﻿ 2022年门源M<sub>S</sub>6.9地震同震应变观测
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 大地测量与地球动力学  2024, Vol. 44 Issue (2): 177-182  DOI: 10.14075/j.jgg.2023.04.175

### 引用本文

WANG Yulong, ZHANG Yan, WANG Dijin. Coseismic Strain Observation of the Menyuan MS6.9 Earthquake in 2022[J]. Journal of Geodesy and Geodynamics, 2024, 44(2): 177-182.

### Corresponding author

ZHANG Yan, PhD, associate researcher, majors in crustal deformation and earthquake prediction, E-mail: 745822270@qq.com.

### 第一作者简介

WANG Yulong, postgraduate, majors in crustal deformation, E-mail: wwyyll2023@163.com.

### 文章历史

2022年门源MS6.9地震同震应变观测

1. 中国地震局地震研究所，武汉市洪山测路40号，430071;
2. 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

1 同震应变观测数据处理

1.1 时间校正

 图 1 门源台时间校正 Fig. 1 Menyuan station time correction
1.2 数据自洽与相对实地标定

 $S_1+S_3=S_2+S_4$ (1)

 $\begin{array}{*{20}{c}} {r=}\\ {\frac{\sum S_{13} S_{24}-\frac{\sum S_{13} \sum S_{24}}{N}}{\sqrt{\left(\sum S_{13}^2-\frac{\left(\sum S_{13}\right)^2}{N}\right)\left(\sum S_{24}^2-\frac{\left(\sum S_{24}\right)^2}{N}\right)}}} \end{array}$ (2)

1.3 应变换算

 $\left\{\begin{array}{l} s_{13}=S_1-S_3 \\ s_{24}=S_2-S_4 \\ s_a=\left(S_1+S_3+S_1+S_3\right) / 2 \end{array}\right.$ (3)

 $\left\{\begin{array}{l} S_1=A\left(\varepsilon_1+\varepsilon_2\right)+B\left(\varepsilon_1-\varepsilon_2\right) \cos 2\left(\theta_1-\varphi\right) \\ S_2=A\left(\varepsilon_1+\varepsilon_2\right)-B\left(\varepsilon_1-\varepsilon_2\right) \sin 2\left(\theta_1-\varphi\right) \\ S_3=A\left(\varepsilon_1+\varepsilon_2\right)-B\left(\varepsilon_1-\varepsilon_2\right) \cos 2\left(\theta_1-\varphi\right) \\ S_4=A\left(\varepsilon_1+\varepsilon_2\right)+B\left(\varepsilon_1-\varepsilon_2\right) \sin 2\left(\theta_1-\varphi\right) \end{array}\right.$ (4)

 $\left\{\begin{array}{l} \varepsilon_1=\frac{1}{4 A} s_a+\frac{1}{4 B} s_s \\ \varepsilon_2=\frac{1}{4 A} s_a-\frac{1}{4 B} s_s \\ \varphi=\frac{1}{2} \arctan \left(\frac{s_{24}}{s_{13}}\right)+\theta_1 \end{array}\right.$ (5)

 $\left\{\begin{array}{l} s_a=2 A\left(\varepsilon_n+\varepsilon_e\right) \\ s_s=2 B\left(\sqrt{\left(2 \varepsilon_{n e}\right)^2+\left(\varepsilon_n-\varepsilon_e\right)^2}\right) \end{array}\right.$ (6)

 $\left\{\begin{array}{l} \varepsilon_N=\frac{\varepsilon_1+\varepsilon_2}{2}+\frac{\varepsilon_1-\varepsilon_2}{2} \cos 2 \varphi \\ \varepsilon_E=\frac{\varepsilon_1+\varepsilon_2}{2}-\frac{\varepsilon_1-\varepsilon_2}{2} \cos 2 \varphi \\ \varepsilon_{N E}=\frac{\varepsilon_1-\varepsilon_2}{2} \sin 2 \varphi \end{array}\right.$ (7)

1.4 滤波处理

 图 2 应变观测值 Fig. 2 Strain observations

2 同震应变模拟值计算 2.1 正演软件QSSP

QSSP是由德国地学研究中心(GFZ)汪荣江教授基于Fortran编程语言编写的一款计算完整合成地震图的软件，内置具有大气、海洋、地幔、液态外核和固态内核多层结构的球对称自引力地球模型[13]，可用于正演计算地震发生后地表任意位置、任意时间范围的应变、应力、速度、位移、重力等参数的同震动态变化值。

2.2 数值模拟

QSSP软件由源代码文件、执行文件和参数输入文件3部分组成，正演计算理论模拟数值时需要修改参数输入文件的内容，并在执行文件中运行，具体需要修改的主要参数见表 3，其余参数可根据需求进行修改。

2.3 模拟值波形

 图 3 应变模拟值 Fig. 3 Strain simulations
3 观测值和模拟值拟合分析

3.1 相关系数

 $\begin{array}{*{20}{c}} & \rho= \\ & \frac{\sum G M-\frac{\sum G \sum M}{n}}{\sqrt{\left(\sum G^2-\frac{\left(\sum G\right)^2}{n}\right)\left(\sum M^2-\frac{\left(\sum M\right)^2}{n}\right)}} \end{array}$ (8)

3.2 拟合结果

 图 4 P波观测值与模拟值拟合 Fig. 4 P wave observations fitting with simulations

4 结语

1) 钻孔应变仪仪器时间的准确性直接关系到观测数据的可信度，本文对17个台站的钻孔应变仪利用P波理论走时的计算方法进行时间校正，消除时间偏差。

2) 对钻孔应变仪4个元件的灵敏度进行一致性检验，计算各元件的灵敏度标定系数。利用这个结果对观测数据进行校正，校正后观测数据的自洽程度得到显著提高，作为自洽评价标准的面应变相关系数普遍达到0.9以上。

3) 17个台站的P波观测波形与模拟波形的拟合效果较好，相关程度普遍达到了高度相关，NS向和EW向的拟合相关系数平均值分别为0.835和0.842。拟合结果表明，钻孔应变仪同震观测数据与同震模拟数据具有较好的一致性，说明钻孔应变观测数据可较好地反映地震破裂信息，具备约束地震破裂过程的潜力，进一步验证钻孔应变观测数据可用于地震破裂过程的研究。

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Coseismic Strain Observation of the Menyuan MS6.9 Earthquake in 2022
WANG Yulong1,2     ZHANG Yan1,2     WANG Dijin1,2
1. Key Laboratory of Earthquake Geodesy, CEA, 40 Hongshance Road, Wuhan 430071, China;
2. Institute of Seismology, CEA, 40 Hongshance Road, Wuhan 430071, China
Abstract: This paper takes the Menyuan MS6.9 earthquake in 2022 as an example, fitting the coseismic strain observations of four component borehole strainmeters at 1sps sampling rate from 17 stations with the coseismic strain simulations obtained by using qssp software forward calculation; we then analyze their correlation. The results show that the north-south and east-west P-wave waveforms of 17 stations fit well, and the average correlation coefficients are 0.835 and 0.842, respectively, reaching a high correlation, indicating that the borehole strain observation data can better reflect the seismic fracture information, which further verifies that borehole strain observation data can be used to study the seismic fracture process in theory.
Key words: borehole strain observation data; coseismic; earthquake rupture process; QSSP; correlation coefficient