利用引力梯度数据计算径向梯度的优化方法

doi:10.11947/j.AGCS.2016.20160007

测绘学报 ›› 2016, Vol. 45 ›› Issue (7): 775-781.doi: 10.11947/j.AGCS.2016.20160007

利用引力梯度数据计算径向梯度的优化方法

孟祥超¹, 万晓云², 于锦海¹, 朱永超¹, 冯炜^3,4

1. 中国科学院计算地球动力学重点实验室, 北京 100049;
2. 钱学森空间技术实验室, 北京100094;
3. 中国科学院测量与地球物理研究所, 湖北武汉 430077;
4. 北京卫星导航中心, 北京 100049

收稿日期:2016-01-13 修回日期:2016-04-15 出版日期:2016-07-20 发布日期:2016-07-28
通讯作者: 万晓云,E-mail:wxy191954@126.com E-mail:wxy191954@126.com
作者简介:孟祥超(1988-),男,博士生,研究方向为GOCE卫星重力数据处理与分析。E-mail:mxc20061115@163.com
基金资助:
国家自然科学基金（41404019；41274034）；国家863计划（2013AA122502-2）；大地测量与地球动力学国家重点实验室开放基金（SKLGED2014-3-5-E）

Optimization Method for Computing Radial Gravity Gradient Using Gravity Gradient Observations

MENG Xiangchao¹, WAN Xiaoyun², YU Jinhai¹, ZHU Yongchao¹, FENG Wei^3,4

1. Key Laboratory of Computational Geodynamics, Chinese Academy of Sciences, Beijing 100049, China;
2. Qian Xuesen Laboratory of Space Technology, Beijing 100094, China;
3. Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China;
4. Beijing Satellite Navigation Center, Beijing 100049, China

Received:2016-01-13 Revised:2016-04-15 Online:2016-07-20 Published:2016-07-28
Supported by:
The National Natural Science Foundation of China(Nos.41404019;41274034);The National High-tech Research and Development Program of China(863 Program)(No.2013AA122502-2);The Open Fund of State Key Laboratory of Geodesy and Earth's Dynamics(No.SKLGED2014-3-5-E)

摘要/Abstract

摘要： 根据重力梯度观测各分量的方差及协方差信息，提出了利用GOCE梯度数据计算径向重力梯度的优化方法。首先给出了径向重力梯度的计算方法，并深入分析了误差传播规律，通过建立相应的条件极值问题，给出了计算径向重力梯度最优组合因子的方法；通过模拟数据验证了本文所提出的优化因子的优越性。实际数据计算表明：相对于传统方法，采用优化组合因子可使反演所得引力位模型的累积大地水准面精度在250阶时提高约2 cm。由于径向重力梯度不仅可以用于地球引力场模型的求解，也可直接应用于地球物理问题的讨论，因此本文所提出的优化方法也可对部分地球动力学问题的讨论提供方便。

关键词: GOCE, 径向重力梯度, 优化方法, 精度

Abstract: This paper proposes an optimization method for computing the radial gravity gradient by using GOCE gradient measurements, based on the variance-covariance information of gradient observations. The approach for computing the gravity gradient and the error propagation are firstly discussed; and then by solving a conditional extremum problem, we can get an optimal combination factor which can improve the calculation accuracy for the radial gravity gradient. The advantage of the combination factor is validated by simulation data. In actual data processing, the geoid accuracy truncated to degree 250 can be improved by 2 cm by using the optimization method. The radial gravity gradient can not only be used in recovering a gravity field model, but also can be used in kinds of geophysical interpretation, so the method provided in the paper can be helpful in the related researches.

Key words: GOCE, radial gravity gradient, optimization method, accuracy

中图分类号:

P228

孟祥超, 万晓云, 于锦海, 朱永超, 冯炜. 利用引力梯度数据计算径向梯度的优化方法[J]. 测绘学报, 2016, 45(7): 775-781.

MENG Xiangchao, WAN Xiaoyun, YU Jinhai, ZHU Yongchao, FENG Wei. Optimization Method for Computing Radial Gravity Gradient Using Gravity Gradient Observations[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(7): 775-781.

