Recognition of small magnitude seismic events type based on time-frequency features and machine learning
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摘要:
本研究聚焦于华北地区小震级（ML≤3.0）地震事件，利用K-近邻算法（KNN）、自适应提升算法（AdaBoost）和轻量级梯度提升机算法（LGBM）对天然地震、人工爆炸以及矿震塌陷事件进行类型识别，得到了较好的效果。对地震事件波形记录和时频谱进行分析，提取了时间、P/S幅值比、频率、过零率、峰值振幅、峰值地面加速度、能量、信号、角度及其它比值10个类别的62个特征，将这些特征作为分类的基础。采用三种分类算法分别对二分类任务和三分类任务进行模型训练，最后对测试数据的类型进行识别，所有分类模型的识别准确率均达90.0%以上，其中LGBM的综合性能最强，AdaBoost次之；不同分类任务中天然地震与矿震分类模型的表现最佳。
Abstract:The identification and classification of seismic events hold significant importance in seismic monitoring and earthquake disaster mitigation. This research primarily focuses on
1935 seismic event data with low magnitude （ML≤3.0） in the North China region, encompassing three distinct types of events: natural earthquakes, artificial explosions, and mining collapses. Preliminary analysis involved the geographical distribution examination, annual trends, and magnitude distribution of these events. Preprocessing of raw seismic data included amplitude normalization, detrending, mean removal, and band-pass filtering （0.5—20 Hz）. Additionally, short-time Fourier transform analysis was utilized to visualize waveform and spectrogram characteristics, facilitating the observation and analysis of both time and frequency domain features. Based on the analysis results, 62 features across 10 categories, including time, P/S amplitude ratio, frequency, zero-crossing rate, peak amplitude, peak ground acceleration, energy, signal characteristics, angle, and other ratios, were extracted as the foundation for classification.This research employed K-Nearest Neighbors （KNN）, Adaptive Boosting （AdaBoost）, and Light Gradient Boosting Machine （LGBM） algorithms to train models using the extracted 62 features for binary and ternary classification tasks of natural earthquakes, artificial explosions, and mining collapses. The basic principles of KNN, AdaBoost, and LGBM algorithms were initially introduced, followed by a description of the training process for the classification models. To ensure balanced sample distribution for each event type, data were selected based on uniform distribution of time and geographical location. Ultimately, 545 events for each event type, totaling
1635 seismic events, were chosen as the sample data for building the classification models. The dataset was divided into training and testing sets using a holdout method, with 75% of the data used for model construction and validation, and 25% for evaluating model performance. The training data covered the main geographical range of the North China region （109.3°—123.5°E, 34.1°—43.7°N）, ensuring the models could capture the region’s diversity and complexity. The testing data covered a slightly different geographical range （110.8°—124.1°E, 34.9°—42.7°N）.The 62 features were used to train classification models by KNN, AdaBoost, and LGBM algorithms. Models were trained with number 0 representing natural earthquakes, number 1 representing artificial explosions, and number 2 representing mining collapses. Various classification models were evaluated using KNN, AdaBoost, and LGBM, with each model trained and tested 100 times for 0−1, 0−2, 1−2, and 0−1−2 classification tasks. AdaBoost and LGBM demonstrated superior performance compared to KNN across all classification tasks, especially in 0−1 and 0−1−2 classification task. LGBM consistently exhibited the best overall performance, maintaining an accuracy of over 95% and showing high stability. In different classification tasks, 0−2 classification yielded the most outstanding results, followed by 1−2 classification.
Following the training of classification models, the focus shifted to comprehensive evaluation of these models using testing data. Each model was used to identify the event types in the testing data, yielding performance results for each model across different classification tasks. Confusion matrices were generated based on identification results, demonstrating excellent performance for each classification task, particularly in the 0−2 classification using three different classification algorithms.
Based on confusion matrices, performance evaluation metrics, including accuracy, precision, recall, and F1 score, were calculated. In the 0−1 classification task, AdaBoost performed the best, achieving an accuracy of 96.69%. In the 0−2 classification task, all three algorithms performed well, with metrics exceeding 99.26%. In the 1−2 and 0−1−2 classifications, LGBM exhibited the best performance. Overall, each classification model demonstrated excellent performance, with accuracy, precision, recall, and F1 score all exceeding 89.71%.
