Construction and verification of onsite ground motion prediction models for seismic intensity instrument
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摘要: 利用初期P波预警参数构建现地地震动预测模型，使其在达到设定阈值时快速发出报警信息，是现地地震预警系统面临的一个关键问题，直接关系到发布信息的准确性和及时性。针对地震烈度仪基于MEMS传感器记录到的数据质量较差，通过两次积分获取的位移记录会存在较大偏差，而引起更多的误报和漏报。本文采用不同阶数（1—4阶）的巴特沃斯滤波器，分别构建了基于P波3秒和全P波段数据的位移幅值Pd、速度幅值Pv和加速度幅值Pa与地震动峰值速度PGV和峰值加速度PGA的现地地震动预测模型，然后利用收集到的川滇示范预警网MEMS地震事件记录进行验证。结果表明，对于地震烈度仪记录，采用1阶巴特沃斯滤波器处理、基于全P波段波形拟合获取到的Pv与PGV的相关性和Pa与PGA的相关性为两种最优现地地震动预测模型。具体应用时，应同时利用2种或以上的统计关系进行现地地震动预测，并将实际地震动观测值作为额外的判定条件，以降低误报和漏报的概率。Abstract: Using the initial P-wave early warning parameters to construct onsite ground motion prediction models, so as to quickly release an alarm message when it reaches the predefined threshold, is a key issue of the onsite earthquake early warning system, which is directly related to the accuracy and timeliness of the early warning information. For MEMS-based seismic intensity instrument （SII） with poor data quality, the obtained displacement record after two integrations has a large deviation, which will lead to more false and missed alarms. Therefore, for waveforms recorded by SII, in this paper, we adopted Butterworth filters of different orders （1−4） to build several onsite ground motion prediction models based on the P-wave 3 seconds data and the whole P-wave window. These models are relationships between Pd and PGV, Pd and peak ground motion acceleration （PGA）, velocity amplitude （Pv） and PGV, Pv and PGA, acceleration amplitude （Pa） and PGV, Pa and PGA, respectively. The models is then verified using the collected MEMS-based seismic event records from the Sichuan-Yunnan Demonstration Early Warning Network. The results show that for the SII records, the two optimal onsite ground motion prediction models are the relationship between Pv and PGV and the one between Pa and PGA obtained by the first-order Butterworth filter processing and derived from the whole P-wave window. In specific applications, two or more statistical relationships should be simultaneously adopted to predict onsite ground motion, and observed ground motion values should be used as additional judgment conditions to reduce the probability of false and missed alarms.
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图 1 本研究所用震例分布
（a） 各震级地震分布；（b） 所用地震记录的震源距—震级分布情况。灰色菱形为我国4.0≤MS≤8.0地震事件记录，红色三角为日本6.5≤Mj≤8.0地震事件记录；（c） 不同震级范围台站记录数—震源距分布
Figure 1. Distribution of earthquakes used in this study
（a） Distribution of the number of events with magnitude；（b） Distribution of hypocentral distance vs. magnitude for the selected earthquake records. The gray diamonds represent earthquake records （4.0≤MS≤8.0） from the China database，while the red triangles indicate selected waveform data （6.5≤Mj≤8.0） from the Japan database；（c） Histogram of records with hypocentral distance for different magnitude ranges
