﻿ 动态与静态平差方法在流动重力数据处理中的对比研究
 文章快速检索 高级检索
 大地测量与地球动力学  2022, Vol. 42 Issue (8): 783-789  DOI: 10.14075/j.jgg.2022.08.003

### 引用本文

HAO Hongtao, WEI Shouchun, WEI Jin, et al. A Comparative Study of Dynamic and Static Adjustment Methods in Mobile Gravity Data Processing[J]. Journal of Geodesy and Geodynamics, 2022, 42(8): 783-789.

### Foundation support

Scientific Research Fund of Institute of Seismology, CEA and National Institute of Natural Hazards, MEM, No.IS201926302, IS20176162; Open Fund of Wuhan Gravitation and Solid Earth Tides, National Observation and Research Station, No.WHYWZ202103; National Natural Science Foundation of China, No.41304059;Special Fund for Earthquake Research of CEA, No.201508009.

### Corresponding author

HU Minzhang, PhD, researcher, majors in gravity field variation and seismic research, E-mail: huminzhang@126.com.

### About the first author

HAO Hongtao, PhD, associate researcher, majors in mobile gravity technology, E-mail: haoht2004@sina.com.

### 文章历史

1. 中国地震局地震大地测量重点实验室，武汉市洪山侧路40号，430071;
2. 湖北省地震局，武汉市洪山侧路40号，430071;
3. 中国地震局第二监测中心，西安市西影路316号，710054

1 平差模型 1.1 静态平差模型

 $\left\{\begin{array}{l} V_{i, j}=\bar{g}_{i}-\bar{g}_{j}-\Delta g_{i j} \\ V_{k}=\bar{g}_{k}-g_{k} \end{array}\right.$ (1)

 $\mathit{\boldsymbol{V}} = \mathit{\boldsymbol{A\bar X}} - \mathit{\boldsymbol{L}}$ (2)

 $\left\{\begin{array}{l} \hat{\boldsymbol{X}}=\left(\boldsymbol{A}^{\mathrm{T}} \boldsymbol{P} \boldsymbol{A}\right)^{-1} \boldsymbol{A}^{\mathrm{T}} \boldsymbol{P L} \\ \boldsymbol{D}_{X X}=\hat{\sigma}_{0}^{2} \boldsymbol{Q}_{X X}=\hat{\sigma}_{0}^{2}\left(\boldsymbol{A}^{\mathrm{T}} \boldsymbol{P} \boldsymbol{A}\right)^{-1} \\ \hat{\sigma}_{0}^{2}=\sqrt{\frac{\boldsymbol{V}^{\mathrm{T}} \boldsymbol{P} \boldsymbol{V}}{r}} \end{array}\right.$ (3)

1.2 动态平差模型

 $\left\{\begin{array}{l} V_{i, j}=\bar{g}_{i}\left(t_{0}\right)+\left(t-t_{0}\right) \bar{g}_{i}-\bar{g}_{j}\left(t_{0}\right)- \\ \quad\left(t-t_{0}\right) \bar{g}_{j}-\Delta g_{i j} \\ V_{k}=\bar{g}_{k}\left(t_{0}\right)+\left(t-t_{0}\right) \bar{g}_{k}-g_{k} \end{array}\right.$ (4)

2 数据与处理

 红色五角星为绝对重力测点, 线段为相对重力测线, 各测区以不同颜色区分 图 1 南北带南段地区重力观测网 Fig. 1 Gravity network in the southern segment of the north-south seismic belt

3 结果分析与讨论 3.1 2种方法重力变化结果的数值差异

 图 2 静态与动态平差方法重力变化结果的差异 Fig. 2 Difference between gravity variations by static and dynamic adjustment methods
3.2 2种方法重力变化图像对比

 图 3 2018-04~08重力变化结果对比 Fig. 3 Gravity variation from April 2018 to August 2018

 图 4 2017-09~2018-08重力变化结果对比 Fig. 4 Gravity variation from September 2017 to August 2018

 图 5 2016-09~2018-08重力变化结果对比 Fig. 5 Gravity variation from September 2016 to August 2018

