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Article(id=1322506534236570596, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1322506406058635943, articleNumber=null, orderNo=null, doi=10.14075/j.jgg.2024.12.586, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1735574400000, receivedDateStr=2024-12-31, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793239728745, onlineDateStr=2026-10-29, pubDate=1763136000000, pubDateStr=2025-11-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793239728745, onlineIssueDateStr=2026-10-29, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793239728745, creator=13701087609, updateTime=1793239728745, updator=13701087609, issue=Issue{id=1322506406058635943, tenantId=1146029695717560320, journalId=1281212831689347082, year='2025', volume='45', issue='11', pageStart='1101', pageEnd='1210', issueExtLink='null', onlineDate='null', pubDate='1763136000000', pubDateStr='2025-11-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793239698184, creator='13701087609', updateTime=1793239698184, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=1127, endPage=1133, ext={EN=ArticleExt(id=1322506534400148453, articleId=1322506534236570596, tenantId=1146029695717560320, journalId=1281212831689347082, language=EN, title=Simulation on Seasonal Microseismic Signals at Gravity Station Using Data-Driven Approaches, columnId=null, journalTitle=Journal of Geodesy and Geodynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

The seasonal microseismic signals at gravity stations are difficult to physically simulate and estimate due to the combined effects of randomness, intermittency, and periodicity. Based on the 1 Hz gravity solid tide data of Wushi continuous gravity observation station from 2008 to 2024, we extract the microseismic signals in DF frequency band using the apparent vertical displacement analysis method. An improved variational mode decomposition(IVMD) coupled with the long short-term memory(LSTM) neural network algorithm is proposed to establish a data model for seasonal gravity microseismic signals. The results show that the IVMD-LSTM model can better reflect the annual variation differences of seasonal signals compared to the LSTM model. Moreover, the correlation coefficient between model data using data-driven methods and the snow depth data from GLDAS and ERA5 models increased to 0.5. This study can provide a new processing method for model establishment using seasonal gravity microseismic signals and their application in earthquake analysis and forecasting.

, authors=Zhengran WANG1, Jin WEI1, *, Huiling LI2, Guangliang YANG1, Minzhang HU1, authorsList=Zhengran WANG, Jin WEI, Huiling LI, Guangliang YANG, Minzhang HU, authorCompany=null, correspAuthors=Jin WEI, authorNote=

WANG Zhengran, postgraduate, major in the analysis and application of continuous gravity observation data, E-mail:

, correspAuthorsNote=null, copyrightStatement=All rights reserved. Unauthorized reproduction is prohibited., copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1322506537856254968, articleId=1322506534236570596, tenantId=1146029695717560320, journalId=1281212831689347082, language=CN, title=数据驱动的重力站季节性微震信号模拟研究, columnId=1322506242858271689, journalTitle=大地测量与地球动力学, columnName=地球物理解释, runingTitle=null, highlight=null, articleAbstract=

重力站季节性微震信号受随机性、间歇性、周期性因素的综合影响, 难以进行物理模拟和推估。本文基于乌什连续重力观测站2008-2024年1 Hz重力固体潮数据, 在采用视垂直位移分析方法提取DF频段微震信号的基础上, 提出改进的变分模态分解(improved variational mode decomposition, IVMD)算法与长短期记忆(long short-term memory, LSTM)神经网络算法相耦合的方法, 建立重力季节性微震信号的数据模型。结果表明, 与LSTM模型相比, IVMD-LSTM模型更能反映季节性信号的年变差异, 且利用数据驱动建立的模型数据与GLDAS和ERA5模型雪深数据的相关系数提升至0.5。本文研究结果可为基于重力微震季节性信号的模型建立和地震分析预报应用提供一种新的处理方法。

, authors=王诤冉1, 韦进1, *, 李惠玲2, 杨光亮1, 胡敏章1, authorsList=王诤冉, 韦进, 李惠玲, 杨光亮, 胡敏章, authorCompany=null, correspAuthors=韦进, authorNote=

