基于方差主轴方法的地震动三分量相关性研究

王元杰, 赵晓芬, 王君杰, 温增平

王元杰,赵晓芬,王君杰,温增平. 2025. 基于方差主轴方法的地震动三分量相关性研究. 地震学报,47(2):254−268. DOI: 10.11939/jass.20230085
引用本文: 王元杰,赵晓芬,王君杰,温增平. 2025. 基于方差主轴方法的地震动三分量相关性研究. 地震学报,47(2):254−268. DOI: 10.11939/jass.20230085
Wang Y J,Zhao X F,Wang J J,Wen Z P. 2025. The correlation between three components of ground motion at the same point based on the variance principal axis method. Acta Seismologica Sinica47(2):254−268. DOI: 10.11939/jass.20230085
Citation: Wang Y J,Zhao X F,Wang J J,Wen Z P. 2025. The correlation between three components of ground motion at the same point based on the variance principal axis method. Acta Seismologica Sinica47(2):254−268. DOI: 10.11939/jass.20230085

基于方差主轴方法的地震动三分量相关性研究

基金项目: 国家自然科学基金面上项目(52078384)资助
详细信息
    作者简介:

    王元杰,在读硕士研究生,主要从事强地面运动与结构抗震方面的研究,e-mail:1903943689@qq.com

    通讯作者:

    赵晓芬,博士,助理研究员,主要从事工程地震学方面的研究,e-mail:929921908@qq.com

  • 中图分类号: P315.9

The correlation between three components of ground motion at the same point based on the variance principal axis method

  • 摘要:

    基于国内外11次中、强地震的近场和远场强震动记录,采用方差主轴方法对地震动三个平动分量的相关性进行了研究。将地震动划分为上升段、强震段和下降段,进行最小主轴的时变特性分析,结果显示,强震段和下降段的最小方差主轴几乎沿竖向,而上升段的主轴变化规律比较复杂,不能简单认为该时段的主轴同样也位于竖向。按照断层距和场地条件进行参数统计分析,结果表明:最大方差主轴在水平面上近似服从均匀分布。对汶川MW7.9、集集MW7.6和花莲MW6.4三次典型地震事件的方差主轴进行了精细化分析,结果显示:在近断层区域,一小部分观测位置的方差主轴存在近似时不变特性,最大方差主轴指向可能与震源机制密切相关。

    Abstract:

    Based on near-field and far-field strong motion records from 11 moderate-to-large earthquakes, the study investigates the correlation of the three translational components of seismic ground motion using the variance principal axis method. And then the correlation is examined at different scales, with the characteristics of the correlation described at both the sample level and the statistical level.

    By considering the time-varying characteristics of the principal axes, the ground motion records are divided into three segments: the ascending phase, the strong ground motion phase, and the descending phase. The study investigates the direction of the minor variance principal axis in these three phases. Both at the sample level and statistical level, it is found that the minor variance principal axis during the strong ground motion and descending phases is nearly vertical. However, the principal axis in the ascending phase exhibits a more complex variation and cannot simply be assumed to be vertical. Since the earthquake intensity during the ascending phase is typically lower or the duration is shorter, it can be approximated as vertical in engineering practice by ignoring the ascending phase.

    Statistical analysis of parameters based on fault distance and site conditions indicates that the major variance principal axis in the horizontal plane follows an approximately uniform distribution. The direction of the major variance principal axis exhibits significant time-dependent variability and strong randomness in the horizontal plane, far exceeding its variability in the vertical direction. Statistically, the occurrence probability of the major variance principal axis in any direction is approximately equal, following a uniform distribution.

    Detailed analysis of the 1999 Chi-Chi earthquake, the 2008 Wenchuan earthquake, and the 2018 Hualien earthquake indicates that in the near-fault region, a small subset of observation points exhibits approximately time-invariant characteristics for the variance principal axes, while many other stations show strong randomness in the direction of the variance principal axes. For the stations with nearly time-invariant principal axes, the orientation may be closely related to the source mechanism. In the vicinity of reverse faults, the major variance principal axis is oriented perpendicular to the fault strike, while in the vicinity of strike-slip faults, it is parallel to the fault strike. In near-fault regions with complex source mechanisms, there exist both components parallel and perpendicular to the fault strike.

  • 图  7   集集 MW7.6 地震近断层周边台站位置及B类台站强震记录最大方差主轴水平投影的分布

    Figure  7.   Location of the stations around near-fault region in the Chi-Chi MW7.6 earthquake and the distribution of horizontal projection of the major variance principal axis of the strong ground motion recordings at B-type stations

    图  1   方差主轴空间参数(a)和主轴在水平面内投影(b)示意图

    Figure  1.   Schematic diagram of spatial parameters of variance principal axis (a) and projection of principal axis on horizontal plane (b)

    图  2   典型强震记录的主轴时程图

    (a) 2008年汶川地震中的51AXT台站记录; (b) 1999年集集地震中的CHY099台站记录;(c) SMART- Ⅰ (40)事件中的C00台站记录;(d) 1996年北岭地震中的ACI台站记录(图中阴影区域代表强震段)

    Figure  2.   The time histories of principal axes of the typical strong ground motion recordings

    (a) The recordings at the station 51AXT in 2008 Wenchuan earthquake;(b) The recordings at the station CHY099 in 1999 Chi-Chi earthquake;(c) The recordings at the station C00 in SMART- Ⅰ (40) event;(d) The recordings at the station ACI in 1996 Northridge earthquake (shaded area represents strong seismic segment)

