GUO Jinyun, WU Kezhi, JIN Xin, ZHOU Maosheng, LIU Xin. A Method to Determine Vertical Gravity Gradient by High-Precision 3D Tracking Parabolic Motion[J]. Geomatics and Information Science of Wuhan University, 2025, 50(3): 462-468. DOI: 10.13203/j.whugis20220711
Citation: GUO Jinyun, WU Kezhi, JIN Xin, ZHOU Maosheng, LIU Xin. A Method to Determine Vertical Gravity Gradient by High-Precision 3D Tracking Parabolic Motion[J]. Geomatics and Information Science of Wuhan University, 2025, 50(3): 462-468. DOI: 10.13203/j.whugis20220711

A Method to Determine Vertical Gravity Gradient by High-Precision 3D Tracking Parabolic Motion

More Information
  • Received Date: November 03, 2023
  • Available Online: March 30, 2023
  • Objectives 

    The vertical gravity gradient plays an important role in the exploration of the earth gravity field. It is more and more widely used in the fields of geodesy, geophysics and geodynamics. Therefore, it is urgent to obtain the vertical gravity gradient with high accuracy quickly and accurately.

    Methods 

    A new method to determine vertical gravity gradients by 3D tracking parabolic motion is proposed. In a vacuum environment, the 3D tracking technology is used to dynamically track the parabolic falling target to obtain the 3D coordinate time series of the target movement, establish the trajectory observation equation, and extract the gravity vertical gradient using the least square method.

    Results 

    When the measurement accuracy of falling target reaches micron level, the main error sources of this measurement method are 3D tracking measurement error and time measurement error, of which the time measurement error has a small impact on the measurement accuracy of vertical gravity gradient. After adding the 3D tracking measurement random error with the standard deviation (STD) is 10 μm and the time measurement random error with the STD is 10 ns to the parabolic motion coordinate time series, the root mean square of the measurement error of vertical gravity gradient is about 1.31 E (1 E=10-9/s2).

    Conclusions 

    The proposed method of vertical gravity gradient measurement is effective and has good stability.

  • [1]
    边少锋, 张赤军. 地形起伏对重力垂直梯度影响的计算[J]. 物探化探计算技术, 1999, 21(2): 133-140.

    BIAN Shaofeng, ZHANG Chijun. Computation of Topographic Effects on Vertical Gravity Gradient[J]. Computing Techniques for Geophysical and Geochemical Exploration, 1999, 21(2): 133-140.
    [2]
    ZAHOREC P, MIKUŠKA J, PAPČO J, et al. Towards the Measurement of Zero Vertical Gradient of Gravity on the Earth’s Surface[J]. Studia Geophysica et Geodaetica, 2015, 59(4): 524-537.
    [3]
    BORNEMISZA S. Vertical Gradient of Gravity[J]. Geophysics, 2002, 23(2): 359-360.
    [4]
    赵珞成, 罗志才, 刘浩, 等. 重力梯度同步观测方法[J]. 武汉大学学报(信息科学版), 2012, 37(4): 428-431.

    ZHAO Luocheng, LUO Zhicai, LIU Hao, et al. Simultaneous Observation Method of Gravity Gradient[J]. Geomatics and Information Science of Wuhan University, 2012, 37(4): 428-431.
    [5]
    张赤军, 边少锋, 周旭华, 等. 重力垂直梯度的测定及其应用与潜力[J]. 地球物理学进展, 2007, 22(6): 1686-1691.

    ZHANG Chijun, BIAN Shaofeng, ZHOU Xuhua, et al. Determination of Gravity Vertical Gradient and Its Application Potential[J]. Progress in Geophysics, 2007, 22(6): 1686-1691.
    [6]
    HEILAND C A. A Rapid Method for Measuring the Profile Components of Horizontal and Vertical Gravity Gradients[J]. Geophysics, 1943, 8(2): 119-133.
    [7]
    DIFRANCESCO D. Advances and Challenges in the Development and Deployment of Gravity Gradiometer Systems[C]//EGM 2007 International Workshop, Capri, Italy, 2007.
    [8]
    党亚民, 章传银, 晁定波, 等. 综合利用海岸带GNSS水准和重力数据精密确定中国高程基准偏差[J]. 武汉大学学报(信息科学版), 2017, 42(11): 1644-1648.