LGBM exhibited superior overall performance, maintaining an accuracy of over 95.90% and demonstrating high stability. KNN still has significant room for improvement, possibly due to its sensitivity to data, resulting in relatively weaker performance compared to AdaBoost and LGBM. AdaBoost’s overall performance lies between LGBM and KNN.
Finally, ROC curves were plotted to visualize the recognition of the testing dataset using three different classification algorithms （KNN, AdaBoost, LGBM）. While KNN algorithm performance for 0−1 and 1−2 classifications requires optimization, all other models performed exceptionally well in the ternary classification scenario. Confusion matrices and evaluation metrics indicate that the constructed classification models perform well on testing data, with ROC curve analysis further confirming the excellent performance of the classification models in various tasks and revealing the applicability of different algorithms in their respective tasks, providing strong support for the practical application of the models.
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Campbell （1982，1983）将贝叶斯概率理论和极值概率模型相结合，发展出一种估算地震发生概率的贝叶斯极值分布模型。在此模型中，地震活动的先验估计值是基于地震矩、滑动速率、地震复发率和震级等数据计算得到的，而后将估计值用于贝叶斯理论的后验估算，或者用于研究区的历史地震活动性的评估方面（李拴虎等，2016）。
假设极端地震发生的贝叶斯概率遵循时间和震级指数的泊松分布（Campbell，1982），在周期T内，贝叶斯估算的最大震级Mmax的概率有时会超过限定的震级幅度m，其基本方程为
$P\left( {{M_{{\rm{max}}}}{\text{＞}} m{\rm{|}}T} \right) {\text{＝}} 1 - {\left( {\frac{{t''}}{{t'' {\text{＋}} T\left[ {1 - F\left( m \right)} \right]}}} \right)^{n''}},$
(1) 式中：P（Mmax＞m|T）表示在周期T内，贝叶斯估算的最大震级Mmax大于阈值震级m的概率；n″为地震发生次数的后验贝叶斯估算值；t″为地震发生时间的后验贝叶斯估算值；F（m）为震级的贝叶斯分布。
一般情况下，假定地震是独立的随机事件，且同一时刻不会发生两次以上地震，则地震发生的时间符合泊松（函数）分布，即
$P\left( {N {\text{＝}} n{\rm{|}}v,t} \right) {\text{＝}} \frac{{{{\left( {vt} \right)}^n}{{\rm{e}}^{ - vt}}}}{{n!}},$
(2) 式中，P（N＝ n|v，t）表示在时间t内发生n次地震的概率，v为地震的平均发生率。考虑到估计值v的不确定性，使用式（3）能更准确地表示贝叶斯的分布函数（Benjamin，1968；Benja-min，Cornell，1970；Campbell，1982），并采用积分方程的形式表示，即
$P\left( {N {\text{＝}} n{\rm{|}}t} \right) {\text{＝}} \mathop \smallint \nolimits_0^\infty P\left( {N {\text{＝}} n{\rm{|}}v} \right)f''\left( v \right){\rm{d}}v,$
(3) 式中f″（v）表示v的后验概率密度函数，由地震发生的前验分布计算得到。假设地震的发生是一个泊松过程，不确定的v可以用伽马分布表示，Mortgat和Shah （1979）把另一个伽马分布应用于后验概率密度函数f″（v）的计算，即
$f''\left( v \right) {\text{＝}} {K_1}{v^{n'' - 1}}{{\rm{e}}^{ - vt''}},$
(4) 式中，标准常数K1可以表示为K1＝ t″n″/Γ（n″），Γ（n″）为参数n″的伽马函数，Campbell （1982）在式（3）的基础上得到了泊松-伽马分布函数，即
