Probabilistic Prediction of Short-Term Strong Earthquake Hazard Based on Bayesian Network Structure Learning
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摘要: 为提升区域月尺度强震风险预测能力，基于贝叶斯网络结构学习提出区域性月尺度地震危险性概率预测模型.首先利用区域与全球地震目录数据构建预测指标，作为网络节点变量；其次采用群智能算法自动确定各节点阈值及节点间的有向连接；最后通过参数估计，目标节点输出目标区域未来一月内发生MW5.0及以上强震的概率.实验结果显示，模型预报效能指标平均达0.783，经Molchan检验验证，其有效性显著，表明该模型能够充分挖掘地震预测指标与强震之间的潜在因果关系.Abstract: To enhance the capability for monthly-scale regional strong earthquake risk prediction, this paper introduces a probabilistic seismic hazard prediction model based on Bayesian network structure learning. Initially, a series of predictive indicators, serving as the nodes of the Bayesian network, are derived from the earthquake catalog. Subsequently, the thresholds for each node and the directed connections among nodes are determined using swarm intelligence algorithms. Ultimately, through parameter estimation, the target node outputs the probability of MW5.0+ strong earthquakes occurring in the target region within the next month. Experimental results indicate that the model achieves an average prediction efficiency metric of 0.783, and validation via the Molchan test confirms its significant effectiveness, demonstrating the model's capacity to comprehensively explore the latent causal relationships between seismic precursors and strong earthquakes.
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图 1 全球1960-2024年Mw7.0以上的地震分布
Fig. 1. Global distribution of earthquakes with magnitude Mw≥7.0 from 1960 to 2024
图 3 模型在测试集上推理结果的混淆矩阵
Fig. 3. Confusion matrix for BESBN inference results on the test set
图 4 不同区域的BESBN网络结构对比
Fig. 4. Comparison of BESBN network structures in different regions
表 1 划定研究区域的范围及构造背景
Table 1. Delineation of the extent of the study region and its structural background
研究区域 划分范围 构造背景 T01(HH) 红河断裂带周边 印度‒欧亚板块碰撞应力控制, 历史强震反映走滑断层闭锁 T02(DX) 滇西和澜沧江地震带 滇缅块体走滑‒逆冲复合, 地震机制多样 T03(HX) 河西走廊、六盘山、兰州、天水 闭锁段应力积累特征突出, 历史强震密集 T04(TK) 塔里木盆地西南和昆仑山东部 耦合板缘俯冲受印度板块北向推挤, 应力加载引发逆冲型地震丛集 T05(TS) 天山山脉 印度‒欧亚碰撞远场效应显著, 断层闭锁度高 T06(FB) 福建省东南沿海、渤海地区和山西东部 历史强震受板块内部弱变形与局部应力集中控制 T07(TG) 唐古拉山脉东部 唐古拉山脉东缘走滑断裂网络, 地震活动反映高原东向扩展变形机制 T08(TD) 台湾东部及沿海 高角度逆冲及走滑断层发育, 地震频发源于板块边界强耦合 
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表 2 贝叶斯网络每个节点的设计细节
Table 2. Design specifics of each node in the Bayesian network
节点 内容 状态0 状态1 A1 全球10年内MW7.0以上地震频率 平静 活跃 A2 全国3年内MW6.0以上地震频率 平静 活跃 B1 区域3月内ML3.0以上地震频率 平静 活跃 B2 全国1年内MW7.0以上地震频率 平静 活跃 B3 全国1年内MW5.0以上地震频率 平静 活跃 C1 区域1月内ML3.0以上地震频率 平静 活跃 C2 区域MW4.0以上地震平静期天数 长时间平静 平静时间短 D 下个月是否发生MW5.0以上地震 不发生 发生
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表 3 不同算法在8个区域的训练集上性能比较
Table 3. Comparison of average performance of different algorithms on training set of 8 regions
算法 AET ASD AKS 迭代轮数 种群数量 ACO+HC 243±2.5 2.75±1.24 939.52±10.25 50 40 SSA+HC 230±3.1 2.12±0.63 1 142.79±1.16 50 40 GWO+HC 238±1.7 1.83±0.53 1 211.68±3.50 50 40 WOA+HC 202±18.0 3.58±1.37 1 416.37±2.44 50 40 BES+HC 203±8.6 1.03±0.11 2 087.29±0.00 50 40 BES+HC 235±11.3 1.00±0.00 2 099.85±0.00 50 50
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表 4 本研究中混淆矩阵的定义