    DANG Yamin, ZHANG Chuanyin, CHAO Dingbo, et al. Precise Determination of National Height Datum Discrepancy from Combination of GNSS/Leveling and Gravity Data in Coastal Areas of China[J]. Geomatics and Information Science of Wuhan University, 2017, 42(11): 1644-1648.
    [9]
    陈楚江, 孙凤华, 李德仁. 西藏墨脱地区工程精化似大地水准面的研究[J]. 武汉大学学报(信息科学版), 2004, 29(7): 638-641.

    CHEN Chujiang, SUN Fenghua, LI Deren. Refining Engineering Quasi-Geoid of Mutuo, Xizang, China[J]. Geomatics and Information Science of Wuhan University, 2004, 29(7): 638-641.
    [10]
    王谦身. 微重力测量: 理论、方法与应用[M]. 北京: 科学出版社, 1995.

    WANG Qianshen. Microgravity Measurement: Theory, Method and Application[M]. Beijing: Science Press, 1995.
    [11]
    FERNÁNDEZ J, TIAMPO K F, RUNDLE J B, et al. On the Interpretation of Vertical Gravity Gradients Produced by Magmatic Intrusions[J]. Journal of Geodynamics, 2005, 39(5): 475-492.
    [12]
    宛家宽, 罗志才, 赵珞成. 利用FG5绝对重力仪观测数据确定重力垂直梯度[J]. 地球物理学报, 2018, 61(1): 119-126.

    WAN Jiakuan, LUO Zhicai, ZHAO Luocheng. Determining Vertical Gradients of Gravity by Observations of the FG5 Absolute Gravimeter[J]. Chinese Journal of Geophysics, 2018, 61(1): 119-126.
    [13]
    HIPKIN R G. Absolute Determination of the Vertical Gradient of Gravity[J]. Metrologia, 1999, 36(1): 47-52.
    [14]
    PÁLINKÁŠ V, KŘEN P, VAĽKO M, et al. On the Determination of Vertical Gravity Gradients by Corner-Cube Absolute Gravimeters[J]. Metrologia, 2019, 56(5): 055006.
    [15]
    田桂娥, 陈晓东, 吴书清, 等. FG5绝对重力仪观测数据的实测重力潮汐改正[J]. 武汉大学学报(信息科学版), 2020, 45(6): 870-878.

    TIAN Guie, CHEN Xiaodong, WU Shuqing, et al. Correction of Measured Gravity Tides with FG5 Absolute Gravimeter Observations[J]. Geomatics and Information Science of Wuhan University, 2020, 45(6): 870-878.
    [16]
    张为民, 王勇, 詹金刚, 等. 中国地壳运动观测网络中的绝对重力测定[J]. 武汉大学学报(信息科学版), 2004, 29(3): 227-230.

    ZHANG Weimin, WANG Yong, ZHAN Jingang, et al. Absolute Gravity Determination in the Crustal Movement Observation Network of China[J]. Geomatics and Information Science of Wuhan University, 2004, 29(3): 227-230.
    [17]
    郭金运, 金鑫, 边少锋, 等. 垂线偏差测量的固体潮和海潮改正[J]. 测绘学报, 2022, 51(7): 1215-1224.

    GUO Jinyun, JIN Xin, BIAN Shaofeng, et al. Corrections of Solid Earth Tide and Ocean Tide for Measurement of Deflection of the Vertical[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(7): 1215-1224.
    [18]
    李红雨, 曹诚, 李凤婷, 等. 航空、航海重力和重力梯度在海洋、未知陆地战略勘探的发展[J]. 地球物理学进展, 2019, 34(1): 316-325.

    LI Hongyu, CAO Cheng, LI Fengting, et al. Deve⁃lopment of Airborne and Marine Gravity Exploration and Gravity Gradient Strategic Exploration for the Ocean and Unknown Land[J]. Progress in Geophy⁃sics, 2019, 34(1): 316-325.
    [19]
    孙中苗, 翟振和, 李迎春. 航空重力仪发展现状和趋势[J]. 地球物理学进展, 2013, 28(1): 1-8.

