scholarly journals The earth’s gravity field recovery using the third invariant of the gravity gradient tensor from GOCE

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Lin Cai ◽  
Xiaoyun Wan ◽  
Houtse Hsu ◽  
Jiangjun Ran ◽  
Xiangchao Meng ◽  
...  

AbstractDue to the independence of the gradiometer instrument’s orientation in space, the second invariant $$I_2$$ I 2 of gravity gradients in combination with individual gravity gradients are demonstrated to be valid for gravity field determination. In this contribution, we develop a novel gravity field model named I3GG, which is built mainly based on three novel elements: (1) proposing to utilize the third invariant $$I_3$$ I 3 of the gravity field and steady-state ocean circulation explorer (GOCE) gravity gradient tensor, instead of using the $$I_2$$ I 2 , similar to the previous studies; (2) applying an alternative two-dimensional fast fourier transform (2D FFT) method; (3) showing the advantages of $$I_3$$ I 3 over $$I_2$$ I 2 in the effect of measurement noise from the theoretical and practical computations. For the purpose of implementing the linearization of the third invariant, this study employs the theory of boundary value problems with sphere approximation at an accuracy level of $$O(J_2^2\cdot T_{ij})$$ O ( J 2 2 · T ij ) . In order to efficiently solve the boundary value problems, we proposed an alternative method of 2D FFT, which uses the coherent sampling theory to obtain the relationship between the 2D FFT and the third invariant measurements and uses the pseudo-inverse via QR factorization to transform the 2D Fourier coefficients to spherical harmonic ones. Based on the GOCE gravity gradient data of the nominal mission phase, a novel global gravity field model (I3GG) is derived up to maximum degree/order 240, corresponding to a spatial resolution of 83 km at the equator. Moreover, in order to investigate the differences of gravity field determination between $$I_3$$ I 3 with $$I_2$$ I 2 , we applied the same processing strategy on the second invariant measurements of the GOCE mission and we obtained another gravity field model (I2GG) with a maximum degree of 220, which is 20 degrees lower than that of I3GG. The root-mean-square (RMS) values of geoid differences indicates that the effects of measurement noise of I3GG is about 20% lower than that on I2GG when compared to the gravity field model EGM2008 (Earth Gravitational Model 2008) or EIGEN-5C (EIGEN: European Improved Gravity model of the Earth by New techniques). Then the accuracy of I3GG is evaluated independently by comparison the RMS differences between Global Navigation Satellite System (GNSS)/leveling data and the model-derived geoid heights. Meanwhile, the re-calibrated GOCE data released in 2018 is also dealt with and the corresponding result also shows the similar characteristics.

2020 ◽  
Vol 222 (1) ◽  
pp. 661-677
Author(s):  
Hao Zhou ◽  
Zebing Zhou ◽  
Zhicai Luo ◽  
Kang Wang ◽  
Min Wei

SUMMARY The goal of this contribution is to investigate the expected improvement of temporal gravity field determination via a couple of high-low satellite-to-satellite tracking (HLSST) missions. The simulation system is firstly validated by determining monthly gravity field models within situ GRACE GPS tracking data. The general consistency between the retrieved solutions and those developed by other official agencies indicates the good performance of our software. A 5-yr full-scale simulation is then performed using the full error sources including all error components. Analysis of each error component indicates that orbit error is the main contributor to the overall HLSST-derived gravity field model error. The noise level of monthly solution is therefore expected to reduce 90 per cent in terms of RMSE over ocean when the orbit accuracy improves for a magnitude of one order. As for the current HLSST mission consisting of a current GNSS receiver and an accelerometer (10−10 and 10−9 m s–2 noise for sensitive and non-sensitive axes), it is expected to observe monthly (or weekly) gravity solution at the spatial resolution of about 1300 km (or 2000 km). As for satellite constellations, a significant improvement is expected by adding the second satellite with the inclination of 70° and the third satellite with the inclination of 50°. The noise reduction in terms of cumulative geoid height error is approximately 51 per cent (or 62 per cent) when the observations of two (or three) HLSST missions are used. Moreover, the accuracy of weekly solution is expected to improve 40–70 per cent (or 27–59 per cent) for three (or two) HLSST missions when compared to one HLSST mission. Due to the low financial costs, it is worthy to build a satellite constellation of HLSST missions to fill the possible gaps between the dedicated temporal gravity field detecting missions.


Knowledge of long-wavelength features of the geopotential is significantly improved by the use of precision satellite tracking with lasers. Tracking data on nine satellites are combined with terrestrial gravimetry to obtain a spherical-harmonics representation of the geopotential complete through degree and order 24. An improved gravity-field model provides better satellite ephemerides and a reference for analysing satellite-to-sea-surface altimetry.


