Seismic Back-Azimuth Estimation Model Based on WaveNet and Full Waveform Data
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摘要: 地震定位是地震预警和地球深部结构研究的核心，但其精度仍面临挑战.本研究基于中国大陆测震台网的三分量波形数据，采用深度学习技术，构建了单台地震反方位角估算方法，对比分析了标准卷积神经网络与WaveNet模型在P波、面波和全波形输入下的性能差异.结果显示，WaveNet结合全波形输入的表现最优，其借助扩张卷积与残差连接结构增强了对长时间序列特征的提取能力，反方位角平均偏差仅为0.04°，拟合优度（R2）达到0.99.独立测试结果表明，该模型具备良好的泛化能力，平均绝对偏差和方差相较于传统面波偏振方法分别降低了58.70%和28.21%.基于全波形输入的深度学习方法可显著提高单台定位精度，为地震预警及极端环境下的地震监测提供有效技术支撑.Abstract: Earthquake location is fundamental to both early warning systems and studies of the Earth's deep structure, yet its accuracy remains challenging to be improved. Using three-component waveform data from the China National Seismic Network, this study develops a single-station back-azimuth estimation method based on deep learning. We compare the performance of a standard convolutional neural network with that of a WaveNet architecture under three input settings: P-wave only, surface-wave only, and full-waveform input. Results show that WaveNet combined with full-waveform input performs best, benefiting from dilated convolutions and residual connections that enhance its ability to extract long-range temporal features. The model achieves an average back-azimuth deviation of only 0.04°, with a coefficient of determination (R2) of 0.99. Independent tests demonstrate strong generalization capability, with the mean absolute deviation and variance reduced by 58.70% and 28.21%, respectively, compared with the traditional surface-wave polarization method. The findings indicate that deep learning with full-waveform input can substantially improve single-station location accuracy, offering effective technical support for earthquake early warning and seismic monitoring in challenging environments.
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Key words:
- earthquake location /
- back-azimuth /
- WaveNet /
- deep learning /
- full waveform /
- seismology
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图 1 研究选取的地震台站与地震事件的空间分布
Fig. 1. Spatial distribution of seismic stations and earthquake events in the study
图 2 单台三分量地震波形以及相应的震相信息时间窗口
Fig. 2. Single-station three-component seismic waveforms and earthquake phase windows
图 3 基于深度学习的单台地震反方位角评估整体流程
Fig. 3. Overall workflow for single-station back-azimuth estimation using deep learning
图 4 基于传统CNN的深度学习模型（a）与基于WaveNet的深度学习模型(b)
Fig. 4. Deep learning model based on traditional CNN (a) and deep learning model based on WaveNet (b)
图 5 CNN模型对P波、面波和全波形输入的测试结果
Fig. 5. Testing results of the CNN model for P-wave, surface wave, and full waveform inputs
图 6 WaveNet模型对P波、面波和全波形输入的测试结果
Fig. 6. Testing results of the WaveNet model for P-wave, surface wave, and full waveform inputs
图 7 CNN与WaveNet模型基于P波输入的反方位角预测误差影响因素分析
Fig. 7. Analysis of influencing factors on back-azimuth prediction errors of CNN and WaveNet models based on P-wave input
图 8 CNN（a）与WaveNet（b）模型全波形输入损失函数曲线