    SUN Zhongmiao, ZHAI Zhenhe, LI Yingchun. Status and Development of Airborne Gravimeter[J]. Progress in Geophysics, 2013, 28(1): 1-8.
    [20]
    许厚泽, 孙和平. 国际GGP计划和武汉超导重力仪观测[J]. 武汉大学学报(信息科学版), 2003, 28(S1): 18-22.

    XU Houze, SUN Heping. GGP Project and Observations Using Wuhan Superconducting Gravimeter[J]. Geomatics and Information Science of Wuhan University, 2003, 28(S1): 18-22.
    [21]
    BODDICE D, METJE N, TUCKWELL G. Quantifying the Effects of Near Surface Density Variation on Quantum Technology Gravity and Gravity Gra-dient Instruments[J]. Journal of Applied Geophysics, 2019, 164: 160-178.
    [22]
    WANG Q B, ZHOU R, SUN W. Precision Analysis of Gravity Vertical Gradient Measurement Based on CG-5 Relative Gravimeter[J]. Advanced Materials Research, 2011, 301: 1036-1041.
    [23]
    JIN X, LIU X, GUO J Y, et al. A Novel All-Weather Method to Determine Deflection of the Vertical by Combining 3D Laser Tracking Free-Fall and Multi-GNSS Baselines[J]. Remote Sensing, 2022, 14(17): 4156.
    [24]
    刘硕, 刘光博, 刘尚国, 等. 激光跟踪仪的测量误差解析与精度仿真[J]. 测绘工程, 2021, 30(6): 21-26.

    LIU Shuo, LIU Guangbo, LIU Shangguo, et al. Measurement Error Analysis and Accuracy Simulation of Laser Tracker[J]. Engineering of Surveying and Mapping, 2021, 30(6): 21-26.
    [25]
    HU C A, LUO S T, LI W Z, et al. Application of Laser Tracker in the Industrial Measurement Field[J]. Journal of Physics: Conference Series, 2021, 1820(1): 012119.
    [26]
    SAWYER D, FRONCZEK C. Laser Tracker Compensation Using Displacement Interferometry[J]. American Society for Precision Engineering, 2003, 30: 351-358.
    [27]
    CVITANIC T, MELKOTE S, BALAKIRSKY S. Improved State Estimation of a Robot End-Effector Using Laser Tracker and Inertial Sensor Fusion[J]. CIRP Journal of Manufacturing Science and Technology, 2022, 38: 51-61.
    [28]
    徐亚明, 郑琪, 管啸. Leica AT960激光跟踪仪测量精度分析[J]. 测绘地理信息, 2020, 45(1): 8-12.

    XU Yaming, ZHENG Qi, GUAN Xiao. Precision Analysis of Leica AT960 Absolute Laser Tracker[J]. Journal of Geomatics, 2020, 45(1): 8-12.
  • Related Articles

    [1]WU Jiaqi, JIANG Yonghua, SHEN Xin, LI Beibei, PAN Shenlin. Satellite Video Motion Detection Supported by Decision Tree Weak Classification[J]. Geomatics and Information Science of Wuhan University, 2019, 44(8): 1182-1190. DOI: 10.13203/j.whugis20180094
    [2]FU Zisheng, LI Qiuping, LIU Lin, ZHOU Suhong. Identification of Urban Network Congested Segments Using GPS Trajectories Double-Clustering Method[J]. Geomatics and Information Science of Wuhan University, 2017, 42(9): 1264-1270. DOI: 10.13203/j.whugis20150036
    [3]DENG Min, CHEN Ti, YANG Wentao. A New Method of Modeling Spatio-temporal Sequence by Considering Spatial Scale Characteristics[J]. Geomatics and Information Science of Wuhan University, 2015, 40(12): 1625-1632. DOI: 10.13203/j.whugis20130842
    [4]FU Zhongliang, LIU Siyuan. MR-tree with Voronoi Diagrams for Parallel Spatial Queries[J]. Geomatics and Information Science of Wuhan University, 2012, 37(12): 1490-1494.
    [5]HE Chu, LIU Ming, XU Lianyu, LIU Longzhu. A Hierarchical Classification Method Based on Feature Selection and Adaptive Decision Tree for SAR Image[J]. Geomatics and Information Science of Wuhan University, 2012, 37(1): 46-49.
    [6]ZHANG Lu, GAO Zhihong, LIAO Mingsheng, LI Xinyan. Estimating Urban Impervious Surface Percentage with Multi-source Remote Sensing Data[J]. Geomatics and Information Science of Wuhan University, 2010, 35(10): 1212-1216.
    [7]HAN Tao, XU Xiaotao, XIE Yaowen. Automated Construction and Classification of Decision Tree Classifier Based on Single-Temporal MODIS Data[J]. Geomatics and Information Science of Wuhan University, 2009, 34(2): 191-194.
    [8]LIAO Mingsheng, JIANG Liming, LIN Hui, YANG Limin. Estimating Urban Impervious Surface Percent Using Boosting as a Refinement of CART Analysis[J]. Geomatics and Information Science of Wuhan University, 2007, 32(12): 1099-1102.
    [9]YU Xin, ZHENG Zhaobao, YE Zhiwei, TIAN Liqiao. Texture Classification Based on Tree Augmented Naive Bayes Classifier[J]. Geomatics and Information Science of Wuhan University, 2007, 32(4): 287-289.
    [10]GUO Jing, LIU Guangjun, DONG Xurong, GUO Lei. 2-Level R-tree Spatial Index Based on Spatial Grids and Hilbert R-tree[J]. Geomatics and Information Science of Wuhan University, 2005, 30(12): 1084-1088.
  • Cited by