参考文献

[1] BALMINO G, RUMMEL R, VISSER P, et al. Gravity Field and Steady-State Ocean Circulation Mission[R]. The Four Candidate Earth Explorer Core Missions. Noordwijk:ESA Publications Division, 1999.
[2] REGUZZONI M, TSELFES N. Optimal Multi-step Collocation:Application to the Space-Wise Approach for GOCE Data Analysis[J]. Journal of Geodesy, 2009, 83(1):13-29.
[3] PAIL R, BRUINSMA S, MIGLIACCIO F, et al. First GOCE Gravity Field Models Derived by Three Different Approaches[J]. Journal of Geodesy, 2011, 85(11):819-843.
[4] PAIL R, GOIGINGER H, SCHUH W D, et al. Combined Satellite Gravity Field Model GOCO01S Derived from GOCE and GRACE[J]. Geophysical Research Letters, 2010, 37(20):L20314.
[5] YI Weiyong. An Alternative Computation of A Gravity Field Model from GOCE[J]. Advances in Space Research, 2012, 50(3):371-384.
[6] YU Jinhai, WAN Xiaoyun. Recovery of the Gravity Field from GOCE Data by Using the Invariants of Gradient Tensor[J]. Science China Earth Sciences, 2013, 56(7):1193-1199.
[7] RUMMEL R, GRUBER T. Product Acceptance Review (PAR)-Level 2 Product Report[R]. Noordwijk:ESA, 2012.
[8] RUMMEL R, VAN GELDEREN M. Spectral Analysis of the Full Gravity Tensor[J]. Geophysical Journal International, 1992, 111(1):159-169.
[9] 朱灼文, 于锦海. 超定大地边值问题的准解[J]. 中国科学(B辑), 1992(1):103-112. ZHU Zhuowen, YU Jinhai. Pseudo-Solution on Geodetic Overdetermined Boundary Value Problems[J]. Science in China (Series B), 1992, 35(6):697-708.
[10] 罗志才. 利用卫星重力梯度数据确定地球重力场的理论和方法[D]. 武汉:武汉测绘科技大学, 1996. LUO Zhicai. The Theory and Methodology for Determining the Earth's Gravity Field Using Satellite Gravity Gradiometry Data[D]. Wuhan:Wuhan Technical University of Surveying and Mapping, 1996.
[11] VAN GELDEREN M, RUMMEL R. The Solution of the General Geodetic Boundary Value Problem by Least Squares[J]. Journal of Geodesy, 2001, 75(1):1-11.
[12] 吴星. 卫星重力梯度数据处理理论与方法[D]. 郑州:信息工程大学, 2009. WU Xing. Theory and Methods of Satellite Gradiometry Data Processing[D]. Zhengzhou:Information Engineering University, 2009.
[13] 于锦海, 赵东明. 引力梯度不变量与相关边界条件[J]. 中国科学D辑:地球科学, 2010, 40(2):178-187. YU Jinhai, ZHAO Dongming. The Gravitational Gradient Tensor's Invariants and the Related Boundary Conditions[J]. Science China Earth Sciences, 2010, 53(5):781-790.
[14] 刘晓刚. GOCE卫星测量恢复地球重力场模型的理论与方法[D]. 郑州:信息工程大学, 2011. LIU Xiaogang. Theory and Methods of the Earth's Gravity Field Model Recovery from GOCE Data[D]. Zhengzhou:Information Engineering University, 2011.
[15] WAN Xiaoyun, YU Jinhai. Derivation of the Radial Gradient of the Gravity Based on Non-full Tensor Satellite Gravity Gradients[J]. Journal of Geodynamics, 2013, 66(2):59-64.
[16] FUCHS M, BOUMAN J, BROERSE T, et al. Observing Coseismic Gravity Change from the Japan Tohoku-Oki 2011 Earthquake with GOCE Gravity Gradiometry[J]. Journal of Geophysical Research, 2013, 118(10):5712-5721.
[17] BOUMAN J, FUCHS M, IVINS E, et al. Antarctic Outlet Glacier Mass Change Resolved at Basin Scale from Satellite Gravity Gradiometry[J]. Geophysical Research Letters, 2014, 41(16):5919-5926.
[18] 赫尔默特·莫里兹. 高等物理大地测量学[M]. 宁津生, 管泽霖, 译. 北京:测绘出版社, 1984:194-198. MORITZ H. Advanced Physical Geodesy[M]. NING Jinsheng, GUAN Zelin, Trans. Beijing:Surveying and Mapping Press, 1984:194-198.
[19] ESA. GOCE Level 1b Products User Handbook[R]. GOCE-GSEG-EOPG-TN-06-0137. Noordwijk:ESA, 2008.
[20] RUMMEL R, YI Weiyong, STUMMER C. GOCE Gravitational Gradiometry[J]. Journal of Geodesy, 2011, 85(11):777-790.
[21] YI Weiyong, RUMMEL R, GRUBER T. Gravity Field Contribution Analysis of GOCE Gravitational Gradient Components[J]. Studia Geophysica et Geodaetica, 2013, 57(2):174-202.
[22] PAVLIS N K, HOLMES S A, KENYON S C, et al. An Earth Gravitational Model to Degree 2160:EGM2008[C]//Presented at the 2008 General Assembly of the European Geosciences Union. Vienna:[s.n.], 2008.
[23] 万晓云, 于锦海, 曾艳艳. GOCE引力梯度的频谱分析及滤波[J]. 地球物理学报, 2012, 55(9):2909-2916. WAN Xiaoyun, YU Jinhai, ZENG Yanyan. Frequency Analysis and Filtering Processing of Gravity Gradients Data from GOCE[J]. Chinese Journal of Geophysics, 2012, 55(9):2909-2916.
[24] 徐新禹. 卫星重力梯度及卫星跟踪卫星数据确定地球重力场的研究[D]. 武汉:武汉大学, 2008. XU Xinyu. Study of Determing the Earth's Gravity Field from Satellite Gravity Gradient and Satellite-to-satellite Tracking Data[D]. Wuhan:Wuhan University, 2008.
[25] 钟波. 基于GOCE卫星重力测量技术确定地球重力场的研究[D]. 武汉:武汉大学, 2010. ZHONG Bo. Study on the Determination of the Earth's Gravity Field from Satellite Gravimetry Mission GOCE[D]. Wuhan:Wuhan University, 2010.
[26] 万晓云, 于锦海. 极地空白对GOCE引力场恢复的影响[J]. 测绘学报, 2013, 42(3):317-322. WAN Xiaoyun, YU Jinhai. Influence of Polar Gaps on Gravity Field Recovery Using GOCE Data[J]. Acta Geodaetica et Cartographica Sinica, 2013, 42(3):317-322.
[27] SCHUH W D. The Processing of Band-limited Measurements; Filtering Techniques in the Least Squares Context and in the Presence of Data Gaps[J]. Space Science Reviews, 2003, 108(1-2):67-78.