Table 4. The definition of confusion matrix in this study
混淆矩阵 下个月发生MW5.0以上强震 下个月未发生MW5.0以上强震 后验概率超过报警值 TP FP 后验概率未超过报警值 FN TN
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表 5 不同区域BESBN的阈值
Table 5. Thresholds for BESBN in different regions
模型 αwarn αA1 αA2 αB1 αB2 αB3 αC1 αC2 BESBN-T01 0.065 6 175.41 21.02 52.93 4.44 52.74 82.20 661.75 BESBN-T02 0.055 3 192.86 19.98 25.57 3.48 30.24 10.39 151.57 BESBN-T03 0.047 2 196.42 16.65 9.74 2.48 35.19 2.98 604.50 BESBN-T04 0.194 8 176.32 17.73 75.16 2.81 45.73 11.43 214.70 BESBN-T05 0.057 5 209.92 17.16 5.91 3.81 40.36 12.82 669.81 BESBN-T06 0.014 6 153.80 20.71 7.76 1.90 34.96 3.19 1187.76 BESBN-T07 0.093 8 147.01 22.26 11.48 4.44 34.78 9.18 607.50 BESBN-T08 0.159 3 174.15 17.92 2.97 1.42 79.14 13.96 378.22
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表 6 不同区域的模型性能比较
Table 6. Comparison of model performances in different regions
研究区域 模型 R Acc AUC FPR T01(HH) BESBN-T01
ETAS
Poisson0.873 0.880 0.980 0.127 0.742 0.821 0.876 0.179 0.612 0.746 0.723 0.254 T02(DX) BESBN-T02 0.649 0.768 0.808 0.240 ETAS 0.548 0.716 0.745 0.284 Poisson 0.421 0.642 0.651 0.358 T03(HX) BESBN-T03 0.892 0.894 0.949 0.107 ETAS 0.769 0.835 0.882 0.165 Poisson 0.634 0.752 0.731 0.248 T04(TK) BESBN-T04 0.659 0.777 0.825 0.250 ETAS 0.556 0.716 0.748 0.284 Poisson 0.418 0.627 0.642 0.373 T05(TS) BESBN-T05 0.825 0.836 0.897 0.175 ETAS 0.697 0.776 0.824 0.224 Poisson 0.573 0.701 0.692 0.299 T06(FB) BESBN-T06 0.832 0.835 0.871 0.168 ETAS 0.714 0.775 0.812 0.225 Poisson 0.588 0.695 0.698 0.305 T07(TG) BESBN-T07 0.790 0.809 0.898 0.210 ETAS 0.672 0.750 0.821 0.250 Poisson 0.534 0.676 0.687 0.324 T08(TD) BESBN-T08 0.740 0.866 0.890 0.136 ETAS 0.628 0.806 0.823 0.194 Poisson 0.495 0.731 0.708 0.269
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表 7 Molchan检验结果
Table 7. Molchan test results
研究区域 模型 1-S Gavg(0.1τ) Gavg(0.2τ) Gavg Gmax T01(HH) BESBN-T01 0.839 7 2.540 1 3.918 4 3.918 4 5.064 6 ETAS 0.765 5 - 2.197 1 2.781 9 3.490 7 Poisson 0.717 5 - 1.359 1 2.236 5 3.053 5 T02(DX) BESBN-T02 0.872 4 4.375 8 4.993 1 4.840 0 5.717 7 ETAS 0.820 4 1.153 9 2.980 4 3.145 7 4.360 5 Poisson 0.726 4 - 1.275 1 2.089 5 3.010 1 T03(HX) BESBN-T03 0.896 9 8.470 7 8.072 5 8.072 5 9.082 6 ETAS 0.748 6 3.923 8 4.472 9 3.845 7 5.022 0 Poisson 0.784 5 - 2.882 9 3.240 3 3.954 9 T04(TK) BESBN-T04 0.818 8 1.741 3 2.745 9 2.966 7 4.510 2 ETAS 0.746 2 - 1.116 7 2.110 2 3.254 8 Poisson 0.683 3 - 0.543 4 1.673 0 2.643 8 T05(TS) BESBN-T05 0.901 2 5.531 3 6.570 4 6.570 4 7.934 6 ETAS 0.848 5 - 4.151 8 4.151 8 5.605 7 Poisson 0.703 0 - 2.108 8 2.447 8 3.434 2 T06(FB) BESBN-T06 0.881 0 5.593 7 6.195 6 6.195 6 6.864 4 ETAS 0.832 5 - 4.161 6 4.333 2 5.192 5 Poisson 0.747 7 - 2.165 2 2.825 0 3.242 9 T07(TG) BESBN-T07 0.817 0 1.777 6 2.729 0 3.178 6 4.228 1 ETAS 0.762 7 - 1.519 2 2.421 3 3.403 1 Poisson 0.678 0 - 0.855 8 1.800 0 2.368 4 T08(TD) BESBN-T08 0.782 8 1.412 3 1.922 1 2.563 8 3.545 5 ETAS 0.725 4 - 0.930 8 2.004 3 2.835 7 Poisson 0.614 6 - 0.704 7 1.535 3 2.201 9
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