王诤冉, 硕士生, 主要从事连续重力观测数据分析与应用研究, E-mail:

, correspAuthorsNote=

韦进, 博士, 副研究员, 主要从事重力数据分析与应用研究, E-mail:

WEI Jin, PhD, associate researcher, major in the analysis and application of gravity data, E-mail:

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WANG Zhengran, postgraduate, major in the analysis and application of continuous gravity observation data, E-mail:

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Ct为神经元t时刻后的记忆单元状态；ht为神经元t时刻后的隐藏状态；xt为输入的信息；σ表示sigmoid激活函数，值域为[0, 1]；tanh表示tanh激活函数，值域为[－1, 1]。虚线框a为神经元记忆单元；虚线框b为遗忘门；虚线框c为输入门；虚线框d为输出门

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Evaluation indexes of estimation models

, figureFileSmall=null, figureFileBig=null, tableContent=
模型 评估指标 Kim/d
10 182 365 730
LSTM RMSE/10-6m 0.028 9 0.029 2 0.025 5 0.025 6
MAE/10-6m 0.018 0 0.018 2 0.013 4 0.014 0
MAPE/% 49.27 49.29 41.70 41.34
IVMD-LSTM RMSE/10-6m 0.022 3 0.022 9 0.023 4 0.024 2
MAE/10-6m 0.012 1 0.012 5 0.012 9 0.013 1
MAPE/% 35.81 36.41 37.34 38.24
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推估模型评估指标

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模型 评估指标 Kim/d
10 182 365 730
LSTM RMSE/10-6m 0.028 9 0.029 2 0.025 5 0.025 6
MAE/10-6m 0.018 0 0.018 2 0.013 4 0.014 0
MAPE/% 49.27 49.29 41.70 41.34
IVMD-LSTM RMSE/10-6m 0.022 3 0.022 9 0.023 4 0.024 2
MAE/10-6m 0.012 1 0.012 5 0.012 9 0.013 1
MAPE/% 35.81 36.41 37.34 38.24
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数据驱动的重力站季节性微震信号模拟研究
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王诤冉 1 , 韦进 1, * , 李惠玲 2 , 杨光亮 1 , 胡敏章 1
大地测量与地球动力学 | 地球物理解释 2025,45(11): 1127-1133
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大地测量与地球动力学 |地球物理解释 2025 , 45 (11) : 1127 -1133
数据驱动的重力站季节性微震信号模拟研究
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王诤冉1 , 韦进1, * , 李惠玲2, 杨光亮1, 胡敏章1
作者信息
  • 1 中国地震局地震大地测量重点实验室, 武汉市洪山测路40号, 430071
  • 2 山东省地震局泰安地震监测中心站, 山东省泰安市罗汉崖2号, 271000
通讯作者:

韦进, 博士, 副研究员, 主要从事重力数据分析与应用研究, E-mail:

WEI Jin, PhD, associate researcher, major in the analysis and application of gravity data, E-mail:

作者简介:

王诤冉, 硕士生, 主要从事连续重力观测数据分析与应用研究, E-mail:

Simulation on Seasonal Microseismic Signals at Gravity Station Using Data-Driven Approaches
Zhengran WANG1 , Jin WEI1, * , Huiling LI2, Guangliang YANG1, Minzhang HU1
Affiliations
  • 1 Key Laboratory of Earthquake Geodesy, CEA, 40 Hongshance Road, Wuhan 430071, China
  • 2 Tai'an Earthquake Monitoring Center Station of Shandong Earthquake Agency, 2 Luohanya, Tai'an 271000, China

    • WANG Zhengran, postgraduate, major in the analysis and application of continuous gravity observation data, E-mail:

