The prediction equations for the significant duration of strong motion in Chinese mainland
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摘要: 基于2007—2015年间我国数字强震动观测台网记录到的MW5.0—6.6地震事件中的强震动记录，综合考虑震源、传播路径及场地的影响，采用随机效应回归分析方法建立了适用于中国大陆地区的地震动显著持时预测方程，并与其它地区的预测方程进行了对比分析。结果显示：显著持时随震级和距离的增大而增大，硬土场地的地震动持时整体上略小于软土场地，而且本文给出的地震动显著持时随预测变量的变化趋势与其它研究地区具有一定的相似性。Abstract: The earthquake damages of engineering structures have been affected by the amplitude, frequency and duration of the strong motion records. However, there are relatively few published duration equations available in Chinese mainland. In this paper, we collected the strong motion records with magnitude MW5.0—6.6 during 2007—2015 from Chinese digital strong motion networks. Considering the effects of source, path and site, the random-effected regression technique was adopted to fit a predictive equation in respect to the significant duration. In comparing the predicted durations with other studies, it is shown that this predicted significant duration increases with the increased earthquake magnitude or the increased distance, and decreases with the increased vS30. Furthermore, it has the similar characteristics with other studied regions.
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Keywords:
- strong motion records /
- significant duration /
- prediction equation /
- regression
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图 1 用于预测方程回归分析的数据集中震级MW与断层距Rrup的分布情况（Rrup＜1 km时，图中显示为Rrup＝1 km）
Figure 1. Magnitude MW versus rupture distance Rrup in the selected dataset for the prediction equations （Rrup＜1 km are shown as Rrup＝1 km）
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图 2 数据集（图1）中台站vS30值来自于NGA-West2场地数据库的台站数量柱状分布图
Figure 2. Histogram of the station numbers with vS30 value from the NGA-West2 dataset
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图 3 显著持时5%—75% （D5-75）和5%-95% （D5-95）的示意图（MW6.5九寨沟地震，051JZB台站，震中距约37 km）
Figure 3. Signification duration D5-75 and D5-95 using the Husid plot for acceleration time history （station 051JZB，R＝37 km） from MW6.5 Jiuzhaigou earthquake
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图 4 5%—75%水平向地震动显著持时的事件间残差和事件内残差及均值和标准差随震级MW，断层距Rrup和vS30的变化
Figure 4. The between-events and within-event residuals for D5-75 along with their binned means and ±1 standard deviations showing their trends with magnitude，rupture distance and vS30
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图 5 5%—95%水平向地震动显著持时的事件间残差和事件内残差及均值和标准差随震级MW，断层距Rrup和vS30的变化
Figure 5. The between-events and within-event residuals for D5-95 along with their binned means and ±1 standard deviations showing their trends with magnitude，rupture distance and vS30
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图 6 事件间残差（左）和事件内残差（右）的标准正态分位数-分位数图
（a） 5%—75%地震动显著持时 D5-75；（b） 5%—95%地震动显著持时 D5-95
Figure 6. Normal quantile-quantile plots of standard normal of between-events residuals （left） and within-event residuals （right）
（a） 5%—75% significant duration D5-75；（b） 5%—95% significant duration D5-95
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图 7 不同震级和不同场地条件下的地震动显著持时的预测值均值
（a） 5%—75%地震动显著持时D5-75；（b） 5%—95%地震动显著持时D5-95
Figure 7. The predicted median of the significant duration of the predictive equations derived in this study with the magnitude and vS30
（a） 5%—75% significant duration D5-75；（b） 5%—95% significant duration D5-95
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图 8 不同场地和不同震级条件下本文5%—75%地震动显著持时回归结果与Bommer等（2009）以及Lee和Green （2014）结果的对比
Figure 8. Comparisons of the D5-75 prediction equation in this study with Bommer et al （2009） model and LG2014 models for CENA and WNA from Lee and Green （2014）
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图 9 不同场地和不同震级条件下本文5%—95%地震动显著持时回归结果与其它回归结果的对比
Figure 9. Comparisons of thie D5-95 prediction equation in this study with those from Bommer et al （2009） model and LG2014 models for CENA and WNA from Lee and Green （2014）
表 1 回归系数和相关不确定性
Table 1 Regression coefficients and uncertainty
震级区间 a b 标准差σ 相关系数R2 MW5.5—6.0 −3.613（±0.272） 0.963（±0.002） 5.835 0.994 MW6.0—6.5 −7.240（±0.270） 0.979（±0.002） 5.952 0.990 MW6.5—7.0 −13.596（±0.301） 0.993（±0.002） 7.313 0.993 
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表 2 D5-75和D5-95预测方程的回归系数、事件间残差的标准差τ、事件内残差的标准差σ及总标准差σtotal
Table 2 Regression coefficients and standard deviation for the between-events τ，within-event σ and total σtotal
a1 a2 a3 a4 a5 a6 σ τ σtotal D5-75 −2.991 9 0.603 7 0.869 4 −0.048 0 2.980 4 −0.130 0 0.439 8 0.250 7 0.506 2 D5-95 0.156 1 0.364 7 0.495 8 −0.014 5 2.5* −0.178 4 0.299 3 0.238 6 0.382 8 *a5为置信区间的参数，D5-95中参照Bommer等（2009）将a5值设定为2.5。
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