精密重力测量中相对重力仪格值系数的贝叶斯估计方法

doi:10.11947/j.AGCS.2020.20200185

测绘学报 ›› 2020, Vol. 49 ›› Issue (12): 1543-1553.doi: 10.11947/j.AGCS.2020.20200185

精密重力测量中相对重力仪格值系数的贝叶斯估计方法

王林海¹, 陈石¹, 庄建仓², 卢红艳¹, 张贝¹, 杨锦玲^1,3

1. 中国地震局地球物理研究所, 北京 100081;
2. 情报与系统研究机构统计数理研究所, 东京 106-8569;
3. 福建省地震局, 福建福州 350003

收稿日期:2020-05-15 修回日期:2020-08-26 发布日期:2020-12-25
通讯作者: 陈石 E-mail:chenshi@cea-igp.ac.cn
作者简介:王林海(1992-),男,博士生,研究方向为精密重力观测数据的处理方法。E-mail:wlh@cea-igp.ac.cn
基金资助:
国家重点研发计划（2018YFC0603502）；国家自然科学基金（41774090；U1939205）；中国地震科学实验场专项（2019CSES0105）

Bayesian estimation of the scale factor of relative gravimeter in precise gravity survey

WANG Linhai¹, CHEN Shi¹, ZHUANG Jiancang², LU Hongyan¹, ZHANG Bei¹, YANG Jinling^1,3

1. Institute of Geophysics, China Earthquake Administration, Beijing 100081, China;
2. The Institute of Statistical Mathematics, Research Organization of Information and Systems, Tokyo 106-8569, Japan;
3. Fujian earthquake agency, China Earthquake Administration, Fuzhou 350003, China

Received:2020-05-15 Revised:2020-08-26 Published:2020-12-25
Supported by:
The National Key Research and Development Program of China (No. 2018YFC0603502);The National Natural Science Foundation of China (Nos. 41774090;U1939205);The China Seismic Experiment Site (No. 2019CSES0105)

摘要/Abstract

摘要： 相对重力仪的格值系数随时间会发生微小的变化，是影响精密重力测量精度的重要因素。通常需定期对相对重力仪进行专门的基线标定来评估仪器格值系数的变化。本文提出了一种利用重力观测数据进行格值系数评估的新方法，原理是利用测网中已知的多个绝对重力基准点作为先验约束，同时考虑仪器的非线性漂移变化，将格值系数作为超参数，基于贝叶斯原理和赤池贝叶斯信息准则（ABIC）估计最优值。通过对模拟数据的测试，该方法在高斯噪声和仪器非线性漂移等不确定性存在的情况下，可以获得格值系数的准确估计结果。对实测重力数据的测试表明：估计的格值系数与测量前在基线场标定的格值系数差值在5×10^-5以内；而且相较于采用标定不准确的格值系数，该方法可以获得与绝对重力测量结果差异更小的平差重力值。本文研究结果为有效提高精密重力测量的效率和精度提供了方法保障。

关键词: 精密重力测量, 相对重力仪, 贝叶斯原理, 格值系数估计

Abstract: The scale factor of the relative gravimeter changes slightly with time, which is an important factor affecting the accuracy of precise gravity survey. It is necessary to regularly perform a special baseline calibration on the relative gravimeter to evaluate the change of the instrument’s scale factor. This study presents a new method that can be used to evaluate the scale factor based on the gravity observation data only. The principle is to use multiple absolute gravity datum stations known in the survey network as constraints, and to take into account the nonlinear drift of the instrument, and then to estimate scale factor as one of the hyper-parameters by Bayesian theory and Akaike’s Bayesian information criterion (ABIC). Through simulation data testing, this method can obtain the accurate estimation of scale factor in the presence of uncertainties such as Gaussian noise and instrument nonlinear drift. The test of the measured gravity data shows that: the differences between the estimated scale factors and the calibration results of baseline field before measurement are within 5×10^-5, and compared with using the inaccurate calibrated scale factors, this method can obtain the better estimation of gravity values which are less different from the results of absolute gravimetry. The results of this study provide method guarantee for effectively improving the efficiency and accuracy of precise gravity survey.