$P\left( {N {\text{＝}} n{\rm{|}}n'',t'',t} \right) {\text{＝}} \frac{{\Gamma \left( {n {\text{＋}} n''} \right)}}{{n!\ \Gamma \left( {n''} \right)}}{\left( {\frac{{t''}}{{t {\text{＋}} t''}}} \right)^{n''}}{\left( {\frac{t}{{t {\text{＋}} t''}}} \right)^n}.$
(5) 式（5）是依据地震发生的泊松分布和v的伽马分布推导出来的，给出了在时间t内发生n次地震事件的概率，且地震发生率的不确定性影响着泊松分布的参数（Galanis et al，2002 ）。参数n″和t″可用下列关系式计算得到，即
${n'' {\text{＝}} {n_0} {\text{＋}} {{\left( {\displaystyle\frac{{v'}}{{\sigma _{{v}}'}}} \right)}^2}},\quad {t'' {\text{＝}} {t_0} {\text{＋}} \displaystyle\frac{{v'}}{{{{\left( {\sigma _{{v}}'} \right)}^2}}}},$
(6) 式中，t0为有记录的历史地震的时间长度，n0为在时间t0内观测到的地震次数，σv ′为参数v的标准偏差的先验值。Campbell （1982）提出了预测地震震级的最终表达式，即双截断贝叶斯指数-伽马分布。
$F\left( {m{\rm{|}}{m_{\rm{l}}},{m_{\rm{u}}}} \right) {\text{＝}} K''\left[ {1 - {{\left( {\frac{{m''}}{{m'' {\text{＋}} m - {m_{\rm{l}}}}}} \right)}^{\eta ''}}} \right],$
(7) $K'' {\text{＝}} {\left[ {1 - {{\left( {\frac{{m''}}{{m'' {\text{＋}} {m_{\rm{u}}} - {m_{\rm{l}}}}}} \right)}^{\eta ''}}} \right]^{ - 1}},$
(8) 式中，mu和ml分别为研究区地震震级的高值和低值，η″为震级大于ml的地震事件数的后验贝叶斯评价，m″为震级介于m与ml之间的地震事件数的后验贝叶斯评价。
先验估计：为了评价震级大于ml的地震发生率v的先验值v′，Campbell （1982）及Stavrakakis和Drakopoulos （1995）推荐了v′的计算方法，即
$v' {\text{＝}} \frac{{\mu uA}}{{{M_0}\left( {{m_{\rm{u}}}} \right)}} \frac{{{C_2} - b'}}{{b'}}{10^{b'\left( {{m_{\rm{u}}} - {m_{\rm{l}}}} \right)}},$
(9) 式中：μ为剪切模量；u为滑动速率；A为断层总面积；M0（mu）为震级上限值的地震矩；参数b′为b的先验估计值，即lgN＝a−bM中的b值；系数C2的定义来自于表达式lgM0＝ C1+mC2。震级-频率参数的先验估计β′可以用下式计算，即
$\beta ' {\text{＝}} b\ln 10.$
(10) 后验估计：v″为震级M＞ml的地震平均发生率v的后验估计；震级-频率参数的后验估计β″的计算公式为
$\left\{ \begin{array}{l}v'' {\text{＝}} \displaystyle\frac{{n''}}{{t''}};\quad V_v^{''} {\text{＝}} \displaystyle\frac{1}{{\sqrt {n''} }};\quad V_v' {\text{＝}} \displaystyle\frac{{{\sigma _v}\!\!'}}{{v'}},\\\beta '' {\text{＝}} \displaystyle\frac{{\eta ''}}{{m''}};\quad V_\beta ^{''}{\text{＝}} \displaystyle\frac{1}{{\sqrt {\eta ''} }};\quad V_\beta ' {\text{＝}} \displaystyle\frac{{{\sigma _\beta }\!\!'}}{{\beta '}};\quad m'' {\text{＝}} {n_0}\left( {\overline m - {m_{\rm l}}} \right) {\text{＋}} \displaystyle\frac{{\beta '}}{{{{\left( {\sigma _\beta '} \right)}^2}}};\quad \eta '' {\text{＝}} {n_0} {\text{＋}} {\left( {\frac{{\beta '}}{{\sigma _\beta '}}} \right)^2}, \end{array} \right.$
