The principle of Torus method in Earth's gravity field determination from GOCE satellite gradiometry data is discussed. The Earth's gravity field model complete to degree and order 200 is recovered using simulated satellite gradiometry observations on a Torus grid, and the degree error RMS is smaller than 10-16, which shows the effectiveness of Torus approach. The gravity field model is also resolved using the simulated satellite gradiometry observations given on GOCE orbits of 61 days. The influences of interpolation and polar gaps are analyzed. Without considering the low-order coefficients the geoid degree errors and cumulative errors are very small after three iterations. The maximums of them are only 0.022 mm and 0.099 mm. The white noise with PSD 5 mE/Hz1/2 is added to the simulated observations and the gravity field model complete to degree and order 200 is also computed. The model is compared with that model which is derived using space-wise LS method and the same observations. It shows that the precision of Torus is slightly lower. Without considering the low-order coefficients the maximum geoid degree errors of Torus and space-wise LS method are 1.58 cm and 1.45 cm, and the maximum cumulative geoid errors are 6.37 cm and 5.55 cm, respectively. But the computational efficiency of Torus is greatly improved by using the two-dimensional FFT and the block-diagonal least-squares adjustment. The numerical results show that Torus method is independent and valid. Meanwhile fast resolution of gravity field based on massive amount of GOCE satellite gradiometry observations is feasible.
LIU Huanling
,
WEN Hanjiang
,
XU Xinyu
,
ZHU Guangbin
. Torus Approach in Gravity Field Determination from Simulated GOCE Observations[J]. Acta Geodaetica et Cartographica Sinica, 2015
, 44(9)
: 965
-972
.
DOI: 10.11947/j.AGCS.2015.20150110
[1] ESA. Gravity Field and Steady-state Ocean Circulation Mission. Reports for Mission Selection of the Four Candidate Earth Explorer Core Missions[R]. ESA Publications Division, ES SP-1233(1), 1999.
[2] DRINKWATER M R, HAAGMANS R, MUZI D, et al. The GOCE Gravity Mission: ESA's First Core Earth Explorer[R]. Proceedings of the 3rd International GOCE User Workshop, Frascati, Italy, ESA Special Publication, SP-627, ISBN 92-9092-938-3, 2006: 1-8.
[3] RUMMEL R, VAN GELDEREN M, KOOP R, et al. Spherical Harmonic Analysis of Satellite Gradiometry[M]. Netherlands Geodetic Commission: Publications on Geodesy, New Series 39, 1993.
[4] KOOP R. Global Gravity Field Modeling Using Satellite Gravity Gradiometry[M]. Netherlands Geodetic Commission: Publications on Geodesy, New Series 38, 1993.
[5] 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.
[6] SNEEUW N J. A Semi-analytical Approach to Gravity Field Analysis from Satellite Observations[D]. Munich, Germany: Institut für Astronomische und Physikalische Geodsie, Technische Universitt München, 2000.
[7] SNEEUW N J. Space-wise, Time-wise, Torus and Rosborough Representations in Gravity Field Modeling[J]. Space Science Reviews, 2003, 108(1-2): 37-46.
[8] KLEES R, DITMAR P. The Performance of the Time-wise Semi-analytical Inversion of Satellite Gravity Gradients[M]//DM J, SCHWARZ K P. Vistas for Geodesy in the New Millennium, International Association of Geodesy Symposia. Berlin Heidelberg: Springer, 2001, 125: 253-258.
[9] SCHUH W D, PAIL R, PLANK G. Assessment of Different Numerical Solution Strategies for Gravity Field Recovery[C]// Proceedings of the 1st International GOCE User Workshop, ESA WPP-188, 87-95, ESA/ESTEC, 2001.
[10] PAIL R, WERMUTH M. GOCE SGG and SST Quick-look Gravity Field Analysis[J]. Advances in Geosciences, 2003, 1: 5-9.
[11] PAIL R, PLANK G. GOCE Gravity Field Processing Strategy[J]. Studia Geophysica et Geodaetica, 2004, 48(2): 289-309.
[12] XU Chen. The Torus-based Semi-analytical Approach in Spaceborne Gravimetry[D]. Calgary: Department of Geomatics Engineering, University of Calgary, 2008.
[13] KAULA W M. Theory of Satellite Geodesy: Applications of Satellites to Geodesy[M]. Waltham Massachusetts: Blaisdell Publishing Company, 1966.
[14] SCHRAMA E J O. The Role of Orbit Errors in Processing of Satellite Altimeter Data[M]. Netherlands Geodetic Commission: Publications on Geodesy, New Series 33, 1989.
[15] PAIL R, PLANK G. Assessment of Three Numerical Solution Strategies for Gravity Field Recovery from GOCE Satellite Gravity Gradiometry Implemented on a Parallel Platform[J]. Journal of Geodesy, 2002, 76(8): 462-474.
[16] ESA. GOCE HPF: GOCE Level 2 Product Data Handbook[R]. Technical Note, GO-MA-HPF-GS-0110, 2010.
[17] CAPITAINE N, WALLACE P T, MCCARTHY D D. Expressions to Implement the IAU 2000 Definition of UT1[J]. Astronomy & Astrophysics, 2003, 406(3): 1135-1149.
[18] PAVLIS N K, HOLMES S A, KENYON S C, et al. An Earth Gravitational Model to Degree 2160: EGM2008[J]. EGU General Assembly, 2008, 10: 13-18.
[19] ESA. GOCE L1b Products User Handbook[R]. Technical Note, GOCE-GSEG-EOPGTN-06-0137, 2006.
[20] SNEEUW N J, VAN GELDEREN M. The Polar Gap[M]//SANSÓ F, RUMMEL R. Geodetic Boundary Value Problems in View of the One Centimeter Geoid. Lecture Notes in Earth Sciences. Berlin Heidelberg: Springer, 1997, 65: 559-568.
[21] XU Xinyu, LI Jiancheng, JIANG Weiping, et al. Simulation Study for Recovering GOCE Satellite Gravity Model Based on Space-wise LS Method[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(6): 697-702. (徐新禹, 李建成, 姜卫平, 等. 基于空域最小二乘法求解 GOCE 卫星重力场的模拟研究[J]. 测绘学报, 2011, 40(6): 697-702.)
[22] RUDOLPH S, KUSCHE J, IIK K H. Investigations on the Polar Gap Problem in ESA's Gravity Field and Steady-state Ocean Circulation Explorer Mission (GOCE)[J]. Journal of Geodynamics, 2002, 33(1-2): 65-74.
[23] XU Xinyu, LI Jiancheng, WANG Zhengtao, et al. The Simulation Research on the Tikhonov Regularization Applied in Gravity Field Determination of GOCE Satellite Mission[J]. Acta Geodaetica et Cartographica Sinica, 2010, 39(5): 465-470. (徐新禹, 李建成, 王正涛, 等. Tikhonov正则化方法在GOCE重力场求解中的模拟研究[J]. 测绘学报, 2010, 39(5): 465-470.)
[24] ZHU Guangbin, LI Jiancheng, WEN Hanjiang, et al. Slepian Localized Spectral Analysis of the Determination of the Earth's Gravity Field Using Satellite Gravity Gradiometry Data[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(1): 1-7. (朱广彬, 李建成, 文汉江, 等. 卫星重力梯度数据确定地球重力场的Slepian局部谱分析方法[J]. 测绘学报, 2012, 41(1): 1-7.)
[25] BAUR O, SNEEUW N, GRAFAREND E W. Methodology and Use of Tensor Invariants for Satellite Gravity Gradiometry[J]. Journal of Geodesy, 2008, 82(4-5): 279-293.
