Research on Shear-wave Velocity Profile VS30 Estimation Model in Xiong'an New District
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摘要: 本文基于雄安新区起步区区域性地震安全性评价工程435个钻孔剖面数据，选取其中300个钻孔剖面进行回归分析，利用剩余的135个钻孔剖面数据进行模型可靠性检验。研究结果表明，当钻孔剖面深度小于15 m时，Boore等模型明显低估了VS30；当深度小于10 m时，本研究中对数线性模型、对数二次模型、对数三次模型存在约3%的低估现象；对数三次模型相对误差、残差标准差均较小，因此，对数三次模型更适用于估算雄安新区缺乏钻孔资料或钻孔剖面深度未达30 m的 VS30。Abstract: In this paper, based on the data of 435 borehole profiles of the regional seismic safety evaluation project in the start-up area of Xiong’an New Area, 300 of the borehole profiles were selected for regression analysis, and the remaining 135 borehole profiles were used for model reliability testing. The results show that the Boore et al. model significantly underestimates VS30 when the borehole profile depth is less than 15 m; When the depth is less than 10 m, the log-linear model, log-quadratic model, and log-three model in this study have about 3% underestimation; the relative errors and standard deviations of residuals of the log-three model are smaller, therefore, the log-three model is more suitable for estimating VS30 in Xiong’an New Area where there is no borehole information or the depth of the borehole profile does not reach 30 m.
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图 4 不同深度下3种模型残差标准差
Figure 4. The standard deviation of residuals of the three modles at different depths
3 不同深度下3种模型与Boore等（2011）模型VSE30和VS30对比
3. Comparison of VSE30 and VS30 between the three models and the Boore model at different depths
图 5 各估算模型相对误差柱状图
Figure 5. Histogram of the relative error of VSE30 estimated by each model
表 1 雄安新区钻孔VS30估算模型拟合系数
Table 1. The fitting coefficients of VS30 estimation models of boreholes in Xiong’an
深度z/m 对数线性模型 对数二次模型 对数三次模型 a b C0 C1 C2 C0 C1 C2 C3 5 2.014 0.176 4.072 −1.678 0.417 2.868 0 −0.361 0.120 6 1.903 0.224 3.772 −1.446 0.373 2.725 0 −0.292 0.102 7 1.799 0.270 2.904 −0.712 0.218 2.4 0 −0.117 0.052 8 1.696 0.314 2.756 −0.623 0.207 2.306 0 −0.080 0.044 9 1.571 0.367 2.507 −0.456 0.181 2.167 0 −0.023 0.030 10 1.446 0.421 2.661 −0.644 0.233 2.233 −0.097 0 0.033 11 1.341 0.465 2.281 −0.355 0.179 1.982 0 0.040 0.018 12 1.232 0.510 2.306 −0.422 0.203 1.938 0 0.044 0.019 13 1.110 0.562 2.749 −0.857 0.307 2.131 −0.102 0 0.041 14 0.993 0.610 3.385 −1.455 0.445 2.504 −0.368 0 0.061 15 0.848 0.671 2.979 −1.163 0.395 2.185 −0.193 0 0.053 16 0.707 0.729 0.707 0.729 0 0.625 0.781 0 −0.003 17 0.573 0.784 0.573 0.784 0 −0.920 1.741 0 −0.058 18 0.434 0.841 0.434 0.841 0 −2.146 2.491 0 −0.100 19 0.316 0.889 0.316 0.889 0 −2.572 2.732 0 −0.111 20 0.213 0.931 0.213 0.931 0 −4.102 3.676 0 −0.165 21 0.145 0.957 0.145 0.957 0 −4.795 4.093 0 −0.187 22 0.118 0.966 0.118 0.966 0 −4.923 4.159 0 −0.190 23 0.074 0.982 0.074 0.982 0 −4.518 3.885 0 −0.172 24 0.031 0.998 0.031 0.998 0 −3.77 3.396 0 −0.141 25 0.009 1.005 0.009 1.005 0 −2.751 2.743 0 −0.102 26 −0.004 1.009 −0.004 1.009 0 −2.073 2.309 0 −0.076 27 −0.004 1.007 −0.004 1.007 0 −0.758 1.480 0 −0.028 28 0.003 1.002 0.003 1.002 0 −0.307 1.196 0 −0.011 29 −0.007 1.005 −0.007 1.005 0 −0.291 1.182 0 −0.010 
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表 2 各估算模型相对误差（单位：%）
Table 2. Relative error range of each estimation model（Unit：%）
深度d/m 模型名称 对数线性模型 对数二次模型 对数三次模型 Boore模型 5 0.01～15.25 0～14.81 0.02～14.79 8.94～27.48 10 0.06～13.70 0～13.25 0.13～13.01 0.26～16.85 15 0.03～12.48 0.55～13.11 0.09～11.13 0.06～8.22 20 0.01～8.70 0.01～8.70 0.03～7.29 0.19～11.71 25 0.01～3.89 0.01～3.89 0.01～4.20 0.60～6.55 29 0～1.12 0.01～3.89 0.01～4.21 0.16～1.51
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