出版时间: 2025-11-15 doi: 10.14075/j.jgg.2024.12.586
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摘要
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重力站季节性微震信号受随机性、间歇性、周期性因素的综合影响, 难以进行物理模拟和推估。本文基于乌什连续重力观测站2008-2024年1 Hz重力固体潮数据, 在采用视垂直位移分析方法提取DF频段微震信号的基础上, 提出改进的变分模态分解(improved variational mode decomposition, IVMD)算法与长短期记忆(long short-term memory, LSTM)神经网络算法相耦合的方法, 建立重力季节性微震信号的数据模型。结果表明, 与LSTM模型相比, IVMD-LSTM模型更能反映季节性信号的年变差异, 且利用数据驱动建立的模型数据与GLDAS和ERA5模型雪深数据的相关系数提升至0.5。本文研究结果可为基于重力微震季节性信号的模型建立和地震分析预报应用提供一种新的处理方法。

gPhone重力仪  /  视垂直位移季节性变化  /  长短期记忆神经网络  /  变分模态分解

The seasonal microseismic signals at gravity stations are difficult to physically simulate and estimate due to the combined effects of randomness, intermittency, and periodicity. Based on the 1 Hz gravity solid tide data of Wushi continuous gravity observation station from 2008 to 2024, we extract the microseismic signals in DF frequency band using the apparent vertical displacement analysis method. An improved variational mode decomposition(IVMD) coupled with the long short-term memory(LSTM) neural network algorithm is proposed to establish a data model for seasonal gravity microseismic signals. The results show that the IVMD-LSTM model can better reflect the annual variation differences of seasonal signals compared to the LSTM model. Moreover, the correlation coefficient between model data using data-driven methods and the snow depth data from GLDAS and ERA5 models increased to 0.5. This study can provide a new processing method for model establishment using seasonal gravity microseismic signals and their application in earthquake analysis and forecasting.