    图  3   不同断层距下岩石场地(a)和软土场地(b)的最小方差主轴与竖向之间夹角$ \phi $3的概率密度分布

    Figure  3.   The probability density distribution of angle $ \phi $3 between the minor variance principal axis and the vertical direction for rock site (a) and soft soil site (b) at different fault distance

    图  4   不同断层距下岩石场地(上)和软土场地(下)的最大方差主轴与断层走向夹角γf统计结果

    Figure  4.   Statistical result of the angle γf between the major variance principal axis and the strike for rock sites (upper) and soft soil sites (bottom) at different fault distance

    (a) 0—10 km;(b) 10—30 km;(c) 30—60 km;(d) 60—200 km

    图  5   不同断层距下岩石场地(上)和软土场地(下)的最大方差主轴与震中方向夹角γe统计结果

    Figure  5.   Statistical result of the angle γe between the major variance principal axis and the epicentral direction for rock sites (upper) and soft soil sites (bottom) at different fault distance

    (a) 0—10 km;(b) 10—30 km;(c) 30—60 km;(d) 60—200 km

    图  6   汶川 MW7.9 地震近断层周边台站位置及B类台站强震记录最大方差主轴水平投影的分布

    Figure  6.   Location of the stations around near-fault region in the Wenchuan MW7.9 earthquake and the distribution of horizontal projection of the major variance principal axis of the strong ground motion recordings at B-type stations

    图  8   花莲 MW6.4 地震近断层周边台站位置及B类台站强震记录最大方差主轴水平投影的分布

    Figure  8.   Location of the stations around near-fault region in the Hualien MW6.4 earthquake and the distribution of horizontal projection of the major variance principal axis of the strong ground motion recordings at B-type statoions

    表  1   地震事件的基本信息

    Table  1   Basic information about earthquake events

    地震事件发震年份MW发震断层类型记录组数
    汶川地震2 0087.90逆断层66
    阿拉斯加地震2 0027.90走滑断层11
    集集地震1 9997.62逆断层−斜滑274
    SMART-I (45)1 9867.30逆断层36
    兰德斯地震1 9927.28走滑断层76
    El Mayor-Cucapah
    地震
    2 0107.20走滑断层166
    北海道地震2 0186.70逆断层67
    北岭地震1 9946.69逆断层98
    花莲地震2 0186.40走滑断层30
    美浓地震2 0166.40走滑断层14
    SMART-I (40)1 9866.32逆断层36
    下载: 导出CSV

    表  2   文献中移动窗格技术的参数选择

    Table  2   Parameter selection for moving window technique in literatures

    文献窗格宽度/s移动步长/s
    Penzien和Watabe (1 9744.04.0
    8.08.0
    10.510.5
    12.012.0
    Kubo和Penzien (1 9795.00.5
    Phung等(2 0064.00.5
    下载: 导出CSV

    表  3   窗格宽度和移动步长对汶川地震中51HYQ台站强震记录的最大方差主轴水平投影与正北夹角的影响

    Table  3   The influence of window width and moving step on the angle between the horizontal projection of major variance principal axis and north of strong motion records at the station 51HYQ during Wenchuan earthquake

    窗格宽度/s 移动步长/s
    0.1 0.3 0.5 1 2 3 4 5
    0.1
    0.3
    0.5
    1
    2
    3
    4
    5
    注:各子图纵坐标为夹角,范围为−90°—90°;横坐标为时间,范围为0—99.3 s。

    下载: 导出CSV

    表  4   窗格宽度和移动步长对SMART- Ⅰ (45)事件中C00台站强震记录的最大方差主轴水平投影与正北夹角的影响

    Table  4   The influence of window width and moving step on the angle between the horizontal projection of major variance principal axis and north of strong motion records at the station C00 during SMART- Ⅰ (45) earthquake

    窗格宽度/s 移动步长/s
    0.1 0.3 0.5 1 2 3 4 5
    0.1
    0.3
    0.5
    1
    2
    3
    4
    5
    注:各子图纵坐标为夹角,范围为−90°—90°;横坐标为时间,范围为0—55 s。
    下载: 导出CSV

    表  5   窗格宽度和移动步长对花莲地震中HWA048台站强震记录的最大方差主轴水平投影与正北夹角的影响

    Table  5   The influence of window width and moving step on the angle between the horizontal projection of majorvariance principal axis and north of strong motion records at the station HWA048 during Hualien earthquake

    窗格宽度/s 移动步长/s
    0.1 0.3 0.5 1 2 3 4 5
    0.1
    0.3
    0.5
    1
    2
    3
    4
    5
    注:各子图纵坐标为夹角,范围为−90°—90°;横坐标范围为时间,范围为0—16.2 s。
    下载: 导出CSV

    表  6   本文选取的各地震事件所使用的移动窗格技术参数

    Table  6   The MWT parameters used for each seismic event selected in this study

    地震事件窗格宽度/s移动步长/s地震事件窗格宽度/s移动步长/s
    汶川地震4.00.1北海道地震3.00.1
    阿拉斯加地震4.00.1北岭地震2.00.1
    集集地震4.00.1花莲地震2.00.1
    SMART- Ⅰ(45)3.00.1美浓地震2.00.1
    兰德斯地震4.00.1SMART- Ⅰ(40)2.00.1
    El Mayor-Cucapah地震3.00.1
    下载: 导出CSV
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    其他类型引用(3)

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出版历程
  • 收稿日期:  2023-07-15
  • 修回日期:  2023-09-15
  • 录用日期:  2023-09-17
  • 网络出版日期:  2023-09-20
  • 刊出日期:  2025-03-27

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