A new method for expressing seismic hazards
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摘要: 为了寻找一种精度较高、超越概率范围较广并且便于应用的方式来表达地震危险性，本文回顾了当前常用的几种地震危险性表达方法，提出基于一个新函数来拟合地震危险性曲线的“特征系数法”，并使用《中国地震动参数区划图》（GB 18306—2015）的基础数据对该函数的拟合效果进行了验证。结果表明，新函数与地震危险性曲线拟合良好，与极值函数相比有明显的提升，能够充分地表达一个场点的地震危险性。另外，本文结果还显示该函数中表征曲线形状的参数k （文中称为特征系数）与场点面临的地震环境有关，k值较低的场点危险性贡献基本来自近场，而k值较高的场点中远距离的贡献是不能忽视的。Abstract: The aim is to find a way to express seismic hazards with high accuracy, a wide range of exceedance probabilities and convenient application. We reviewed several commonly used methods for seismic hazards expression, and the "characteristic coefficient method" based on a new function to fit the seismic hazard curve is proposed, and the effect of this function was also verified by using the base data of the Seismic Parameter Zoning Map of China （GB 18306−2015）. The results show that the new function could effectively fit the seismic hazard curve, with a significant improvement compared to the extreme value function, and can adequatelyexpress the seismic hazards of a site. In addition, it is found that the parameter k （referred to as the characteristic coefficient in the paper）, which characterizes the shape of the curve in this function, is related to the seismic environment faced by the site, that is, the hazard contribution for sites with low values of k essentially came from the near field, while the contribution for sites with high values of k from long distances could not be ignored.
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Keywords:
- seismic hazards /
- characteristic coefficient /
- curve fitting /
- seismic environment
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图 1 某城市PGA危险性曲线与极值函数的拟合
Figure 1. Results of the PGA hazard curve fitting the extreme value function for a city
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图 2 某城市PGA危险性曲线与新函数的拟合
Figure 2. Results of the PGA hazard curve fitting the new function for a city
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图 3 全国0.2°×0.2°间隔2万4 043个场点特征系数k的频数分布
Figure 3. Distribution of the frequency of the characteristic coefficient k for the national 24 043 sites with interval of 0.2°×0.2°
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图 4 特征系数法的拟合残差Res统计对比
Figure 4. Statistical comparison of fitting residuals for shape parameter method at 24 043 sites
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图 5 四个城市基于特征系数法拟合得到的地震危险性曲线
Figure 5. Seismic hazard curves based on the characteristic coefficient method for the four cities
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图 6 某城市基于特征系数法的谱加速度危险性曲线拟合结果
Figure 6. Results of fitting for the spectral acceleration hazard curve of a city based on the characteristic coefficient method
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图 7 拉萨和常德两场点PGA年超越概率曲线对比
Figure 7. Comparison of the annual PGA exceedance probability curves for the two sites in Lhasa and Changde
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图 8 拉萨和常德两场点PGA危险性曲线分解结果对比
横坐标表示计算时离散化微元到场点的距离，纵坐标代表不同距离微元贡献的百分比即概率密度函数PDF（a） 50年超越概率10%的PGA；（b） 50年超越概率2%的PGA
Figure 8. Comparison of the results of the PGA hazard curve decomposition at the Lhasa and Changde sites
The horizontal coordinate represents the distance from the discretized microelements to the field point at the time of calculation，and the vertical coordinate represents the percentage of contribution from microelements at different distances， that is，the probability density function PDF （a） PGA for 10% probability being exceeded in 50 years； （b）PGA for 2% probability being exceeded in 50 years
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图 9 拉萨和常德两场点潜在震源区分布
Figure 9. Distribution of potential source areas at the sites of Lhasa and Changde
表 1 4个城市特征系数法拟合的地震危险性曲线相对残差Res结果
Table 1 Fitting results of the relative residuals for seismic hazard curves by the characteristic coefficient method for four cities
超越概率 PGAfit/g PGAcal/g Res 北京 上海 兰州 成都 北京 上海 兰州 成都 北京 上海 兰州 成都 50年63% 0.068 0.025 0.053 0.038 0.064 0.025 0.053 0.038 6.70% 2.70% 0.20% 0.80% 50年50% 0.109 0.041 0.083 0.056 0.104 0.040 0.080 0.056 4.80% 2.40% 4.40% 1.50% 50年5% 0.350 0.138 0.259 0.150 0.347 0.141 0.268 0.150 0.80% 2.00% 3.10% 0.20% 50年2% 0.500 0.200 0.368 0.202 0.483 0.205 0.381 0.204 3.50% 2.30% 3.70% 1.00% 50年0.5% 0.806 0.328 0.585 0.301 0.730 0.338 0.586 0.305 9.40% 3.00% 0.00% 1.30% 
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表 2 低k值场点期望距离计算结果
Table 2 Calculated expected distances for low k-value sites
序号 场点名称 东经/° 北纬/° PGA475/g k PGA475期望距离/km PGA2475期望距离/km 1 临沂 118.6 35.0 0.199 0.25 24.63 17.97 2 宿迁 118.4 34.0 0.176 0.28 27.22 19.01 3 唐山 118.1 39.6 0.245 0.30 21.42 16.51 4 黄山 118.4 29.8 0.034 0.30 20.84 14.15 5 佛山 113.0 23.0 0.071 0.30 26.30 19.99 6 漳州 117.6 24.6 0.115 0.28 27.71 18.28 7 渭南 109.6 34.4 0.199 0.28 26.60 19.37 8 临汾 111.6 36.2 0.238 0.29 20.96 17.50 9 当雄 90.6 30.2 0.410 0.31 21.38 17.93 10 格尔木 91.6 36.0 0.256 0.28 27.67 20.14 11 若羌县 91.4 38.8 0.256 0.27 26.63 19.93 12 白银 104.6 36.8 0.260 0.29 25.13 19.16 13 常德 111.8 29.4 0.178 0.27 14.69 11.86 14 松原 124.8 45.2 0.176 0.30 17.08 13.55 15 锡林浩特 116.0 44.0 0.054 0.29 21.44 16.35 16 赤峰 119.0 42.0 0.142 0.28 19.32 14.21
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表 3 高k值场点期望距离计算结果
Table 3 Calculated expected distances for high k-value sites
序号 场点名称 东经/° 北纬/° PGA475/g k PGA475期望距离/km PGA2475期望距离/km 1 济宁 116.6 35.4 0.064 0.43 46.08 39.69 2 淮安 119.2 33.4 0.057 0.41 50.55 39.62 3 开封 114.2 34.8 0.083 0.42 49.71 47.54 4 晋城 112.8 35.6 0.059 0.41 49.47 39.00 5 沧州 117.4 38.2 0.063 0.45 52.53 43.20 6 东营 118.6 37.4 0.074 0.42 50.92 39.77 7 衡水 116.0 37.6 0.067 0.42 49.13 46.09 8 秦皇岛 119.6 40.0 0.069 0.42 49.88 47.00 9 鹤壁 114.8 35.8 0.116 0.43 47.92 44.00 10 济南 117.2 36.6 0.061 0.42 42.67 36.23 11 林周县 91.4 30.0 0.170 0.45 58.54 53.83 12 林芝 94.6 30.0 0.176 0.43 43.25 36.59 13 那曲地区 92.2 31.6 0.132 0.49 60.90 53.21 14 白银 104.4 36.4 0.119 0.41 57.66 56.34 15 临沧 100.0 23.8 0.178 0.47 39.39 34.42 16 凉山彝族自治州 103.2 27.6 0.134 0.50 40.22 35.96
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