gPhone gravimeter  /  seasonal variation of apparent vertical displacement  /  long short-term memory(LSTM) neural network  /  variational mode decomposition(VMD)
王诤冉, 韦进, 李惠玲, 杨光亮, 胡敏章. 数据驱动的重力站季节性微震信号模拟研究. 大地测量与地球动力学, 2025 , 45 (11) : 1127 -1133 . DOI: 10.14075/j.jgg.2024.12.586
Zhengran WANG, Jin WEI, Huiling LI, Guangliang YANG, Minzhang HU. Simulation on Seasonal Microseismic Signals at Gravity Station Using Data-Driven Approaches[J]. Journal of Geodesy and Geodynamics, 2025 , 45 (11) : 1127 -1133 . DOI: 10.14075/j.jgg.2024.12.586
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在地面重力观测方式中，连续重力观测仪具有频带宽、时间分辨率高等优点，其中gPhone重力仪是当前应用广泛的一种连续重力仪，分辨率通常可达μGal级别。季节性微震信号通常指地球上由于季节性变化而产生的微小地震活动，可能由多种因素引起，包括气候变化、降水、冰川融化或冻土变化等，主要涉及物质运移引起的重力季节性变化。近年来，除在潮汐频段[1]外，微震信号频段也发现可能存在与地震震源有关的异常信号[2]。这些信号可为判断观测站周边未来地震活动形势提供一类新的依据。然而，受重力站周边各类因素的影响，微震信号常表现出非线性、随机性、昼夜差异性和季节性等特征[3]，特别是在沿海地区和临海站，微震信号的异常变化多被判定为海浪激发的第二类脉动信号[4]。这些因素都会对判断震源产生的异常信号造成干扰[5-6]。在分析这类重力信号的影响时，很难利用统一的物理模型解释所有的变化规律[4, 7]，因此可采用模态分解和物理模型相结合的方法进行研究。胡小刚等[8]利用小波分析方法分析时变重力信号的气压效应；王迪晋等[9]利用集合经验模态分解(EEMD)方法研究mHz频段的气压负荷影响规律。
近年来随着基于数据驱动的数据建模方法的快速发展，利用人工神经网络建立高时空分辨率数据模型的方法被应用于水利、电力行业中，且针对数据的推估和预测已取得较好的效果[10-11]。同时，在GRACE等效水高和地表形变量预测及数据预处理时，采用LSTM神经网络对时间序列进行预测可提高其长期特征的提取能力[12-13]。但这些研究在采用耦合模型时主要依靠人为或经验选取神经网络的结构参数、数据分解层数等，这会影响数据建模效率。
本研究采用数据驱动建模方法，利用新疆乌什重力站2008—2024年1 Hz观测数据进行时频分析和视垂直位移分析，提出改进的变分模态分解(IVMD)算法与长短期记忆(LSTM)神经网络相结合的方法，构建重力季节性微震信号的数据模型。通过均方根误差(RMSE)、平均绝对误差(MAE)和平均绝对百分比误差(MAPE)等指标对模型进行评估，验证LSTM和IVMD-LSTM模型的可行性。同时，探讨模型数据与GLDAS和ERA5冰雪数据的相关性，以评估方法的可靠性。
1 基于IVMD-LSTM方法的微震信号模型建立
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1.1 乌什重力站及视垂直位移变化特征
乌什重力站位于新疆天山南麓的阿克苏地区(图 1(a))，自2008年建站以来，gPhone重力仪以1 Hz频率连续观测17 a，仅在2018-02因更换电源短暂停测。对乌什重力站观测数据进行时频分析和视垂直位移计算[7]，结果如图 1(b)、1(c)所示，可以看出季节性变化特征：春冬季高值、夏秋季低值。由时频分析结果(图 1(b))可知，0.1~0.3 Hz范围内的季节性信号存在间歇性增强。基于上述分析结果，本文建立LSTM和IVMD-LSTM模型。
1.2 长短期记忆神经网络
长短期记忆(LSTM)神经网络是在分析具有长期依赖关系的时间序列数据时，为克服循环神经网络(recurrent neural network, RNN)的梯度消失和梯度爆炸问题，在隐含层中增加记忆单元状态，同时建立遗忘门、输入门和输出门3个控制单元的神经网络(图 2)。
在利用LSTM对时间序列进行建模时，将时间序列t-1时刻的数据作为输入信息，代入到LSTM模型中计算出t时刻的预测值。然后根据预测值和实际值之间的误差进行反向计算，更新遗忘门、输入门、输出门以及激活函数的权值和阈值，直到满足最大迭代次数。
在训练LSTM模型时，假设时间序列样本数为NS，本文选择前NP个样本作为训练数据，剩余部分采样数为NT。设定延时步长数为Kim，推估数为Zim。利用视垂直位移建立训练数据矩阵Train和测试数据矩阵Test，其中训练数据矩阵Train由特征数据矩阵PTrain(图 2中ht-1和xt)和响应序列矩阵TTrain组成。延时步长数Kim等于神经元数，与特征数据矩阵PTrain有关；推估数Zim与未来的响应序列矩阵TTrain有关。
