﻿ 利用四元件钻孔应变观测资料研究佘山地区主应变及主方向变化特征
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 大地测量与地球动力学  2019, Vol. 39 Issue (10): 1091-1095  DOI: 10.14075/j.jgg.2019.10.020

### 引用本文

NI Youzhong, YE Qing, ZHU Guohao, et al. On Variation Characteristics of Main Strain and Main Direction in Sheshan Area Using Four Element Borehole Strain Observations[J]. Journal of Geodesy and Geodynamics, 2019, 39(10): 1091-1095.

### Foundation support

Science and Technology Special Project of Shanghai Earthquake Agency, No.2018 S1.

### 第一作者简介

NI Youzhong, engineer, majors in earthquake, geostress and strain observation, 329676647@qq.com.

### 文章历史

1. 佘山地震基准台，上海市外青松公路9279号，201602

1 观测背景 1.1 地理环境及地质构造环境

1.2 仪器安装情况

2 基本公式

1) 设有等距节点Xk=X0+kh(k=0, 1, …, n)，其中，步长h为常数。

2) 记fk=f(Xk)，称相邻两个节点XkXk+1函数值的增量fk+1fk(k=0, 1, …, n－1)为函数f(x)在点Xk处以h为步长的一阶差分，记为Δfk，则有Δf0=f1f0、Δf1=f2f1等。

1) 元件i的孔径相对变化测值为：

 ${\mathit{S}_\mathit{i}}\mathit{ = }{\mathit{K}_\mathit{i}}\mathit{ }{\mathit{R}_\mathit{i}}$ (1)

2) 利用自检方程：

 ${\mathit{S}_1}{\rm{ + }}{\mathit{S}_{\rm{3}}}{\rm{ = }}{\mathit{S}_2}{\rm{ + }}{\mathit{S}_4}$ (2)

 ${K_1}{R_1} - {K_2}{R_2} - {K_3}{R_3} - {K_4}{R_4} = 0$ (3)

 ${K_{11}}{R_1} - {K_{21}}{R_2} + {K_{31}}{R_3} - {K_{41}}{R_4} = 0$ (4)

 ${K_{12}}{R_1} - {K_{22}}{R_2} + {K_{32}}{R_3} - {K_{42}}{R_4} = 0$ (5)
 ${K_{13}}{R_1} - {K_{23}}{R_2} + {K_{33}}{R_3} - {K_{43}}{R_4} = 0$ (6)
 ${K_{14}}{R_1} - {K_{24}}{R_2} + {K_{34}}{R_3} - {K_{44}}{R_4} = 0$ (7)

 ${K_i} = \frac{1}{4}\sum\limits_{j = 1}^4 {{K_{ij}}\;} , (i = 1, 2, 3, 4)$ (8)

 $\left\{ \begin{array}{l} {S_{13}} = {S_1} - {S_3}\\ {S_{24}} = {S_2} - {S_4}\\ Sa = ({S_1} + {S_2} + {S_3} + {S_4})/2 \end{array} \right.$ (9)

 ${S_\theta } = A({\mathit{\varepsilon }_1} + {\mathit{\varepsilon }_2}) + B({\mathit{\varepsilon }_1} - {\mathit{\varepsilon }_2})\cos 2(\theta - \varphi )$ (10)

 $\left\{ \begin{array}{l} {S_1} = {S_{{\theta _1}}} = A({\varepsilon _1} + {\varepsilon _2}) + B({\varepsilon _1} - {\varepsilon _2})\cos 2({\theta _1} - \varphi )\\ {S_2} = {S_{{\theta _1} + {\raise0.5ex\hbox{$\scriptstyle \pi $} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 4$}}}} = A({\varepsilon _1} + {\varepsilon _2}) - B({\varepsilon _1} - {\varepsilon _2})\sin 2({\theta _1} - \varphi )\\ {S_3} = {S_{{\theta _1} + {\raise0.5ex\hbox{$\scriptstyle \pi $} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}} = A({\varepsilon _1} + {\varepsilon _2}) - B({\varepsilon _1} - {\varepsilon _2})\cos 2({\theta _1} - \varphi )\\ {S_4} = {S_{{\theta _1} + {\raise0.5ex\hbox{$\scriptstyle {3\pi }$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 4$}}}} = A({\varepsilon _1} + {\varepsilon _2}) + B({\varepsilon _1} - {\varepsilon _2})\sin 2({\theta _1} - \varphi ) \end{array} \right.$ (11)

 $\left\{ \begin{array}{l} {S_{_{13}}} = 2B({\varepsilon _1} - {\varepsilon _2})\cos 2({\theta _1} - \varphi )\\ {S_{_{24}}} = - 2B({\varepsilon _1} - {\varepsilon _2})\sin 2({\theta _1} - \varphi )\\ {S_a} = 2A({\varepsilon _1} + {\varepsilon _2}) \end{array} \right.$ (12)

 $\left\{ \begin{array}{l} \frac{1}{{2B}}\sqrt {{S^{{}^2}}_{13} + {S^{{}^2}}_{24}} = {\varepsilon _1} - {\varepsilon _2}\\ \frac{1}{{2A}}{S_a} = {\varepsilon _1} + {\varepsilon _2} \end{array} \right.$ (13)
 $\frac{{{S_{24}}}}{{{S_{13}}}} = - \tan 2({\theta _1} - \varphi )$ (14)

