Study on Nonlinear Statistical Characteristics of Surface/Downhole Response Spectrum Ratio and Influencing Factors
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摘要: 浅地表软弱覆盖层对地震动的影响具有强非线性，但因观测记录样本量过小，难以通过参考谱比法等直接方法予以可靠分析。本文基于日本KiK-net台网136个竖向钻井台阵获取的141881组加速度记录的统计分析，研究了地表/井下反应谱比值随地震动强度变化的非线性变化规律与主要影响因素。利用变窗口尺度的滑动窗口平均法加强数据线性度，并确定了与地震动强度相关的台站最小记录样本量，统计结果表明地表/井下反应谱比值平台值随地震动强度变化的非线性衰减指数为−0.24～−0.08。利用套索（Lasso）算法统计回归发现，本研究12个场地特性表征参数中，30 m平均剪切波速（
$ {V}_{\mathrm{s}30} $ ）、场地卓越频率与地表/井下反应谱比值非线性衰减指数具有较好的正相关性；较弱强度地震动作用下地表/井下傅里叶谱比值峰值、地表/井下反应谱比值峰值与地表/井下反应谱比值非线性衰减指数具有较好的负相关性。Abstract: The influence of shallow soft overburden on ground motion is strongly nonlinear, but it is difficult to make reliable analysis by direct methods such as reference spectral ratio method because of the small sample size of observation records. In this study, based on the statistical analysis of 141881 sets of acceleration records obtained from 136 vertical borehole array in Japan’s KiK-net network, the nonlinear variation of surface/downhole response spectrum ratio and its main influencing factors of field motion intensity were studied. The sliding window average method with variable window scale was used to enhance the linearity of the data, and the minimum sample size related to the ground motion intensity was determined. The statistical results show that the nonlinear attenuation index of ground motion intensity variation is between −0.24 and −0.08 for the platform value of the surface/underground response spectrum ratio. According to Lasso regression statistics, the average shear wave velocity of 30 m ($ {V}_{S30} $ ) and site predominant frequency have a good positive correlation with the nonlinear attenuation index of surface/downhole response spectrum ratio among the 12 site characteristic parameters studied. However, the peak values of the surface/downhole fourier spectrum ratio and the surface/downhole response spectrum ratio are negatively correlated with the nonlinear attenuation index of the surface/downhole response spectrum ratio under the weak ground motion.-
Key words:
- Strong motion /
- Site effect /
- Response spectrum /
- Nonlinear /
- Vertical borehole arrays
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图 1 本研究选取台阵的空间分布与场地类别划分
Figure 1. The spatial distribution and site types of the selected array in this paper
图 2 本研究选取地震记录的震级、震中距和地面加速度峰值分布
Figure 2. The magnitude and epicentre distance along with the peak ground acceleration(PGA) of the selected recordings
图 3 地表/井下反应谱比值曲线与标定结果
Figure 3. The ratio of surface/downhole response spectrum shifted to the long period and the calibration results under different groups of input ground motion intensity
图 4 典型台阵（IBRH13）地表/井下反应谱比值平台值与地震动强度的相关性
Figure 4. The correlation between the surface/downhole response spectrum ratio and ground motion intensity of a typical array(IBRH13)
图 5 分组滑动平均法窗口长度选取方法与分布情况
Figure 5. The window length selection method and distribution of the grouping moving average method
图 6 所选台阵在各分组区间内的地震事件个数与台阵筛选
Figure 6. The number of seismic eventsand array selection of the selected array in each grouping interval
图 7 典型台阵归一化地表/井下反应谱比值平台值一元线性回归结果
Figure 7. Linear regression of the normalized surface/downhole response spectrum ratio platform value of a typical array
图 8 相关性前4的场地条件表征参数与地表/井下反应谱比值平台值非线性衰减指数的关系
Figure 8. Correlation of the first four site parameters and the nonlinear attenuation index of the surface/downhole response spectrum ratio platform value
表 1 不同地震动强度分组下的最小可信样本量
Table 1. Minimum reliable sample size for different ground motion intensity groups
组别 1 2 3 4 5 6 7 8 9 10 11 12 分组标准/cm·s−2 0.178～
0.5620.316～
1.0000.562～
1.7801.000～
3.1601.780～
5.6203.160～
10.0005.620～
17.80010.000～
31.60017.800～
56.20031.600～
100.00056.200～
177.800>100.000 n0平均值/个 30 27 25 21 17 14 10 7 5 3 2 1 
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表 2 场地条件表征参数
Table 2. The site characterization parameters selected in this paper
参数 含义 定义 参考文献 $ {V}_{\rm{se}} $ 我国规范定义的等效剪切波速 ${V}_{\rm{se}}={d}_{0}/{\displaystyle\sum }_{i=1}^{n}\left({d}_{i}/{V}_{\mathrm{s}i}\right)$ 中华人民共和国住房和城乡建设部等，2010 $ {V}_{\mathrm{S}30} $ 美国规范定义的平均剪切波速 ${V}_{\mathrm{S}30}=30/{\displaystyle\sum }_{i=1}^{n}\left({d}_{i}/{V}_{\mathrm{s}i}\right)$ BSSC，2001（美国NEHRP规范） $ {B}_{30} $ 剪切波速剖面梯度 $ {\mathrm{log}}_{10}{V}_{\mathrm{s}}\left(z\right)={B}_{Z\mathrm{m}\mathrm{a}\mathrm{x}}{\mathrm{log}}_{10}\left(z\right)+{A}_{Z\mathrm{m}\mathrm{a}\mathrm{x}}\pm {\sigma }_{Z\mathrm{m}\mathrm{a}\mathrm{x}} $ Régnier等，2013 $ {Z}_{0.5} $ 0.5 km/s覆盖层厚度 剪切波速达0.5 km/s时的土层深度 中华人民共和国住房和城乡建设部等，2010 $ {Z}_{0.8} $ 0.8 km/s覆盖层厚度 剪切波速达0.8 km/s时的土层深度 Zhu等，2020 $ {Z}_{1.0} $ 1.0 km/s覆盖层厚度 剪切波速达1.0 km/s时的土层深度 Zhu等，2020 $ {V}_{\mathrm{s}\mathrm{a}\mathrm{v}} $ 整个土层沉积平均剪切波速 地表到$ {V}_{\mathrm{s}}>800 $ m/s的“地震基岩”
土层厚度内的走时平均剪切波速Pitilakis等，2013 $ {f}_{\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{d}} $ 场地卓越频率 弱震平均傅里叶谱放大系数峰值对应的频率 Régnier等，2013 $ {f}_{\mathrm{s}} $ 场地基本频率 弱震HVSR曲线峰值对应的频率 陈国兴等，2020 $ {T}_{\mathrm{s}} $ 场地基本周期 $ {f}_{\mathrm{s}} $的倒数 陈国兴等，2020 $ {A}_{\mathrm{s}} $ 弱震平均傅里叶谱放大系数峰值 — Régnier等，2013 $ {A}_{\mathrm{s}\mathrm{r}} $ 弱震平均反应谱放大系数峰值 —
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