2017 ◽  
Vol 59 (6) ◽  
Author(s):  
Alexander N. Marchenko ◽  
Dmitriy A. Marchenko ◽  
Alexander N. Lopushansky

<p class="Default">The GOCE satellite mission is one of the main achievements of the satellite geodesy for the Earth’s gravitational field recovery. Three different approaches have been developed for the estimation of harmonic coefficients from gradiometry data measured on board of GOCE-satellite. In this paper a special version of the space-wise method based on the second method of Neumann for fast determination of the harmonic coefficients <em>C<sub>nm</sub>, S<sub>nm</sub></em> of the Earth’s gravitational potential is given based on the radial gravity gradients of the EGG_TRF_2 product, except of two polar gaps filled by radial gradients from the EGM2008 gravity model. In the pre-processing stage GOCE-based second degree radial derivatives were averaged to the regular grid through Kalman static filter with additional Gaussean smoothing of residual radial derivatives. All computations are made by iterations. As the first step the determination of the preliminary NULP-01S<strong> </strong>model up to degree/order 220 derived from the Gaussean grid of the GOCE radial derivatives with respect to the WGS-84 reference field was developed based only one of the radial gradients EGG_TRF_2 in the EFRF-frame. In the second iteration the same algorithm is applied to build the NULP-02S gravity field model up to degree/order 250 using the same Gaussean grid with respect to the NULP-01S reference field. The NULP-02S model was verified by means of applying various approaches for the construction of the gridded gravity anomalies and geoid heights in the Black sea area using processing of datasets from six altimetry satellite missions. Comparison of different models with GNSS-levelling data in the USA area demonstrates the independent verification of achieved accuracy of the constructed NULP-02S Earth’s gravity field model.</p>


2009 ◽  
Vol 39 (4) ◽  
pp. 273-299 ◽  
Author(s):  
Mehdi Eshagh

On the convergence of spherical harmonic expansion of topographic and atmospheric biases in gradiometryThe gravity gradiometric data are affected by the topographic and atmospheric masses. In order to fulfill Laplace-Poisson's equation and to simplify the downward continuation process, these effects should be removed from the data. However, if the analytical downward continuation is considered, the gravity gradients can be continued downward disregarding such effects but the result will be biased. The topographic and atmospheric biases can be expressed in terms of spherical harmonics and studying these biases gives some ideas about analytical downward continuation of these quantities to sea level. In formulation of harmonic coefficients of the topographic and atmospheric biases, a truncated binomial expansion of topographic height is used. In this paper, we show that the harmonics are convergent to the third term of this binomial expansion. The harmonics of the biases onVzzare convergent to the first term and they are convergent inVxyfor all the terms. The harmonics of the other components of the gravity gradient tensor are convergent to the second terms, while the third terms are only asymptotically convergent. This means that in terrestrial and airborne gradiometry the biases should be computed just to the second order term, while in satellite gravity gradiometry, e.g. GOCE, the third term can also be considered.


2012 ◽  
Vol 329-330 ◽  
pp. 22-30 ◽  
Author(s):  
C. Hirt ◽  
W.E. Featherstone

2020 ◽  
Vol 94 (7) ◽  
Author(s):  
P. Zingerle ◽  
R. Pail ◽  
T. Gruber ◽  
X. Oikonomidou

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Ignazio Ciufolini ◽  
Antonio Paolozzi ◽  
Erricos C. Pavlis ◽  
Giampiero Sindoni ◽  
John Ries ◽  
...  

Abstract We report the improved test of frame-dragging, an intriguing phenomenon predicted by Einstein’s General Relativity, obtained using 7 years of Satellite Laser Ranging (SLR) data of the satellite LARES (ASI, 2012) and 26 years of SLR data of LAGEOS (NASA, 1976) and LAGEOS 2 (ASI and NASA, 1992). We used the static part and temporal variations of the Earth gravity field obtained by the space geodesy mission GRACE (NASA and DLR) and in particular the static Earth’s gravity field model GGM05S augmented by a model for the 7-day temporal variations of the lowest degree Earth spherical harmonics. We used the orbital estimator GEODYN (NASA). We measured frame-dragging to be equal to $$0.9910 \pm 0.02$$0.9910±0.02, where 1 is the theoretical prediction of General Relativity normalized to its frame-dragging value and $$\pm 0.02$$±0.02 is the estimated systematic error due to modelling errors in the orbital perturbations, mainly due to the errors in the Earth’s gravity field determination. Therefore, our measurement confirms the prediction of General Relativity for frame-dragging with a few percent uncertainty.


Radio Science ◽  
2010 ◽  
Vol 45 (2) ◽  
pp. n/a-n/a ◽  
Author(s):  
Q. Liu ◽  
F. Kikuchi ◽  
K. Matsumoto ◽  
S. Goossens ◽  
H. Hanada ◽  
...  

2007 ◽  
Vol 50 (1) ◽  
pp. 110-115 ◽  
Author(s):  
Xing-Fu ZHANG ◽  
Yun-Zhong SHEN ◽  
Lei-Ming HU

Sign in / Sign up

Export Citation Format

Share Document