 20.119 90.058 20.054 80.105 20.152 30.195 80.235 80.398 80.510 60.593 00.651 8
    4.500.266 10.195 90.127 10.061 90.057 70.110 70.159 40.204 40.246 10.411 30.525 20.606 30.663 9
    5.000.277 20.205 80.133 70.064 90.060 00.114 50.164 40.210 30.252 40.418 90.531 00.609 50.665 2
    下载: 导出CSV

    表  7   阻尼修正系数模型事件内标准差

    Table  7   Within-event standard deviations of DCF model

    谱周期
    /s    		事件内标准差
    ξ＝1%ξ＝2%ξ＝3%ξ＝4%ξ＝6%ξ＝7%ξ＝8%ξ＝9%ξ＝10%ξ＝15%ξ＝20%ξ＝25%ξ＝30%
    0.030.0080.0060.0040.0020.0020.0040.0050.0070.0080.0150.0200.0250.028
    0.040.1370.0780.0430.0190.0150.0260.0360.0440.0520.0770.0930.1050.114
    0.050.1600.0930.0530.0230.0190.0340.0470.0580.0680.1030.1250.1410.154
    0.060.1780.1070.0610.0270.0220.0410.0560.0700.0820.1260.1550.1760.192
    0.070.1860.1150.0660.0300.0250.0460.0640.0800.0940.1460.1800.2050.223
    0.080.1860.1160.0680.0310.0260.0480.0660.0830.0970.1520.1890.2160.236
    0.090.1780.1130.0670.0310.0260.0470.0660.0820.0970.1530.1900.2180.239
    0.100.1770.1120.0670.0300.0250.0470.0660.0820.0970.1530.1920.2200.241
    0.120.1680.1080.0650.0300.0250.0460.0650.0800.0950.1500.1870.2130.233
    0.140.1610.1030.0620.0280.0240.0440.0620.0770.0900.1420.1760.2020.221
    0.150.1590.1000.0600.0280.0240.0440.0600.0740.0870.1380.1720.1970.217
    0.160.1590.1010.0610.0280.0240.0430.0600.0740.0870.1360.1700.1950.215
    0.180.1530.0980.0580.0260.0220.0410.0570.0700.0830.1310.1650.1900.210
    0.200.1510.0970.0580.0270.0230.0410.0570.0720.0840.1330.1670.1930.214
    0.250.1540.0980.0590.0270.0220.0410.0570.0720.0830.1320.1670.1960.220
    0.300.1510.0970.0580.0270.0220.0410.0570.0710.0840.1330.1700.2010.227
    0.350.1480.0960.0580.0270.0220.0400.0570.0710.0830.1340.1710.2030.231
    0.400.1530.0970.0570.0260.0230.0410.0580.0720.0850.1360.1750.2080.237
    0.450.1510.0960.0570.0260.0220.0410.0570.0710.0850.1360.1770.2120.243
    0.500.1500.0960.0580.0270.0220.0410.0570.0720.0840.1370.1800.2170.250
    0.600.1550.0990.0590.0270.0230.0430.0600.0750.0890.1470.1930.2330.268
    0.700.1570.1010.0600.0280.0240.0440.0610.0770.0920.1530.2030.2470.285
    0.800.1590.1030.0620.0290.0240.0450.0640.0810.0960.1610.2150.2600.300
    0.900.1550.1000.0600.0280.0240.0450.0640.0820.0980.1670.2250.2730.315
    1.000.1570.1020.0620.0290.0250.0480.0680.0860.1030.1750.2340.2840.326
    1.250.1580.1040.0630.0300.0260.0500.0710.0900.1080.1870.2500.3020.345
    1.500.1660.1090.0670.0310.0280.0530.0760.0970.1170.2000.2670.3210.364
    2.000.1670.1120.0700.0330.0300.0570.0820.1040.1260.2140.2820.3350.377
    2.500.1650.1120.0710.0340.0310.0590.0850.1090.1310.2200.2870.3380.378
    3.000.1680.1180.0750.0360.0330.0630.0900.1150.1370.2300.2960.3460.384
    3.500.1660.1190.0770.0370.0350.0660.0940.1200.1440.2380.3040.3520.389
    4.000.1700.1230.0800.0390.0350.0670.0960.1230.1460.2400.3050.3520.388
    4.500.1710.1250.0810.0390.0360.0680.0980.1240.1480.2420.3060.3530.387
    5.000.1750.1290.0840.0410.0370.0690.0980.1250.1490.2420.3050.3500.383
    下载: 导出CSV