Key words: precise gravity survey, relative gravimeter, Bayesian theory, scale factor estimation

中图分类号:

P312

王林海, 陈石, 庄建仓, 卢红艳, 张贝, 杨锦玲. 精密重力测量中相对重力仪格值系数的贝叶斯估计方法[J]. 测绘学报, 2020, 49(12): 1543-1553.

WANG Linhai, CHEN Shi, ZHUANG Jiancang, LU Hongyan, ZHANG Bei, YANG Jinling. Bayesian estimation of the scale factor of relative gravimeter in precise gravity survey[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(12): 1543-1553.

参考文献

[1] 李辉, 申重阳, 孙少安, 等. 中国大陆近期重力场动态变化图像[J]. 大地测量与地球动力学, 2009, 29(3):1-10. LI Hui, SHEN Chongyang, SUN Shaoan, et al. Dynamic gravity change in recent years in China continent[J]. Journal of Geodesy and Geodynamics, 2009, 29(3):1-10.
[2] 申重阳, 李辉, 孙少安, 等. 重力场动态变化与汶川Ms8.0地震孕育过程[J]. 地球物理学报, 2009, 52(10):2547-2557. SHEN Chongyang, LI Hui, SUN Shaoan, et al. Dynamic variations of gravity and the preparation process of the Wenchuan Ms8.0 earthquake[J]. Chinese Journal of Geophysics, 2009, 52(10):2547-2557.
[3] 祝意青, 刘芳, 李铁明, 等. 川滇地区重力场动态变化及其强震危险含义[J]. 地球物理学报, 2015, 58(11):4187-4196. ZHU Yiqing, LIU Fang, LI Tieming, et al. Dynamic variation of the gravity field in the Sichuan-Yunnan region and its implication for seismic risk[J]. Chinese Journal of Geophysics, 2015, 58(11):4187-4196.
[4] CHEN Shi, LIU Mian, XING Lelin, et al. Gravity increase before the 2015Mw7.8 Nepal earthquake[J]. Geophysical Research Letters, 2016, 43(1):111-117.
[5] 陈石, 王谦身. 蒙古及周边地区重力异常和地壳不均匀体分布[J]. 地球物理学报, 2015, 58(1):79-91. CHEN Shi, WANG Qianshen. Gravity anomalies and the distributions of inhomogeneous masses in the crust of Mongolia and its surrounding regions[J]. Chinese Journal of Geophysics, 2015, 58(1):79-91.
[6] 王谦身, 滕吉文, 张永谦, 等. 陕渝黔桂1800 km超长探测剖面重力异常场特征及深部地壳结构探榷[J]. 地球物理学报, 2016, 59(11):4139-4152. WANG Qianshen, TENG Jiwen, ZHANG Yongqian, et al. Discussion on the gravity anomaly and deep crustal structure of an 1800 km long profile crossing Shaanxi, Chongqing, Guizhou and Guangxi[J]. Chinese Journal of Geophysics, 2016, 59(11):4139-4152.
[7] 张为民, 王勇, 许厚泽, 等. 用FG5绝对重力仪检测青藏高原拉萨点的隆升[J]. 科学通报, 2000, 45(20):2213-2216. ZHANG Weimin, WANG Yong, XU Houze, et al. Test of the uplift of Tibetan plateau by FG5 absolute gravimeter at Lhasa station[J]. Chinese Science Bulletin, 2000, 45(20):2213-2216.
[8] 王勇, 张为民, 詹金刚, 等. 重复绝对重力测量观测的滇西地区和拉萨点的重力变化及其意义[J]. 地球物理学报, 2004, 47(1):95-100. WANG Yong, ZHANG Weimin, ZHAN Jingang, et al. Gravity change detected by repeated absolute gravity measurements in the western Yunnan and Lhasa, China and its implication[J]. Chinese Journal of Geophysics, 2004, 47(1):95-100.
[9] SUN Wenke, WANG Qi, LI Hui, et al. Gravity and GPS measurements reveal mass loss beneath the Tibetan Plateau:geodetic evidence of increasing crustal thickness[J]. Geophysical Research Letters, 2009, 36(2):L02303.
