融合震中距几何辅助信息与台站维自注意力机制的HR-GNSS大震震级估算

doi:10.11947/j.AGCS.2026.20260104

测绘学报 ›› 2026, Vol. 55 ›› Issue (9): 1542-1554.doi: 10.11947/j.AGCS.2026.20260104

融合震中距几何辅助信息与台站维自注意力机制的HR-GNSS大震震级估算

李艳艳(), 王澳, 涂锐()

山东科技大学测绘与空间信息学院，山东　青岛　266590

收稿日期:2026-04-07 修回日期:2026-09-08 出版日期:2026-10-28 发布日期:2026-10-28
通讯作者: 涂锐 E-mail:yylee@sdust.edu.cn;turui-2004@126.com
作者简介:李艳艳（1987—），女，副教授，研究方向为GNSS高精度数据处理、时空数据质量提升及地壳形变监测等。　E-mail：yylee@sdust.edu.cn
基金资助:
国家自然科学基金(42574065; 42404043; 42274019);山东省自然基金(ZR2025MS603; ZR2024JQ024; ZR2024QD 111);国家重点研发计划(2025YFE0104000)

Great earthquake magnitude estimation using HR-GNSS with epicentral-distance geometric auxiliary information and attention mechanisms

Yanyan Li(), Ao Wang, Rui Tu()

College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao 266590, China

Received:2026-04-07 Revised:2026-09-08 Online:2026-10-28 Published:2026-10-28
Contact: Rui Tu E-mail:yylee@sdust.edu.cn;turui-2004@126.com
About author:Li Yanyan (1987—), female, associate professor, majors in high-precision GNSS data processing, spatio-temporal data quality enhancement, and crustal deformation monitoring. E-mail: yylee@sdust.edu.cn
Supported by:
The National Natural Science Foundation of China(42574065; 42404043; 42274019);The Natural Science Foundation of Shandong Province(ZR2025MS603; ZR2024JQ024; ZR2024QD 111);The National Key Research and Development Program of China(2025YFE0104000)

摘要/Abstract

摘要：

快速准确的地震震级估算对灾后应急响应与防震减灾至关重要。高频全球导航卫星系统（HR-GNSS）可快速捕获近场同震形变信息，为大震震级估算提供了重要的数据基础，但现有方法仍面临震级估算饱和、低信噪比、台站分布不均，以及现有深度学习模型对震源与台站间几何关系利用不足等挑战。针对上述问题，本文提出了一种融合震中距几何辅助信息与台站维自注意力机制的卷积神经网络（EDGSA-CNN）模型。该模型利用卷积神经网络（CNN）提取多台站三分量位移波形特征，通过自注意力机制建模台站间特征相关性，并采用多层感知机（MLP）对震中距进行非线性编码，融合波形特征与几何辅助信息，用于大震矩震级估算。智利俯冲带合成HR-GNSS数据集试验表明，EDGSA-CNN模型的震级估算误差总体低于纯波形CNN基线模型和峰值地表位移经验模型，并在高震级样本中保持较低误差。震中距扰动、跨区域合成和真实强震测试表明，模型对早期震中定位误差具有一定稳健性，在不同数据来源和观测条件下具有一定的适用性和稳定性。本研究可为大震震级准确估算、地震预警应用等提供潜在技术支持。

关键词: 高频GNSS, 深度学习, 注意力机制, 震中距, 震级估算

Abstract:

Rapid and accurate earthquake magnitude estimation is crucial for post-earthquake emergency response and earthquake disaster prevention and mitigation. High-rate global navigation satellite system (HR-GNSS) observations can rapidly capture near-field coseismic deformation and provide important data for magnitude estimation of large earthquakes. Existing methods, however, still face magnitude saturation, low signal-to-noise ratios, uneven station distributions, and insufficient use of source-station geometry in deep-learning models. To address these problems, this study proposes an epicentral-distance geometry-assisted station-wise attention convolutional neural network (EDGSA-CNN) model. The model uses a convolutional neural network (CNN) to extract three-component displacement waveform features from multiple stations. It employs a self-attention mechanism to model feature correlations among stations and a multilayer perceptron (MLP) to nonlinearly encode epicentral distances. The waveform features and geometric auxiliary information are then fused to estimate the moment magnitude of large earthquakes. Experiments using synthetic data from the Chilean subduction zone show that EDGSA-CNN generally yields lower magnitude-estimation errors than the waveform-only CNN baseline and peak ground displacement (PGD) empirical model, while maintaining relatively low errors for high-magnitude samples. Epicentral-distance perturbation tests indicate that the model is robust to early epicentral-location errors to some extent. Cross-regional synthetic tests and tests using observations from real large earthquakes further indicate that the model exhibits a certain degree of applicability and stability across different data sources and observational conditions. This study can provide potential technical support for accurate magnitude estimation of large earthquakes and earthquake early warning applications.