图 2 最优相关性前四名对应的拟合曲线
（a） Pvall与PGV相关性；（b） Paall与PGA相关性；（c） Pdall与PGV相关性；（d） Paall与PGV相关性。黑色实线表示线性拟合曲线，灰色虚线表示一倍标准方差
Figure 2. Fitting curves for the top four best correlations
Relationships between （a） Pvall and PGV，（b） Paall and PGA，（c） relationship between Pdall and PGV，（d） Paall and PGV. Solid black line indicates the least square fit and the two gray dashed lines show the range of one standard deviation
表 1 位移幅值Pd与地震动峰值参数PGX相关性
Table 1. Correlation between displacement amplitude Pd and peak ground motion parameter PGX
参数 滤波器极点数 系数A 系数B 标准偏差STD 相关系数R Pd3与PGV 1 0.673 2 1.392 0 0.373 4 0.794 6 2 0.677 6 1.448 1 0.367 8 0.801 5 3 0.679 5 1.491 4 0.368 5 0.802 6 4 0.678 2 1.545 4 0.363 5 0.806 7 Pdall与PGV 1 0.610 6 1.063 5 0.362 5 0.807 9 2 0.624 8 1.162 5 0.339 9 0.833 5 3 0.614 6 1.212 1 0.328 3 0.845 7 4 0.603 8 1.235 5 0.325 9 0.848 1 Pd3与PGA 1 0.501 3 2.472 1 0.343 6 0.727 1 2 0.503 2 2.511 8 0.341 3 0.731 5 3 0.503 4 2.550 2 0.340 0 0.733 8 4 0.501 7 2.580 8 0.340 3 0.733 4 Pdall与PGA 1 0.424 4 2.194 6 0.362 3 0.690 0 2 0.438 0 2.268 0 0.348 4 0.718 0 3 0.431 8 2.304 1 0.342 0 0.730 2 4 0.423 1 2.319 0 0.341 9 0.730 4 
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表 2 速度幅值Pv与地震动峰值参数PGX相关性
Table 2. Correlation between velocity amplitude Pv and peak ground motion parameter PGX
参数 滤波器极点数 系数A 系数B 标准偏差STD 相关系数R Pv3与PGV 1 0.805 4 0.983 9 0.415 2 0.737 8 2 0.788 6 0.977 6 0.421 6 0.725 0 3 0.760 1 0.961 9 0.432 6 0.711 0 4 0.766 8 0.973 6 0.430 6 0.714 1 Pvall与PGV 1 0.947 7 0.885 6 0.277 9 0.892 1 2 0.943 3 0.889 3 0.279 7 0.890 6 3 0.924 8 0.886 6 0.292 9 0.879 4 4 0.942 6 0.905 3 0.281 9 0.888 8 Pv3与PGA 1 0.652 9 2.206 8 0.339 4 0.735 0 2 0.638 2 2.201 0 0.345 1 0.724 2 3 0.615 6 2.188 6 0.353 6 0.707 7 4 0.621 0 2.198 0 0.352 1 0.710 7 Pvall与PGA 1 0.714 9 2.099 8 0.281 4 0.827 0 2 0.709 4 2.101 5 0.284 2 0.823 1 3 0.694 4 2.098 9 0.292 4 0.811 6 4 0.707 2 2.112 6 0.286 8 0.819 5
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表 3 加速度幅值Pa与地震动峰值参数PGX相关性
Table 3. Correlation between acceleration amplitude Pa and peak ground motion parameter PGX
相关性 滤波器极点数 系数A 系数B 标准偏差STD 相关系数R Pa3与PGV 1 0.642 1 −0.109 8 0.512 8 0.552 3 2 0.664 0 −0.096 2 0.503 9 0.573 6 3 0.657 5 −0.074 0 0.503 0 0.575 7 4 0.676 0 −0.074 8 0.497 0 0.589 1 Paall与PGV 1 0.995 3 −0.582 2 0.359 5 0.811 5 2 1.008 2 −0.548 7 0.334 3 0.828 6 3 0.988 3 −0.504 9 0.348 3 0.824 3 4 1.007 4 −0.504 6 0.335 7 0.837 9 Pa3与PGA 1 0.620 9 1.240 5 0.377 6 0.656 3 2 0.624 8 1.266 5 0.374 5 0.663 4 3 0.609 3 1.294 3 0.377 9 0.655 7 4 0.619 7 1.298 3 0.374 4 0.663 7 Paall与PGA 1 0.848 6 0.896 0 0.263 4 0.850 3 2 0.842 7 0.940 6 0.262 7 0.851 2 3 0.816 9 0.985 5 0.273 6 0.837 4 4 0.826 4 0.991 5 0.267 9 0.844 7
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表 4 最优相关性汇总
Table 4. Summary of optimal correlations
