Optimization Method for Computing Radial Gravity Gradient Using Gravity Gradient Observations

doi:10.11947/j.AGCS.2016.20160007

Abstract

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

CLC Number:

P228

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.

References

[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.