利用引力梯度数据计算径向梯度的优化方法

Optimization Method for Computing Radial Gravity Gradient Using Gravity Gradient Observations

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	王任享, 王建荣. 我国卫星摄影测量发展及其进步[J]. 测绘学报, 2022, 51(6): 804-810.
[2]	潘娟霞, 邹贤才. GOCE引力梯度内部校准方法[J]. 测绘学报, 2022, 51(2): 192-200.
[3]	黄谟涛, 邓凯亮, 吴太旗, 欧阳永忠, 陈欣, 刘敏, 王许. 重力异常向上延拓严密改化模型及向下延拓应用[J]. 测绘学报, 2022, 51(1): 41-52.
[4]	谢俊峰, 刘仁. 全波形星载激光测距误差抑制的滑动窗口高斯拟合算法[J]. 测绘学报, 2021, 50(9): 1240-1250.
[5]	王乐洋, 李志强. 非线性模型精度评定的Bootstrap方法及其加权采样改进方法[J]. 测绘学报, 2021, 50(7): 863-878.
[6]	李涛, 唐新明, 高小明, 陈乾福, 张祥. SAR卫星业务化地形测绘能力分析与展望[J]. 测绘学报, 2021, 50(7): 891-904.
[7]	王乐洋, 陈涛, 邹传义. 病态乘性误差模型的加权最小二乘正则化迭代解法及精度评定[J]. 测绘学报, 2021, 50(5): 589-599.
[8]	袁运斌, 李敏, 霍星亮, 李子申, 王宁波. 北斗三号全球导航卫星系统全球广播电离层延迟修正模型(BDGIM)应用性能评估[J]. 测绘学报, 2021, 50(4): 436-447.
[9]	陈鑑华, 张兴福, 沈云中, 陈秋杰, 李伟超. GOCE卫星重力梯度观测值的时变重力场变化改正及影响分析[J]. 测绘学报, 2021, 50(3): 324-332.
[10]	唐新明, 谢俊峰, 莫凡, 窦显辉, 李新, 李少宁, 李松, 黄庚华, 付兴科, 刘仁, 朱广彬, 欧阳斯达, 唐洪钊, 陈辉. 高分七号卫星双波束激光测高仪在轨几何检校与试验验证[J]. 测绘学报, 2021, 50(3): 384-395.
[11]	巩秀强, 袁俊军, 胡小工, 王彬, 陈俊平, 周善石. 北斗广播电文钟差模型精度评估及改善策略[J]. 测绘学报, 2021, 50(2): 181-188.
[12]	李国元, 唐新明, 陈继溢, 么嘉棋, 刘诏, 高小明, 左志强, 周晓青. 高分七号卫星激光测高数据处理与精度初步验证[J]. 测绘学报, 2021, 50(10): 1338-1348.
[13]	章传银, 马旭, 章磊, 丁剑. 基于GNSS水准和重力场误差特性的大地水准面精度评估方法[J]. 测绘学报, 2021, 50(1): 12-17.
[14]	刘伟平, 郝金明, 吕志伟, 谢建涛, 刘婧, 焦博. 北斗三号空间信号测距误差评估与对比分析[J]. 测绘学报, 2020, 49(9): 1213-1221.
[15]	刘焕玲, 文汉江, 徐新禹, 赵永奇, 蔡剑青. GOCE实测数据反演高阶重力场模型的Torus方法[J]. 测绘学报, 2020, 49(8): 965-973.