    Periodical cited type(13)

    1. 陈月,王磊,池深深,王羽,戚鑫鑫,朱尚军. 基于SBAS-InSAR和CNN-GRU模型的采动村庄地表沉降监测预计. 金属矿山. 2025(02): 138-144 .
    2. 何毅,姚圣,陈毅,闫浩文,张立峰. ConvLSTM神经网络的时序InSAR地面沉降时空预测. 武汉大学学报(信息科学版). 2025(03): 483-496 .
    3. 倪尔瑞,张建新,邱明剑,权力奥,朱晓峻. 基于SBAS-InSAR技术的淮北市地表沉降监测分析. 北京测绘. 2024(03): 312-317 .
    4. 吴启琛,于瑞鹏,王丽,赵乙泽,范开放. 利用Sentinel-1的山东枣庄高新区地面沉降监测与分析. 地理空间信息. 2024(06): 80-83 .
    5. 杨芳,丁仁军,李勇发. 基于SBAS-InSAR技术的金沙江流域典型滑坡时空演化特征分析. 测绘通报. 2024(11): 102-107 .
    6. 祝杰,李瑜,师宏波,刘洋洋,韩宇飞,邵银星,王坦. 鹤岗煤矿区地面沉降时空特征InSAR时间序列监测研究. 中国地震. 2023(03): 596-608 .
    7. 柴龙飞,魏路,张震. 基于SBAS-InSAR的安徽省宿州市埇桥区2019—2022年地面沉降监测及影响因素分析研究. 安徽地质. 2023(04): 348-352 .
    8. 祝杰,韩宇飞,王坦,李瑜,王阅兵,师宏波,刘洋洋,樊俊屹,邵银星. 2017年九寨沟M_S7.0地震同震地表三维形变场解算研究. 中国地震. 2022(02): 348-359 .
    9. 吴毅彬,葛红斌,刘光庆,刘海旺. 基于MT-InSAR技术的厦门新机场填海区沉降监测. 工程勘察. 2021(02): 57-61 .
    10. 翟振起. 基于InSAR沉降监测技术的城市供水管线安全监测系统开发. 水利科学与寒区工程. 2021(01): 103-106 .
    11. 廖明生,王茹,杨梦诗,王楠,秦晓琼,杨天亮. 城市目标动态监测中的时序InSAR分析方法及应用. 雷达学报. 2020(03): 409-424 .
    12. 熊寻安,王明洲,龚春龙. MT-InSAR技术监测水库土石坝表面变形研究. 测绘地理信息. 2019(05): 78-81 .
    13. 王茹,杨天亮,杨梦诗,廖明生,林金鑫,张路. PS-InSAR技术对上海高架路的沉降监测与归因分析. 武汉大学学报(信息科学版). 2018(12): 2050-2057 .

    Other cited types(4)

Catalog

    Article views PDF downloads Cited by(17)
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return