[10] 邢乐林, 孙文科, 李辉, 等. 用拉萨点大地测量资料检测青藏高原地壳的增厚[J]. 测绘学报, 2011, 40(1):41-44, 58. XING Lelin, SUN Wenke, LI Hui, et al. Present-day crust thickness increasing beneath the Qinghai-Tibetan plateau by using geodetic data at Lhasa station[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(1):41-44, 58.
[11] 王林松, 陈超, 马险, 等. 基于SRTM-DEM数据的三峡库区蓄水负荷模型及其地表重力与形变响应模拟[J]. 测绘学报, 2016, 45(10):1148-1156. DOI:10.11947/j.AGCS.2016.20160016. WANG Linsong, CHEN Chao, MA Xian, et al. A water storage loading model by SRTM-DEM data and surface response simulation of gravity and deformation in the three gorges reservoir of China[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(10):1148-1156. DOI:10.11947/j.AGCS.2016.20160016.
[12] CARBONE D, RYMER H. Calibration shifts in a LaCoste-and-Romberg gravimeter:comparison with a Scintrex CG-3M[J]. Geophysical Prospecting, 1999, 47(1):73-83.
[13] Scintrex Ltd. CG-5 Scintrex autograv system operation manual, part I # 867700 Revision 8[M]. Concord:Scintrex Limited, 2012.
[14] VALLIANT H D. Gravity meter calibration at LaCoste and Romberg[J]. Geophysics, 1991, 56(5):705-711.
[15] 孙少安, 项爱民, 吴维日. LCR-G型重力仪仪器参数的时变特征[J]. 大地测量与地球动力学, 2002, 22(2):101-105. SUN Shaoan, XIANG Aimin, WU Weiri. Time-varying characteristics of LCR-G gravimeter parameters[J]. Journal of Geodesy and Geodynamics, 2002, 22(2):101-105.
[16] PARSELIUNAS E, PETROSKEVICIUS P, BIRVYDIENE R, et al. Investigation of the automatic gravimeters Scintrex CG-5 and analysis of gravimetric measurements[C]//Proceedings of the 8th International Conference on Environmental Engineering. Vilnius, Lithuania:Vilnius Gediminas Technical University Publishing House "Technika", 2011:1416-1423.
[17] 梁伟锋, 刘芳, 祝意青, 等. 重力仪一次项系数对重力场动态变化的影响研究[J]. 大地测量与地球动力学, 2015, 35(5):882-886. LIANG Weifeng, LIU Fang, ZHU Yiqing, et al. Research on the effect of one degree term of chromatic polynomial of gravimeter on gravity dynamic change[J]. Journal of Geodesy and Geodynamics, 2015, 35(5):882-886.
[18] 郝洪涛, 李辉, 刘子维, 等. 基于重力差方法检测重力仪一次项格值系数变化[J]. 大地测量与地球动力学, 2011, 31(1):87-90. HAO Hongtao, LI Hui, LIU Ziwei, et al. Study on change of scale parameters in linear term of gravimeter with gravity difference method[J]. Journal of Geodesy and Geodynamics, 2011, 31(1):87-90.
[19] MEURERS B. Scintrex CG5 used for superconducting gravimeter calibration[J]. Geodesy and Geodynamics, 2018, 9(3):197-203.
[20] 隗寿春, 祝意青, 赵云峰, 等. CG-5重力仪格值系数对重力数据处理的影响[J]. 大地测量与地球动力学, 2019, 39(2):210-214. WEI Shouchun, ZHU Yiqing, ZHAO Yunfeng, et al. Impact on gravity data process of scale factor coefficient of CG-5 gravimeter[J]. Journal of Geodesy and Geodynamics, 2019, 39(2):210-214.