 图 6 2015-08~2018-08重力变化结果对比 Fig. 6 Gravity variation from August 2015 to August 2018
3.2.1 0.5 a尺度

3.2.2 1 a尺度

3.2.3 2 a尺度

3.2.4 3 a尺度

4 讨论

 图 7 忽略单期内观测时间差异时2种方法获得的约0.5 a时间尺度下的重力变化结果差异 Fig. 7 Difference between gravity variations for 0.5 a time scale by two methods without considering observation time difference

5 结语

1) 南北地震带南段地区流动重力网单期观测持续时间约3个月，观测期间的重力时变因素会导致静态平差方法计算的重力变化结果存在误差，但随着重力变化时间尺度的增加，其影响会逐步减小。对于0.5 a、1 a、2 a和3 a尺度下的重力变化结果，重力时变因素的最大影响分别约为19 μGal、9.5 μGal、5.5 μGal和4.0 μGal。

2) 动态平差和静态平差2种方法的重力变化图像在整体空间分布态势上保持一致，但0.5 a和1 a时间尺度图像在重力变化量级和等值线分布细节上存在一定的差异，2 a和3 a时间尺度下的重力变化图像则基本相同。因此对于计算0.5 a和1 a时间尺度下的重力变化宜采用动态平差方法。

3) 近期研究区内3次6级以上地震的发震地点均与重力变化零值线具有较好的对应关系，基于动态平差方法获得的0.5~3 a时间尺度下的重力场变化图像可反映3次地震的发震背景。