参数 滤波器极点数 系数A 系数B 标准偏差STD 相关系数R Pvall与PGV 1 0.947 7 0.885 6 0.277 9 0.892 1 Paall与PGA 1 0.848 6 0.896 0 0.263 4 0.850 3 Pdall与. PGV 4 0.603 8 1.235 5 0.325 9 0.848 1 Paall与PGV 4 1.007 4 −0.504 6 0.335 7 0.837 9 Pvall与PGA 1 0.714 9 2.099 8 0.281 4 0.827 0 Pd3与PGA 3 0.503 4 2.550 2 0.340 0 0.733 8
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表 5 本工作选取的MEMS地震事件测试用例
Table 5. MEMS seismic event test cases selected in this work
发震时刻
年-月-日 时:分:秒东经/º 北纬/º 震源深度/km 震级 GL-P2B台站记录数 2017-01-04 23:14:29 29.536 102.154 23 4.4 8 2017-01-18 22:35:14 28.134 104.710 10 4.7 1 2017-03-12 20:21:18 27.072 103.421 12 5.1 41 2017-03-30 07:48:18 27.120 103.356 7 4.1 7 2017-04-04 04:57:40 27.093 103.411 8 3.8 6 2017-05-04 13:40:21 28.234 104.922 21 5.1 2 2017-07-02 03:40:58 27.081 103.244 7 3.7 15 2017-10-18 02:54:21 28.326 102.815 15 3.8 33 2018-02-27 03:00:53 29.403 102.131 18 3.8 12 2018-05-02 04:28:45 28.502 102.704 14 3.8 30 2018-05-08 23:11:33 28.140 103.478 10 4.5 37 2018-05-16 16:44:03 29.201 102.265 11 3.9 33 2018-05-16 16:46:11 29.190 102.262 12 4.6 54 2018-05-16 16:46:40 29.180 102.270 9 4.9 51 2018-05-18 02:40:29 27.413 103.958 4 3.6 3 2018-08-11 14:11:31 28.623 103.317 9 4.1 32 2018-08-18 01:36:38 27.400 103.984 10 4.2 5 2018-10-28 08:25:16 28.074 103.538 6 3.6 11 2018-10-30 05:00:05 28.105 103.529 11 4.3 21 2018-10-31 16:29:56 27.700 102.080 19 5.1 28 2018-11-19 22:29:51 29.484 104.499 11 3.3 16 2018-11-20 06:01:11 27.697 102.092 18 3.9 25 2018-12-23 22:22:40 28.116 103.588 10 3.7 15 2019-05-16 04:33:31 28.070 103.530 10 4.7 65
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表 6 1阶巴特沃斯滤波器带通滤波后数据的测试结果（
Table 6. Test results with data filtered by one-pole Butterworth bandpass filter
类别 GL-P2B台站记录数 站总记录数的百分比 成功不预警 478 86.75% 成功预警 40 7.26% 漏报 14 2.54% 误报 19 3.45%
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表 7 成功预警测试震例理论预警发布时间列表（1阶巴特沃斯带通滤波器）
Table 7. Theoretical warning release time list for successful early warning test earthquake cases with data filtered by one-pole Butterworth bandpass filter
理论预警发布时间/s GL-P2B台站记录数 占总记录数的百分比 0.5 28 70.0/% 1.0 5 12.5/% 1.5 5 12.5/% 2.5 1 2.5/% 4.0 1 2.5/%
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表 8 成功预警测试震例理论预警时间列表（1阶巴特沃斯带通滤波器）
Table 8. Theoretical lead-time list for successful early warning test earthquake cases with data filtered by one-pole Butterworth bandpass filter
理论预警时间/s GL-P2B台站记录数 占总记录数的百分比/ ＜0.0 3 7.5% （0.0，1.0] 11 27.5% （1.0，2.0] 9 22.5% （2.0，5.0] 13 32.5% ＞5.0 4 10.0%
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表 9 1—4阶巴特沃斯滤波器带通滤波后数据测试结果
Table 9. Summary of test results with data filtered by Butterworth bandpass filter with poles of one to four
滤波器阶数 成功不预警占比/% 成功预警占比/% 漏报占比/% 误报占比/% 成功处理占比/% 成功处理（加入漏报）占比/% 1 86.75 7.26 2.54 3.45 94.01 96.55 2 86.75 7.08 2.72 3.45 93.83 96.55 3 86.75 6.72 3.09 3.45 93.47 96.56 4 86.57 6.53 3.27 3.63 93.10 96.37
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