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研究范围选取河套断陷带区域（106.3°E—110.5°E，40.1°N—41.4°N），该地区位于鄂尔多斯地块北缘，主要活动断裂有狼山山前断裂、正谊关断裂、乌拉山山前断裂和包头断裂等，具有较强的发震背景，同时河套平原又是人口和经济比较集中的地区，所以研究此区域的地震发震概率具有重大的科学意义。本研究所用的地震目录来源于中国地震台网中心，选取时段为1970—2017年，中国地震台网中心的地震目录提供了完整的地震信息，包括发震的地点、时间和震级，这是贝叶斯极值分布评估地震发生概率的基础数据。目前，经验性的公式MS＝0.8ML＋0.83被认为是适合中国的震级转换公式（Bormann et al，2007 ），但Wang等（2014a）通过对龙门山断裂带的研究，认为公式MS＝1.01ML－1.02更符合南北地震带的实际情况，由于本文研究区域处于南北地震带的北段，所以采用此经验公式来进行震级转换。研究区内特定震级的贝叶斯概率，分别使用时段t为5，20，100年来计算。
岩石力学测试表明，应力差Δσ与b值之间存在反比关系，所以b值被认为是地壳的“应力计”（Schorlemmer et al，2005 ），区域的应力水平可以通过b值来得以反映（Wiemer，Schorlem-mer，2007）。根据古登堡-里克特（Gutenberg-Richter，简写为G-R）公式lgN＝a−bM来计算b值，考虑到研究区地震目录的完整性，选取MS≥2.0的地震事件，通过地震目录分布情况拟合出G-R公式中的b值（图1）。
滑动速率u在平均地震发生率的估算中起着重要作用，Brune （1968）的模型尤其适合计算接近块体边界区域的滑动速率（Tselentis et al，1988 ），即
$u {\text{＝}} \frac{{\mathop \sum \nolimits {M_0}}}{{\mu {t_0}A}},$
(12) 式中，∑M0为过去t0时段内所发生地震的地震矩之和，A为断层滑动区域的面积，μ为剪切模量（Stavrakakis，Drakopoulos，1995）。地震矩的计算使用Hanks和Kanamori （1979）提出的公式lgM0＝16.1＋1.5M，剪切模量μ一般采用默认值3×104 MPa，此值通用于整个地壳。有多种方法可以计算A值，不同的计算方法会导致不同的结果，一般由多边形顶点测量出的A值可能是最大的（Wang et al，2014a ），但地震区域的边界不可能是直线，所以此测量方法只是一种近似计算。在本文中，较低震级为MS5.0，较大震级为目录时段内发生的最大地震的震级，贝叶斯计算所需参数值列于表1。
表 1 河套断陷带的贝叶斯估计参数Table 1. Parameters of the Bayesian estimate for the Hetao riftu/（cm·a–1） A/km2 历史最大震级MS mu $\scriptstyle{\overline m}$ 
n0 b 0.22 38 875 7.0 7.0 7.5 8.0 8.5 5.3 37 0.76 假设Vv′和Vβ′的3个变异系数均为0.10，0.25，1.0，河套断陷带的地震活动参数的后验估计列于表2。变异系数Vv是一个非常重要的参数（Campbell，1983；Stavrakakis，Drakopoulos，1995），会导致历史数据先验估计值出现偏差，分析Vv′＝0.1，0.25，1.0等3种情况下的结果可知：当Vv′＝1.0时，地震事件的发生主要由历史地震事件控制；当Vv′＝0.1时，地震事件的发生主要基于先验值的估计值（Campbell，1983；Parvez，2007）。贝叶斯分布的一个重要特点就是条件关联性，即把地震活动先验估计与历史地震事件结合起来，但是贝叶斯极值的灵敏度不会随着参数数量的增加而降低，不同来源的信息均应纳入到现有的统计范畴，以便更全面地评估孕震区内的地震危险性（Wang et al，2014b ，2015）。
表 2 研究区内参数v和β的先验估计和后验估计Table 2. Prior and posterior estimates of parameters v and β for the studied areamu 先验估计 后验估计 v′ β′ Vv′，Vβ′ v″ β″ Vv″，Vβ″ 7.0 4.84 1.54 0.10 0.36 1.64 0.09 4.84 1.54 0.25 0.15 1.84 0.14 4.84 1.54 1.00 0.11 1.98 0.16 7.5 1.86 1.54 0.10 0.33 1.64 0.09 1.86 1.54 0.25 0.15 1.84 0.14 1.86 1.54 1.00 0.11 1.98 0.16 8.0 0.72 1.54 0.10 0.28 1.64 0.09 0.72 1.54 0.25 0.14 1.84 0.14 0.72 1.54 1.00 0.11 1.98 0.16 8.5 0.28 1.54 0.10 0.19 1.64 0.09 0.28 1.54 0.25 0.13 1.84 0.14 0.28 1.54 1.00 0.11 1.98 0.16 在Vv′和Vβ′的3个变异系数分别为0.10，0.25，1.0的条件下，分别预测t为5，20，100年这3个时段内MS≥5.0地震的发生概率（图2）。地震发生概率随着震级的增大而不断衰减，当接近最大震级时，衰减最为严重。随着mu的减小和t的增大，地震事件的发生概率增大。研究中使用的起始震级为MS5.0，此震级通常被认为是破坏性地震的震级阈值（Parvez，2007）。在t＝5 a时，研究区内MS5.0地震的发震概率小于0.36，MS8.0地震的发震概率小于0.000 05。地震发生概率在MS＝5.0，Vv′＝0.1的条件下最小；在Vv′＝1.0，mu＝7.0，7.5，8.0，8.5时最大，与t值的相关性不大。当t＝5，20，100 a时，MS5.0地震的发震概率分别为0.06—0.36，0.20—0.82，0.68—1.0。