 [1] 申重阳, 祝意青, 胡敏章, 等. 中国大陆重力场时变监测与强震预测[J]. 中国地震, 2020, 36(4): 729-743 (Shen Chongyang, Zhu Yiqing, Hu Minzhang, et al. Time-Varying Gravity Field Monitoring and Strong Earthquake Prediction on the Chinese Mainland[J]. Earthquake Research in China, 2020, 36(4): 729-743) (0) [2] 祝意青, 申重阳, 刘芳, 等. 重力观测地震预测应用研究[J]. 中国地震, 2020, 36(4): 708-717 (Zhu Yiqing, Shen Chongyang, Liu Fang, et al. Application of Earthquake Prediction Based on Gravity Observation[J]. Earthquake Research in China, 2020, 36(4): 708-717) (0) [3] 刘绍府, 刘冬至, 李辉. 高精度重力测量平差及其软件[J]. 地震, 1991, 11(4): 57-66 (Liu Shaofu, Liu Dongzhi, Li Hui. Adjustment of High Precision Gravity Measurements and Its Software[J]. Earthquake, 1991, 11(4): 57-66) (0) [4] 康开轩, 李辉, 申重阳, 等. 基于绝对重力基准控制的流动重力观测资料动态平差方法研究[J]. 大地测量与地球动力学, 2015, 35(3): 508-511 (Kang Kaixuan, Li Hui, Shen Chongyang, et al. Method of Dynamic Adjustment on Repeated Gravity Measurements under the Constraint of Absolute Gravity Observations[J]. Journal of Geodesy and Geodynamics, 2015, 35(3): 508-511) (0) [5] 贾民育, 詹洁晖. 中国地震重力监测体系的结构与能力[J]. 地震学报, 2000, 22(4): 360-367 (Jia Minyu, Zhan Jiehui. The Structure and Ability of the China Seismological Gravity Monitoring System[J]. Acta Seismologica Sinica, 2000, 22(4): 360-367 DOI:10.3321/j.issn:0253-3782.2000.04.004) (0) [6] 祝意青, 王庆良, 徐云马. 我国流动重力监测预报发展的思考[J]. 国际地震动态, 2008, 38(9): 19-25 (Zhu Yiqing, Wang Qingliang, Xu Yunma. Thoughts on the Development of Earthquake Monitoring and Prediction in Mobile Gravity[J]. Recent Developments in World Seismology, 2008, 38(9): 19-25 DOI:10.3969/j.issn.0253-4975.2008.09.004) (0) [7] Pagiatakis S D, Salib P. Historical Relative Gravity Observations and the Time Rate of Change of Gravity Due to Postglacial Rebound and other Tectonic Movements in Canada[J]. Journal of Geophysical Research: Solid Earth, 2003, 108(B9) (0) [8] 隗寿春, 徐建桥, 周江存. 重力网的分段线性动态平差[J]. 测绘学报, 2016, 45(5): 511-520 (Wei Shouchun, Xu Jianqiao, Zhou Jiangcun. Piece-Wise Linear Dynamic Adjustment for Gravity Network[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(5): 511-520) (0) [9] 胡敏章, 郝洪涛, 李辉, 等. 地震分析预报的重力变化异常指标分析[J]. 中国地震, 2019, 35(3): 417-430 (Hu Minzhang, Hao Hongtao, Li Hui, et al. Quantitative Analysis of Gravity Changes for Earthquake Prediction[J]. Earthquake Research in China, 2019, 35(3): 417-430 DOI:10.3969/j.issn.1001-4683.2019.03.001) (0) [10] 阚荣举, 张四昌, 晏凤桐, 等. 我国西南地区现代构造应力场与现代构造活动特征的探讨[J]. 地球物理学报, 1977, 20(2): 96-109 (Kan Rongju, Zhang Sichang, Yan Fengtong, et al. Present Tectonic Stress Field and Its Relation to the Characteristics of Recent Tectonic Activity in Southwestern China[J]. Chinese Journal of Sinica, 1977, 20(2): 96-109) (0) [11] 苏有锦, 秦嘉政. 川滇地区强地震活动与区域新构造运动的关系[J]. 中国地震, 2001, 17(1): 24-34 (Su Youjin, Qin Jiazheng. Strong Earthquake Activity and Relation to Regional Neotectonic Movement in Sichuan-Yunnan Region[J]. Earthquake Research in China, 2001, 17(1): 24-34 DOI:10.3969/j.issn.1001-4683.2001.01.004) (0) [12] 张培震, 邓起东, 张国民, 等. 中国大陆的强震活动与活动地块[J]. 中国科学: 地球科学, 2003, 33(增1): 12-20 (Zhang Peizhen, Deng Qidong, Zhang Guomin, et al. Active Tectonic Blocks and Strong Earthquakes on the Chinese Mainland[J]. Science China: Earth Sciences, 2003, 33(S1): 12-20) (0) [13] 祝意青, 梁伟锋, 湛飞并, 等. 中国大陆重力场动态变化研究[J]. 地球物理学报, 2012, 55(3): 804-813 (Zhu Yiqing, Liang Weifeng, Zhan Feibing, et al. Study on Dynamic Change of Gravity Field in China Continent[J]. Chinese Journal of Geophysics, 2012, 55(3): 804-813 DOI:10.6038/j.issn.0001-5733.2012.03.010) (0)
A Comparative Study of Dynamic and Static Adjustment Methods in Mobile Gravity Data Processing
HAO Hongtao1,2     WEI Shouchun3     WEI Jin1,2     LIU Shaoming1,2     HU Minzhang1,2
1. Key Laboratory of Earthquake Geodesy, CEA, 40 Hongshance Road, Wuhan 430071, China;
2. Hubei Earthquake Agency, 40 Hongshance Road, Wuhan 430071, China;
3. The Second Monitoring and Application Center, CEA, 316 Xiying Road, Xi'an 710054, China
Abstract: To analyze the influence of the time-varying gravity factors on mobile gravimetry data processing, we use static and dynamic adjustment methods to process gravimetry data in the area of southern segment of the north-south seismic belt, comparing the results of the two methods. The results show that: 1) The time-varying gravity factors cause errors in the gravity changes by the static adjustment method, which have a relatively obvious impact on gravity variations of the 0.5 a and 1 a time scales, but less impact on the gravity variations of more than 2 a time scale. Therefore, it is appropriate to use the dynamic adjustment method to calculate the 0.5 a and 1 a time scales gravity variations. 2) The locations of the Jiuzhaigou M7.0, Changning M6.0 and Yangbi M6.4 earthquakes have a good corresponding relationship with the zero-value of gravity variations. The gravity variations image reflects the seismogenic background of the 3 earthquakes.
Key words: mobile gravity observation; static adjustment; dynamic adjustment; gravity variation