Key words: high-rate GNSS, deep learning, attention mechanism, epicentral distance, magnitude estimation

中图分类号:

P228

李艳艳, 王澳, 涂锐. 融合震中距几何辅助信息与台站维自注意力机制的HR-GNSS大震震级估算[J]. 测绘学报, 2026, 55(9): 1542-1554.

Yanyan Li, Ao Wang, Rui Tu. Great earthquake magnitude estimation using HR-GNSS with epicentral-distance geometric auxiliary information and attention mechanisms[J]. Acta Geodaetica et Cartographica Sinica, 2026, 55(9): 1542-1554.

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模块	参数
输入波形	Case Ⅰ：3×181×3；Case Ⅱ：7×181×3 Case Ⅲ：7×501×3
波形CNN卷积核	6层Conv2D，通道数12、24、36、64、128、256（1，3）
池化	Conv1、Conv3、Conv5后设置最大池化层，池化窗口为（1，2）
注意力	，A=Softmax（QK^T），X_Attn=AV
震中距编码分支	32→64→128
特征拼接	256维波形特征+128维震中距特征=384维
回归网络	256→128→32→1
损失函数	均方误差
优化器	Adam
批次大小	128
最大训练轮数	200
提前停止	验证集损失连续20轮无改善停止

实验场景	每个地震所选台站数（Δ：震中距）	时间序列窗口长度/s	输入数据维度（台站数，时长，通道数）
Case Ⅰ	3个台站，Δ≤3°	181	（3，181，3）
Case Ⅱ	7个台站，Δ≤3°	181	（7，181，3）
Case Ⅲ	7个台站：其中3~5个Δ≤3°，其余台站Δ>3°	501	（7，501，3）

模型	Case Ⅰ	Case Ⅱ	Case Ⅲ	Case Ⅲ（M_w≥8.5）
CNN	0.104	0.093	0.075	0.082
CNN-Attn	0.100	0.098	0.054	0.057
CNN-MLP	0.084	0.078	0.042	0.045
EDGSA-CNN	0.080	0.078	0.044	0.050

事件	方法	RMSE/M_w	MAE/M_w
Case Ⅰ	PGD经验模型	0.232	0.150
Case Ⅰ	EDGSA-CNN	0.080	0.046
Case Ⅱ	PGD经验模型	0.227	0.138
Case Ⅱ	EDGSA-CNN	0.078	0.039
Case Ⅲ	PGD经验模型	0.173	0.135
Case Ⅲ	EDGSA-CNN	0.044	0.034

扰动幅度/km	Case Ⅰ	Case Ⅱ	Case Ⅲ
0	0.080	0.078	0.044
10	0.081	0.078	0.045
30	0.082	0.081	0.048
50	0.084	0.085	0.054

融合震中距几何辅助信息与台站维自注意力机制的HR-GNSS大震震级估算

Great earthquake magnitude estimation using HR-GNSS with epicentral-distance geometric auxiliary information and attention mechanisms

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图/表 14

参考文献 30

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Metrics

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台站	归一化台站重要性	震中距/km	方位角/（°）	PGD/m	幅值—初始波动比	低频能量占比	屏蔽后\|ΔM_w\|
CNBA	1.000	27.7	46.5	1.183 2	219.22	0.961	0.042
JUNT	0.000	232.5	40.8	0.263 1	41.48	0.849	0.003
LSCH	0.112	189.2	12.5	0.257 4	81.44	0.843	0.015
OVLL	0.680	116.2	22.6	0.785 0	298.38	0.956	0.008
PCMU	0.710	326.5	184.7	0.048 8	20.52	0.777	0.047
PEDR	0.688	123.7	49.2	0.575 6	228.68	0.955	0.011
PFRJ	0.244	99.6	1.9	1.437 1	259.00	0.972	0.036

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