Biao Lu1,2,3 · Zhicai Luo4,5 · Bo Zhong1,6 · Hao Zhou4 · Frank Flechtner2,3 · Christoph Förste2 · Franz Barthelmes2 · Rui Zhou7
Received: 19 July 2016 / Accepted: 13 October 2017
© Springer-Verlag GmbH Germany, part of Springer Nature 2017
1 School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, People’s Republic of China
2 GFZ German Research Centre for Geosciences, Telegrafenberg, 14473 Potsdam, Germany
3 Department of Geodesy and Geoinformation Science, Technical University of Berlin, 10623 Berlin, Germany
4 MOE Key Laboratory of Fundamental Physical Quantities Measurement, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China
5 Institute of Geophysics, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China
6 Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, Wuhan University, Wuhan 430079, People’s Republic of China
7 Zhengzhou Information Engineering University, Zhengzhou 450052, People’s Republic of China
Abstract
Based on tensor theory, three invariants of the gravitational gradient tensor (IGGT) are independent of the gradiometer reference frame (GRF). Compared to traditional methods for calculation of gravity field models based on the gravity field and steady-state ocean circulation explorer (GOCE) data, which are affected by errors in the attitude indicator, using IGGT and least squares method avoids the problem of inaccurate rotation matrices. The IGGT approach as studied in this paper is a quadratic function of the gravity field model’s spherical harmonic coefficients. The linearized observation equations for the least squares method are obtained using a Taylor expansion, and the weighting equation is derived using the law of error propagation. We also investigate the linearization errors using existing gravity field models and find that this error can be ignored since the used a-priori model EIGEN-5C is sufficiently accurate. One problem when using this approach is that it needs all six independent gravitational gradients (GGs), but the components Vxy and Vyz of GOCE are worse due to the non-sensitive axes of the GOCE gradiometer. Therefore, we use synthetic GGs for both inaccurate gravitational gradient components derived from the a-priori gravity field model EIGEN-5C. Another problem is that the GOCE GGs are measured in a band-limited manner. Therefore, a forward and backward finite impulse response band-pass filter is applied to the data, which can also eliminate filter caused phase change. The spherical cap regularization approach (SCRA) and the Kaula rule are then applied to solve the polar gap problem caused by GOCE’s inclination of 96.7◦.With the techniques described above, a degree/order 240 gravity field model called IGGT_R1 is computed. Since the synthetic components of Vxy and Vyz are not band-pass filtered, the signals outside the measurement bandwidth are replaced by the a-priori model EIGEN-5C. Therefore, this model is practically a combined gravity field model which contains GOCE GGs signals and long wavelength signals from the a-priori model EIGEN-5C. Finally, IGGT_R1’s accuracy is evaluated by comparison with other gravity field models in terms of difference degree amplitudes, the geostrophic velocity in the Agulhas current area, gravity anomaly differences as well as by comparison to GNSS/leveling data.
Journal of Geodesy
https://doi.org/10.1007/s00190-017-1089-8