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图 2 不同条件下的地震发生概率Figure 2. Probabilities of earthquake occurrence under different conditions基于极值分布的贝叶斯概率理论将各种不确定性的参数用于地震活动性的量化分析，其重要特点是当有新的信息加入模型时，当前的概率值也会随着变化，这将有利于地震活动、断裂构造、地质资料和历史观测资料等有用信息的整合，进而对地震发生的概率进行综合判定。这也体现出，当历史资料不是很完整、时间覆盖相对较短或数据量不充足时，贝叶斯概率理论则具有明显的优势。
本文地震目录采用中国地震台网中心的最新数据，成都理工大学王莹博士提供了计算程序并对计算进行了指导，作者在此一并表示感谢。
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图 1 华北地区训练数据（a）和测试数据（b）的地震事件分布图
Figure 1. Distribution map of train （a） and test （b） data of seismic events in North China
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图 2 2008—2016年华北地区地震事件年度分布
Figure 2. Annual distribution of seismic events of North China area during 2008−2016
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图 3 训练数据（a）和测试数据（b）地震事件震级分布统计
Figure 3. Magnitude distribution statistics of train （a） and test data （b） seismic events
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图 4 天然地震（a）、人工爆炸（b）、矿震塌陷（c）的波形记录和时频图
Figure 4. Waveform records and time-frequency spectrograms of natural earthquake （a），artificial explosion （b） and mining collapse （c），respectively
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图 5 特征分布图
（a） 阈值之上的平均下降频率特征分布；（b） 滤波波段为9.5—10.5 Hz的P/S振幅比特征分布；（c） 1—20 Hz频带的P/S振幅比特征分布
Figure 5. Distribution of features
（a） Distributions of features of the decay average frequency above the threshold；（b） The P/S amplitude ratio distribution at 9.5—10.5 Hz filter band;（c） The P/S amplitude ratio distribution at the frequency band from 1 to 20 Hz
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图 6 采用KNN （a），AdaBoost （b），LGBM （c）对分类模型训练100次的准确率
Figure 6. The accuracy of classification models trained 100 times using KNN （a）， AdaBoost （b）， and LGBM （c），respectively
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图 7 分类模型对测试数据的识别结果混淆矩阵
Figure 7. Confusion matrix of identification results of test data by classification model （a）—（d） KNN；（e）—（h） AdaBoost；（i）—（l） LGBM
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图 8 不同分类模型的ROC曲线
（a） 测试集0−1，0−2，1−2；（b） 测试集0−1−2
Figure 8. ROC curves of different classification models
（a） 0−1，0−2，1−2 classification models；（b） 0−1−2 classification model
