The numerical treatment of the downward continuation problem for the gravity potential

  • W.-D. Schuh
  • B. Kargoll
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 127)


This paper discusses numerical and statistical techniques used to recover the gravity potential from GOCE mission data. In particular, in a closed loop simulation, it is shown that two completely different and independent solution strategies, i.e. the direct method and the semi-analytic approach, lead to essentially identical results. Both methods can give only a finite representation of the gravity potential. The truncation of the infinite series leads to a special type of regularization, denoted as spectral leakage. The size of this effect is estimated in a closed loop simulation. To verify the quality of the gravity field recovery a detailed analysis of the whole adjustment procedure is necessary. Therefore, a step-by-step statistical test strategy is introduced to validate the deterministic model as well as the stochastic assumptions by analyzing the residuals of the decorrelated adjustment problem. First of all a test of randomness is applied to check the assumption of uncorrelated residuals. The assumption of stationarity is checked by variance analysis of different observation groups. Finally, the autocorrelation function and the periodogram of the transformed residuals are tested for significant correlations. To eliminate the remaining correlations the filter model and thus the stochastic model is improved.


Spherical harmonic analysis spectral leakage gradiometry mission GOCE diagnostic checking model validation 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • W.-D. Schuh
    • 1
  • B. Kargoll
    • 1
  1. 1.Institute of Theoretical Geodesy (ITGB)University of BonnBonnGermany

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