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RECOVERY OF THE EARTH’S GRAVITY FIELD FROM GOCE SATELLITE GRAVITY GRADIOMETRY: A Case Study

RECOVERY OF THE EARTH’S GRAVITY FIELD FROM GOCE SATELLITE GRAVITY GRADIOMETRY: A Case Study. Oleg Abrikosov and Peter Schwintzer GeoForschungsZentrum Potsdam Department 1 “ Geodesy and Remote Sensing”. Contents.

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RECOVERY OF THE EARTH’S GRAVITY FIELD FROM GOCE SATELLITE GRAVITY GRADIOMETRY: A Case Study

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  1. RECOVERY OF THE EARTH’S GRAVITY FIELD FROM GOCE SATELLITE GRAVITY GRADIOMETRY:A Case Study Oleg AbrikosovandPeter Schwintzer GeoForschungsZentrum Potsdam Department 1 “Geodesy and Remote Sensing”

  2. Contents • Algorithm for computation of the gravity gradients in the gradiometer reference frame • Simulation of GOCE SGG data • Contribution of main geopotential constituents into the gravity gradients • Decorrelation of GOCE SGG data contaminated by colored noise • Results of recovery of the Earth gravity model from simulated SGG data • Conclusions

  3. Computation of the gravity gradients

  4. Simulation of GOCE SGG data Software: EPOS-OC 5.3 Potential models Orbit Local orbital reference frame

  5. Distribution of simulated SGG data Along-track distances between consecutive points  40 km Distances between two ground-tracks 50 – 170 km Number of points 483 840

  6. Statistics of gravity gradients (mE)

  7. PSD of the component RR Maximal amplitudes Statistics (mE/Hz) in MBW

  8. PSD of the component TT Maximal amplitudes Statistics (mE/Hz) in MBW

  9. PSD of the component NN Maximal amplitudes Statistics (mE/Hz) in MBW

  10. If one can define a matrixFsuch that then we can apply it to the system of observation equations: and after that, solve the equivalent system containing uncorrelated noise • We follow the assumption that Cnnis a symmetric circulant Toeplitz matrix of order N equal to the number of observation points. If we additionally require F to be a matrix of the same type, we define it completely by its first row: Decorrelation of the gravity gradients

  11. Performed tests • Filter should be truncated to a relatively short length comparable with the MBW of GOCE gradiometry. We have tested sucha truncation for 2 practical cases • amplitudes |F(n)|come from a-priori given PSD of the gradiometer noise • amplitudes |F(n)|are estimated as DFT of the sum of the measured diagonal components of the gradient tensor • Colored noise was generated for samp-ling rates 1s – 5 s with various behavior of the noise spectrum below 1 mHz

  12. In the frequency band not covered by the filter we got the ratioindependently from the filter length and from the sampling rate Filtering results (an example of filter length 450 s)

  13. Relative magnitudes ofoff-diagonal coefficients Maximal 20.8%Mean 0.7%R.m.s. 1.8% Recovery of the Earth gravity model • Simulated observations: • 3 diagonal components of the gradient tensor computed from the GPM98CR model up to degree 720 contaminated by • colored noise with below1 mHz • The filter of length 450 s was applied • The normal system has been computed for 32757 coefficients up to degree 180 • The normal matrix has a diagonally dominant structure • Solution technique:Cholesky decomposition without any stabilization

  14. Accuracy of the recovered gravity model • The GOCE mission baseline accuracy for the geoid (1 cm) is fulfilled for harmonic coefficients from degree 34 to at least 180, and for gravity (1 mGal) from degree 7 to at least 180

  15. Conclusions • Various aspects of the direct approach to process GOCE SGG data have been investigated • A solution for the Earth gravity field has been obtained complete to degree/order 180 meeting the baseline accuracy requirements, not taking into account the long wavelength part ( > 1000 km) which will be recovered by GPS-GOCE satellite-to-satellite tracking • Observation equations were computed directly in the gradiometer reference frame in order to avoid frame transformations degrading the exploitation of GOCE SGG data • The observations were to a large extent de-correlated by filtering taking into account a realistic colored noise model • Problems like solution stabilization when going to higher resolutions and the polar gap infecting the accuracy of solved-for zonal and near-zonal terms need to be investigated within the proposed approach

  16. Acknowledgements The German Ministry of Education and Research (BMBF) supports the GOCE data exploitation development within the GEOTECHNOLOGIEN R&D special program under grant 03F0329D The presented work also largely benefits from the activities of the European GOCE Gravity Consortium (EGG-C) Thank you !

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