利用推估数Zim、延时步长数Kim以及训练数NP将观测数据组成PTrain和TTrain矩阵。然后对由Kim个神经元组成的神经元网络进行1次LSTM前向计算，根据优化的神经元各门和激活函数的权值和阈值，得到新的神经网络。重复该步骤直至满足设定的最大训练次数就可得到训练模型。
1.3 变分模态分解(VMD)及其优化(IVMD)
变分模态分解(VMD)是一个完全非递归分解模型，目标是将输入信号f(t)分解为离散的子信号μk。在VMD算法中，分解模态数K需要合理选择，过小的K值会造成欠分解，而过大的K值会造成过分解。本文提出的改进变分模态分解(IVMD)方法(图 3)综合考虑分解精度与计算效率，以确定K值的最优解Kbest。将“分解残差”定义为原始数据与各分解模态之和的差(简称残差)。逐步增加K值，对分解残差进行Durbin-Watson检验(DW检验)，直至检验d值在2左右，表明分解残差自相关特征已不明显。
1.4 基于IVMD-LSTM的视垂直位移耦合模型建立流程
IVMD和LSTM耦合模型建模步骤如下：1)选定前n个月的视垂直位移序列作为模型的输入；2)利用IVMD方法对该序列进行分解，得到最优的k个分量序列；3)将每个分量分别输入到LSTM预测模型中，得到k个预测模型；4)将k个预测模型的预测值相加，得到微震信号的预测值。
2 视垂直位移模型建立与评估
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2.1 基于IVMD的微震信号分解方法研究
针对2008—2024年乌什重力站视垂直位移时间序列，利用IVMD方法按K=1, …, 4进行分解，计算分解残差。本文不仅使用DW检验方法进行检验，同时利用Quantile-Quantile图(一种用于比较2个概率分布的图形化工具，常用于检验数据是否符合某一特定分布或者比较2个数据集的分布形状，下文简称Q-Q图)再次进行检验。
利用VMD方法对视垂直位移进行K层模态分解，结果如图 4所示。可以看出，分解的第1模态(IMF1)均表现出季节性变化特征，且分解量级为(0.02~0.12)×10-6 m，为重力站视垂直位移变化的主要模态。其他模态虽也都表现出季节性变化特征(春冬季幅值高、夏秋季幅值低)，但量级不超过0.03×10-6 m，且高模态的量级小于低模态。
图 5(a)为DW检验结果，可以看出，当K增大到3时，DW检验d值在1.5~2之间，而当K增大到4时，d值超过2。图 5(b)为Q-Q图检验结果，可以看出，随着K值增大，残差分位数和标准分位数的关系趋于直线。检验结果均表明当K=4时，分解残差趋于不相关和白噪声，可以用K=4时的分解模态进行数学建模。
2.2 基于IVMD-LSTM的微震信号视垂直位移模型建立与评估
本文不仅将视垂直位移作为训练数据代入LSTM神经网络中进行训练建模，同时将K=4时的VMD分解模态作为LSTM训练数据进行建模，比较2种模型与观测数据之间的误差指标。
2.2.1 LSTM神经网络训练、测试和推估比较
在利用LSTM进行神经网络训练时，本文选择延时步长数Kim为10 d、182 d、365 d、730 d，推估数Zim为10 d，训练数据为所有采样数的1/2，建立4个模型并进行比较。
从模型测试与推估结果来看，当延时步长数Kim较小时(图 6(a)、6(b))，无法复现视垂直位移的季节性变化特征。当Kim=365 d时(图 6(c))，季节性信号得以被推估，整体量级为0.05×10-6 m。当Kim=730 d时(图 6(d))，推估的季节性信号幅值与Kim=365 d时相比变化不明显。
2.2.2 IVMD-LSTM模型训练、测试和推估比较
前文分析认为，当K=4时，残差趋于白噪声。图 7为IVMD-LSTM模型的训练、测试与推估结果，其中训练数据和测试数据为K=4时IVMD各模态之和。可以看出，当Kim较小时(图 7(a))，可以较好地复现视垂直位移的季节性变化特征，且该信号量级在(0.09~0.1)×10-6 m之间，更接近原视垂直位移幅值。随着神经元数量的增加(图 7(b)~(d))，推估结果之间并未表现出明显差异。由此可见，利用LSTM对IVMD模型分解结果进行数据建模时，可以使用更少的神经网络来完成训练、测试和推估工作。
2.2.3 模型推估差异及其评估指标分析
将LSTM和IVMD-LSTM模型的推估残差进行对比(图 8)，并将残差的均方根误差(RMSE)、平均绝对误差(MAE)、平均绝对百分比误差(MAPE)作为模型评估指标，计算结果见表 1。为保持评估时长一致，选择Kim=365 d、730 d和K=4进行比较。
从图 8可以看出，无论是LSTM还是IVMD-LSTM模型都能改正季节性信号。对于安静时段(夏季)，2种方法结果中依然存在部分季节性信号，但量级已经小于0.01×10-6 m(图 8(b)、8(d))，表明2种方法都能改正视垂直位移中的季节性信号。不同的是，利用LSTM改正后安静时段残差的季节性变化量级约为0.01×10-6 m(图 8(b))，而IVMD-LSTM只有0.005×10-6 m(图 8(d))，说明组合模型能够更准确地推估出季节性信号。对于噪声水平较高的春冬季，IVMD-LSTM模型4种策略结果的振幅(图 7)也都大于LSTM模型(图 6)，表明组合模型在噪声水平较高时也能准确推估季节性信号。