3 分析结果

3.1 佘山台测点主方向φ的确定

 图 1 佘山台用于应变换算的3个替代观测值(Sa、S13、S24)曲线 Fig. 1 Three alternative observations (Sa, S13, S24) for strain conversion at Sheshan station

 图 2 差分值及变化值计算得到的历年主方向 Fig. 2 The main direction of the calendar year calculated by the difference value and the change value
3.2 佘山台测点面应变及最大剪应变分析

 图 3 佘山台小时值面应变、最大剪应变曲线(无校正) Fig. 3 Hour strain and maximum shear strain curvs of Sheshan station (no correction)

 图 4 佘山台小时值面应变、最大剪应变曲线(变化校正) Fig. 4 Hour strain and maximum shear strain curves of Sheshan station (change correction)

 图 5 佘山台小时值面应变、最大剪应变曲线(差分校正) Fig. 5 Hour surface strain and maximum shear strain curves of Sheshan station (differential correction)

 图 6 佘山台应变换算结果εa、εs年变化速率趋势分析 Fig. 6 Trend analysis of strain rate εa and εs at Sheshan station

4 结语

1) 在主方向φ的确定上，应使用差分值，观测数据是否进行校正对于主方向的结果判定影响不大。通过差分方法得到的3组主方向φ结果基本一致，2013年以来基本维持在95°左右。

2) 2013年以来，佘山台的面应变整体呈下降趋势，最大剪应变在逐步增大。校正前后面应变的年变化速率差别不大；2013~2017年，校正后最大剪应变的年变化速率明显变小，但从2017年开始，校正后最大剪应变的年变化速率大于校正前。

 [1] 邱泽华, 石耀霖, 欧阳祖熙. 四分量钻孔应变观测的实地相对标定[J]. 大地测量与地球动力学, 2005, 25(1): 118-122 (Qiu Zehua, Shi Yaolin, Ouyang Zuxi. Relative In-Situ Calibration of 4-Component Borehole Strain Observation[J]. Journal of Geodesy and Geodynamics, 2005, 25(1): 118-122) (0) [2] 邱泽华. 钻孔应变观测理论和应用[M]. , 北京: 地震出版社, 2017 (Qiu Zehua. Theory and Application of Borehole Strain Observation[M]. Beijing: Seismological Press, 2017) (0) [3] 苏恺之, 张钧, 李秀环, 等. 钻孔环境在钻孔地形变观测中的作用[J]. 地震地磁观测与研究, 2005, 26(6): 46-55 (Su Kaizhi, Zhang Jun, Li Xiuhuan, et al. The Effect of Borehole Environment at Borehole Deformation Observation[J]. Seismological and Geomagnetic Observation and Research, 2005, 26(6): 46-55 DOI:10.3969/j.issn.1003-3246.2005.06.008) (0) [4] 钟继茂, 李祖宁, 谢志招, 等. 用多分量钻空应变仪资料推算测区附加应变场方向[J]. 大地测量与地球动力学, 2011, 31(1): 29-33 (Zhong Jimao, Li Zuning, Xie Zhizhao, et al. Determination of Direction of Additional Strain Field in Observation Area from Data of Multi-Component Borehole Strainmeter[J]. Journal of Geodesy and Geodynamics, 2011, 31(1): 29-33) (0) [5] 刘序俨. 应变固体潮主应变及剪应变的计算——四川姑咱台应变固体潮分析[J]. 地球物理学报, 1994, 37: 213-221 (Liu Xuyan. Analysis on Earth Strain Tide of Guza Seismic Station[J]. Acta Geophysica Sinica, 1994, 37(S1): 213-221) (0) [6] 邱泽华, 池顺良. YRY-4型钻孔应变仪观测的P波剪应变[J]. 地震, 2013, 33(4): 64-70 (Qiu Zehua, Chi Shunliang. Shear Strains of P Wave Observed with YRY-4 Borehole Strainmeter[J]. Earthquake, 2013, 33(4): 64-70 DOI:10.3969/j.issn.1000-3274.2013.04.007) (0) [7] 刘序俨, 王紫燕, 方宏芳, 等. 对当前四分量钻孔应变观测的审视——以应变不变量为标尺[J]. 地球物理学报, 2014, 57(10): 3332-3346 (Liu Xuyan, Wang Ziyan, Fang Hongfang, et al. Analysis of 4-Component Borehole Strain Observation Based on Strain Invariant[J]. Chinese Journal of Geophysics, 2014, 57(10): 3332-3346 DOI:10.6038/cjg20141020) (0)
On Variation Characteristics of Main Strain and Main Direction in Sheshan Area Using Four Element Borehole Strain Observations
NI Youzhong1     YE Qing1     ZHU Guohao1     FANG Tao1
1. Sheshan Seismic Reference Station, 9279 Waiqingsong Road, Shanghai 201602, China
Abstract: In order to study the variation characteristics of strain field in Sheshan area, three sets of annual strain rate, maximum shear strain rate and their responses are obtained using the borehole-lined model formula, the variation and difference values of observed data from 2013 to 2018 of Sheshan station, and three strain conversion methods, including no correction, change correction and difference correction. Three sets of surface strain annual rate, maximum shear strain annual rate change and strain main direction calculation results were obtained.It is found that the difference value is more effective in calculating the main direction of strain and extracting the characteristic curves of annual strain rate and maximum shear strain rate.
Key words: four element borehole strainmeter; principal strain; main direction; maximum shear strain; surface strain