Fig. 8. Full waveform input loss function curves of the CNN (a) and WaveNet (b) models
图 9 WaveNet模型对IC.BJT台站更小震级事件的反方位角预测误差分布
Fig. 9. Influencing factors on back-azimuth prediction errors of WaveNet model for smaller magnitude earthquake events at IC.BJT station
图 10 WaveNet和传统偏振方法在独立测试数据集上的角度误差分布对比
WaveNet选取全波形输入的推理结果.传统面波偏振分析方法为DLOPy，仅统计互相关系数 > 0.7的样本数据.绿色小提琴图展示深度学习方法的误差分布，粉色小提琴图表示传统方法的误差分布，圆点标记平均误差
Fig. 10. Comparison of angular error distributions between WaveNet and traditional polarization methods on the independent test dataset
表 1 模型训练与测试结果统计
Table 1. Statistics of model training and testing results
输入 模型 参数量 训练时长(s)
Nvidia RTX 3090单次推理平均时间(s) MAC M1 平均偏差 平均方差 R2 成功率10°误差 P波 CNN 64 450 6×120 0.000 1 ‒0.34 28.97 0.83 0.559 WaveNet 33 346 7×120 0.000 5 ‒0.26 25.33 0.87 0.580 面波 CNN 15 711 746 11.4×120 0.001 7 ‒0.05 8.86 0.98 0.915 WaveNet 198 146 13.5×120 0.032 9 0.09 9.77 0.98 0.929 全波形 CNN 79 674 882 45×120 0.006 2 0.08 7.65 0.99 0.968 WaveNet 1 970 690 121×120 0.778 1 0.04 6.24 0.99 0.988 
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表 2 WaveNet面波输入消融实验结果统计
Table 2. Statistics of the ablation experiment results for surface wave input in the WaveNet model
实验设置 平均偏差 方差 $ {R}^{2} $ 成功率(10°) 完整WaveNet 0.09 9.77 0.98 0.928 9 残差块数=5 ‒0.09 14.38 0.95 0.901 5 残差块数=12 ‒0.22 10.87 0.97 0.932 6 仅时间平移 ‒0.19 11.24 0.97 0.918 8 仅噪声增强 ‒0.14 12.04 0.97 0.913 5 仅振幅缩放 ‒0.15 11.66 0.97 0.925 4 无数据增强 ‒0.19 11.87 0.97 0.907 9 无学习率调度器 0.48 12.04 0.97 0.880 9
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表 3 模型泛化能力测试结果统计
Table 3. Statistics of model generalization capability test results
台站 区域 事件数 平均偏差 方差 $ {R}^{2} $ 成功率(10°) IC.BJT 北京 1 112 ‒0.78 8.47 0.98 0.982 9 IC.ENH 恩施 1 072 1.91 10.65 0.98 0.962 7 IC.HIA 呼伦贝尔 1 107 0.94 8.47 0.98 0.955 7 IC.KMI 昆明 1 054 1.85 11.18 0.98 0.904 2 IC.LSA 拉萨 915 4.45 15.57 0.95 0.780 0 IC.MDJ 牡丹江 1 058 ‒1.5 9.24 0.98 0.957 5 IC.QIZ 琼中 1 111 1.33 11.92 0.98 0.943 3 IC.SSE 上海 1 047 ‒0.8 7.37 0.99 0.975 2 IC.WMQ 乌鲁木齐 1 041 1.5 12.36 0.96 0.871 3 IC.XAN 西安 1 042 ‒0.13 11.67 0.97 0.949 1 平均 0.975 0.928 19
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表 4 WaveNet与传统模型对比结果统计
Table 4. Statistics of comparison results between WaveNet and traditional models
台站名称 区域 方法 有效事件数量 平均绝对偏差 方差 $ {R}^{2} $ IC.BJT 北京 AI 1 112 0.78 8.47 0.98 偏振 695 0.77 12.51 0.98 IC.ENH 恩施 AI 1 072 1.91 10.65 0.98 偏振 605 2.25 17.71 0.95 IC.HIA 呼伦贝尔 AI 1 107 0.94 8.47 0.98 偏振 696 0.26 10.31 0.98 IC.KMI 昆明 AI 1 054 1.85 11.18 0.98 偏振 621 1.10 17.51 0.95 IC.LSA 拉萨 AI 915 4.45 15.57 0.95 偏振 518 2.95 15.45 0.96 IC.MDJ 牡丹江 AI 1 058 1.50 9.24 0.98 偏振 690 0.47 13.02 0.97 IC.QIZ 琼中 AI 1 111 1.33 11.92 0.98 偏振 651 1.33 14.43 0.97 IC.SSE 上海 AI 1 047 0.80 7.37 0.99 偏振 657 2.17 15.19 0.96 IC.WMQ 乌鲁木齐 AI 1 041 1.50 12.36 0.96 偏振 674 3.54 15.33 0.97 IC.XAN 西安 AI 1 042 0.13 11.67 0.97 偏振 642 0.91 17.41 0.95 IC平均 中国大陆 AI 1 055.9 1.52 10.69 0.98 偏振 644.9 3.68 14.89 0.96
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