[21] ONIZAWA S Y. Apparent calibration shift of the Scintrex CG-5 gravimeter caused by reading-dependent scale factor and instrumental drift[J]. Journal of Geodesy, 2019, 93(9):1335-1345.
[22] 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.
[23] 邢乐林, 李辉, 李建国, 等. 陆态网络绝对重力基准的建立及应用[J]. 测绘学报, 2016, 45(5):538-543. DOI:10.11947/j.AGCS.2016.20140653. XING Lelin, LI Hui, LI Jianguo, et al. Establishment of absolute gravity datum in CMONOC and its application[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(5):538-543. DOI:10.11947/j.AGCS.2016.20140653.
[24] CHEN Shi, ZHUANG Jiancang, LI Xiaoyi, et al. Bayesian approach for network adjustment for gravity survey campaign:methodology and model test[J]. Journal of Geodesy, 2019, 93(5):681-700.
[25] GU Yongwei, GUI Qingming, ZHANG Xuan, et al. Iterative solution of regularization to ill-conditioned problems in geodesy and geophysics[J]. Journal of Geodesy and Geoinformation Science, 2019, 2(1):59-65.
[26] AKAIKE H. Likelihood and the Bayes procedure[M]//BERNARDO J M, DEGROOT M H, LINDLEY D V, et al. Bayesian Statistics. Valencia:Valencia University Press, 1980:143-166.
[27] FUKAHATA Y, WRIGHT T J. A non-linear geodetic data inversion using ABIC for slip distribution on a fault with an unknown dip angle[J]. Geophysical Journal International, 2008, 173(2):353-364.
[28] TOYOSHIMA M, SHIBUYA H, MATSUSHIMA M, et al. Equivalent source mapping of the lunar crustal magnetic field using ABIC[J]. Earth, Planets and Space, 2008, 60(4):365-373.
[29] UCHIDA T. Smooth 2-D inversion for Magnetotelluric data based on statistical criterion ABIC[J]. Journal of Geomagnetism and Geoelectricity, 1993, 45(9):841-858.
[30] NELDER J A, MEAD R. A simplex method for function minimization[J]. The Computer Journal, 1965, 7(4):308-313.
[31] DEHANT V, DEFRAIGNE P, WAHR J M. Tides for a convective earth[J]. Journal of Geophysical Research:Solid Earth, 1999, 104(B1):1035-1058.
[32] MERRIAM J B. Atmospheric pressure and gravity[J]. Geophysical Journal International, 1992, 109(3):488-500.
[33] 国家地震局. 地震重力测量规范[M]. 北京:地震出版社, 1997. State Seismological Bureau. Seismological gravimetric standard[M]. Beijing:Seismological Press, 1997.

精密重力测量中相对重力仪格值系数的贝叶斯估计方法

Bayesian estimation of the scale factor of relative gravimeter in precise gravity survey

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 3

编辑推荐

Metrics

本文评价

[1]	孙和平, 徐建桥, 崔小明. 重力场的地球动力学与内部结构应用研究进展[J]. 测绘学报, 2017, 46(10): 1290-1299.
[2]	高春春陆洋张子占史红岭杜宗亮朱传东. GOCE地球重力场模型在青藏地区的评价及分析[J]. 测绘学报, 2014, 43(1): 21-29.
[3]	董杰, 张泽宇, 文汉江, 孙文科. 超导重力数据检测到的2011年日本东北大地震(M_w 9.0)震前重力异常及同震重力变化[J]. 测绘学报, 2022, 51(1): 63-70.