表 1 所提取的特征表
Table 1 Table of extracted features
特征 物理意义 数量 时间 地震波形从起始点到达波峰所需的时间；从波峰到达结束点所需的时间；从起始点到结束点所经历的总时间；地震波形超过设定阈值的持续时间；地震波形在超过设定阈值后到达波峰所需的时间；地震波形在超过设定阈值后从波峰到结束点所需的时间；地震波形在超过设定阈值前波形的上升、下降时间；两个相邻的波峰或波谷之间的时间间隔，即两个相邻波峰或波谷之间的周期长度（Kim et al，2 021；薛思敏等，2 022）。 9 P/S幅值比 P波与S波峰值振幅之比（Yıldırım et al，2 011）；对P波、S波进行傅里叶变换，滤波波段为1—20 Hz时振幅之比（Wang et al，2 021）。 21 频率 地震信号中波形每秒振动的次数，为周期的倒数（Levshin et al，1995）；中心频率，地震信号在频率域中的中心位置；主频率，地震信号中振幅最大的频率；平均频率，地震信号频谱的加权平均频率；地震波形在上升或下降阶段的平均频率；波形上升、下降时，地震信号在超过设定阈值的情况下的平均频率；地震信号复倒频谱的实部（魏富胜，黎明，
2 003）。9 过零率 地震波形从正向值变为负向值，或从负向值变为正向值的次数；地震信号在超过设定阈值的情况下的过零率；峰值振幅前、后的过零率；地震信号在超过设定阈值的情况下的最大振幅前、后的过零率（Dargahi-Noubary，1998）。 6 峰值振幅 地震波形中振幅达到的最大值（Horasan et al，2009；Badawy et al，2019）。 1 峰值地面加速度 地震信号中垂直地面方向的最大加速度值（Goforth et al，2006）。 1 能量 地震信号总能量；峰值振幅前吸收能量、峰值振幅后衰减能量（刘莎等，2012）。 3 信号 地震信号强度；信号均方根（Laasri et al，2015；Saad et al，2019）。 2 其它比值 地震波形的上升时间、下降时间与峰值振幅之比（the ratio of rise time to amplitude，缩写为RA；the ratio of decay time to amplitude，缩写为DA）；阈值之上的上升、下降时间和振幅的比值；RA，DA与地震波形的平均频率之比（ratio of RA to average frequency，缩写为RA/AF；ratio of DA to average frequency，缩写为DA/AF）（吴顺川等，2020）。 6 角度 地震波形的上升、下降角度，为RA，DA的反正切函数（Ma et al，2015）；地震信号在超过设定阈值的情况下的上升、下降角度。 4 
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表 2 不同分类模型准确率平均值、最大值、最小值
Table 2 Average，maximum and minimum accuracy of different classification model
分类模型 0−1准确率 0−2准确率 1−2准确率 0−1−2准确率 平均值 最大值 最小值 平均值 最大值 最小值 平均值 最大值 最小值 平均值 最大值 最小值 KNN 89.66% 91.22% 87.80% 98.84% 99.61% 98.05% 94.73% 95.90% 93.07% 89.19% 90.68% 87.30% AdaBoost 96.99% 97.95% 94.63% 99.28% 99.80% 98.24% 98.12% 99.51% 97.07% 95.17% 96.35% 93.94% LGBM 97.03% 98.05% 95.90% 99.10% 99.71% 98.34% 97.95% 98.73% 96.98% 97.01% 97.98% 96.16%
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表 3 不同分类模型对不同分类任务的评价指标
Table 3 Evaluation metrics of different classification models for different classification task
分类模型 评价指标 0−1 0−2 1−2 0−1−2 KNN 准确率 90.81% 99.63% 94.49% 91.75% 精度 91.73% 100.00% 94.81% 93.15% 召回率 89.71% 99.26% 94.12% 93.03% F1分数 90.71% 99.63% 94.47% 93.03% AdaBoost 准确率 96.69% 99.63% 98.16% 95.10% 精度 94.41% 100.00% 98.52% 96.11% 召回率 99.26% 99.26% 97.79% 98.99% F1分数 96.75% 99.63% 98.15% 97.52% LGBM 准确率 96.32% 99.26% 98.53% 97.30% 精度 93.75% 99.26% 98.53% 97.31% 召回率 99.26% 99.26% 98.53% 97.30% F1分数 96.44% 99.26% 98.53% 97.30%
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