从表 1可以看出，当Kim增大时，LSTM模型各评估指标逐渐收敛，这应该与Kim=365 d时才能估计出周期性信号有关(图 6)。而IVMD-LSTM模型各评估指标普遍优于LSTM模型，且当Kim=10 d时，各指标就已经优于LSTM模型Kim=730 d时的计算结果。这表明IVMD-LSTM模型采用更少的神经元数量就可获得更完整且精度更高的季节性信号。综上可知，IVMD-LSTM模型可以利用更少的神经元数量给出与观测数据更接近的季节性信号。
2.3 数据驱动的模型数据与气象数据集的相关性研究
研究表明，本文研究频段的季节性变化可能与降雨、冰雪等数据存在相关性[4]。为此，本文采用美国NASA发布的全球陆地数据同化系统(GLDAS)和欧洲中期天气预报中心(ECMWF)发布的第五代全球大气再分析数据集(ERA5)进行分析。
比较2008年以来2个全球气象数据集(降雨、降雪、雪深等)与乌什重力站模型数据(观测数据、LSTM和IVMD-LSTM模型视垂直位移)的相关性。从模型数据来看(图 9(a))，IVMD-LSTM结果更贴近重力观测数据，并且能更加凸显季节性变化振幅差异。从乌什重力站模型数据与GLDAS和ERA5数据集的互相关结果来看(图 9(b)、9(c))，相关系数都超过0.41。降雨与模型数据都表现为负相关，相关系数最高可达-0.72；降雪和雪深与模型数据表现为正相关，相关系数最高可达0.53。其中GLDAS的降雨、雪深数据集与数据驱动的模型数据的相关系数都超过0.5，表明本文提出的利用数据驱动的建模方法有利于后续开展微震信号季节性因素影响研究。
3 结语
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乌什重力站2008—2024年1 Hz采样的重力固体潮观测数据的时频分析结果表明，功率谱密度和0.1~0.5 Hz的视垂直位移时间序列都具有春冬季值高、夏秋季值低的季节性变化特征。在建立季节性变化序列模型时，IVMD-LSTM耦合模型可以利用更少的神经网络获得更加接近观测数据的季节性变化特征模型。IVMD-LSTM模型的RMSE、MAE、MAPE评估指标都优于LSTM模型。
GLDAS和ERA5气象数据集与模型数据的相关性分析结果表明，利用数据驱动方法获得的模型数据与2个数据集中雪深数据的相关系数都接近或超过0.5。该方法可为基于数据驱动的地球物理观测数据模型的建立提供参考，也能为冰雪对乌什重力站微震信号的影响分析提供有效的研究方法。
基金
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  • 国家自然科学基金(41204058)
  • 中国地震局地震科技星火计划(XH23026C)
  • 科技基础资源调查专项(2023FY101500)
文献
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2025年第45卷第11期
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文章信息
doi: 10.14075/j.jgg.2024.12.586
  • 接收时间：2024-12-31
  • 首发时间：2026-10-29
  • 出版时间：2025-11-15
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出版历史
  • 收稿日期：2024-12-31
基金
National Natural Science Foundation of China(41204058)
国家自然科学基金(41204058)
The Spark Program of Earthquake Technology of CEA(XH23026C)
中国地震局地震科技星火计划(XH23026C)
Special Fund for Science and Technology Basic Resources Investigation(2023FY101500)
科技基础资源调查专项(2023FY101500)
作者信息
    1 中国地震局地震大地测量重点实验室, 武汉市洪山测路40号, 430071
    2 山东省地震局泰安地震监测中心站, 山东省泰安市罗汉崖2号, 271000

通讯作者:

韦进, 博士, 副研究员, 主要从事重力数据分析与应用研究, E-mail:

WEI Jin, PhD, associate researcher, major in the analysis and application of gravity data, E-mail:

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https://castjournals.cast.org.cn/joweb/ddcl/CN/10.14075/j.jgg.2024.12.586
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