    表  6   阻尼修正系数模型的事件间标准差

    Table  6   Between-event standard deviations of DCF model

    谱周期
    /s    		事件间标准差
    ξ＝1%ξ＝2%ξ＝3%ξ＝4%ξ＝6%ξ＝7%ξ＝8%ξ＝9%ξ＝10%ξ＝15%ξ＝20%ξ＝25%ξ＝30%
    0.030.012 30.004 30.001 70.000 60.000 50.001 00.001 60.002 10.003 10.005 30.007 50.009 40.011 0
    0.040.069 40.037 80.020 10.008 40.006 30.011 60.016 10.019 90.023 30.035 70.044 10.050 60.055 8
    0.050.077 60.044 30.024 90.010 80.008 80.016 10.022 10.027 40.032 20.049 80.062 00.071 10.078 2
    0.060.076 00.046 70.027 10.012 00.011 60.018 50.025 80.032 40.038 60.061 30.076 40.087 90.096 7
    0.070.071 00.045 50.032 60.011 90.009 10.019 10.033 00.034 10.040 60.066 30.084 00.097 50.107 6
    0.080.066 90.042 60.024 80.011 30.012 70.018 70.033 10.033 30.040 10.066 30.084 40.098 30.108 7
    0.090.059 10.038 80.023 40.010 90.011 80.017 80.025 40.032 40.038 90.064 60.083 10.096 60.106 9
    0.100.054 10.034 70.021 20.013 70.012 00.017 20.024 30.031 00.037 20.061 90.079 00.091 90.101 7
    0.120.047 60.028 60.017 10.008 00.007 30.019 10.020 30.034 10.031 80.054 00.069 30.080 40.088 4
    0.140.051 00.030 40.017 40.007 60.006 50.017 00.017 50.022 40.036 20.044 50.057 40.066 60.072 9
    0.150.045 10.034 30.013 90.009 40.008 20.009 80.014 30.028 80.034 60.039 10.051 30.059 30.065 3
    0.160.050 20.028 90.015 90.011 90.005 60.010 60.015 20.034 30.041 10.040 10.051 30.059 30.064 9
    0.180.048 10.029 20.016 50.009 50.005 90.010 80.015 20.025 20.022 90.037 20.047 10.054 20.059 6
    0.200.051 10.035 80.016 20.009 00.007 10.012 90.018 10.017 20.026 50.032 60.041 30.047 10.052 0
    0.250.049 60.029 90.016 40.009 10.007 10.013 00.018 00.016 60.026 60.032 90.042 60.050 20.057 6
    0.300.050 40.033 30.018 40.007 70.006 00.010 70.017 90.018 20.021 20.034 50.046 30.058 40.071 1
    0.350.054 30.037 60.022 10.009 50.007 30.015 70.018 70.023 50.034 40.046 70.063 90.080 30.097 8
    0.400.053 10.038 80.023 70.010 80.008 60.015 80.021 90.027 50.032 40.055 40.077 30.098 80.120 6
    0.450.056 80.041 10.024 90.011 10.008 90.016 30.023 00.030 00.035 00.061 00.085 80.110 30.135 4
    0.500.056 50.042 00.024 90.011 10.009 50.017 80.025 30.032 10.038 50.067 00.094 20.121 30.148 2
    0.600.058 40.040 90.025 10.011 20.009 50.017 70.025 30.032 50.039 50.072 90.104 80.134 70.163 9
    0.700.057 40.039 20.023 50.010 90.009 30.017 60.025 60.033 40.041 00.077 50.112 10.144 40.175 7
    0.800.063 20.042 20.025 50.011 80.010 20.019 40.028 50.037 30.046 20.087 30.125 70.160 50.193 3
    0.900.068 00.046 90.028 60.013 10.011 50.022 00.032 30.042 20.052 10.098 20.141 40.179 00.214 0
    1.000.068 10.047 90.029 00.013 60.012 30.023 70.034 80.045 70.056 60.107 90.153 50.194 10.230 4
    1.250.077 80.057 00.035 50.016 70.016 40.029 70.043 70.057 30.070 50.134 00.189 00.236 50.277 6
    1.500.092 40.068 00.043 00.020 10.018 60.036 30.053 60.070 30.086 90.162 40.226 20.278 80.323 8
    2.000.114 80.085 10.054 00.025 90.024 40.048 10.070 90.092 70.113 60.209 10.282 40.342 90.390 1
    2.500.143 10.106 00.067 20.032 60.030 80.059 80.087 90.114 80.139 60.248 10.332 00.396 80.445 5
    3.000.160 30.117 10.074 80.036 00.034 00.066 50.097 20.126 10.154 10.269 60.359 60.426 70.474 3
    3.500.174 20.128 80.083 10.040 00.037 80.073 80.107 70.140 10.169 90.296 20.388 00.454 10.503 6
    4.000.187 50.138 40.089 70.043 60.041 90.081 00.118 20.152 70.184 90.318 30.409 30.477 10.523 9
    4.500.203 60.150 50.097 70.047 70.045 00.087 00.126 20.162 40.196 40.332 70.426 60.493 10.539 2
    5.000.214 80.160 30.104 00.050 50.047 30.091 10.131 80.169 30.204 00.342 10.435 10.499 30.544 0
    下载: 导出CSV
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  • 收稿日期:  2019-03-14
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  • 发布日期:  2019-10-31

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