Accuracy of unmodified Stokes’ integration in the R-C-R procedure for geoid computation

Zahra Ismail (1, 2) , Olivier Jamet (1)

1 LAREG - LAboratoire de REcherche en Géodésie [Paris]
2 UPD7 - Université Paris Diderot - Paris 7

Geoid determinations by the Remove-Compute-Restore (R-C-R) technique involve the application of Stokes' integral on reduced gravity anomalies. Numerical Stokes' integration produces an error depending on the choice of the integration radius, grid resolution and Stokes' kernel function. In this work, we aim to evaluate the accuracy of Stokes' integral through a study on synthetic gravitational signals derived from EGM2008 on three different landscape areas with respect to the size of the integration domain and the resolution of the anomaly grid. The influence of the integration radius was studied earlier by several authors. Using real data, they found that the choice of relatively small radii (less than 1 •) enables to reach an optimal accuracy. We observe a general behaviour coherent with these earlier studies. On the other hand, we notice that increasing the integration radius up to 2 • or 2.5 • might bring significantly better results. We also note that, unlike the smallest radius corresponding to a local minimum of the error curve, the optimal radius in the range 0 • to 6 • depends on the terrain characteristics. We find also that the high frequencies, from degree 600, improve continuously with the integration radius in both semi-mountainous and mountain areas. Finally, we note that the relative error of the computed geoid heights depends weakly on the anomaly spherical harmonic degree in the range from degree 200 to 2000. It remains greater than 10% for any integration radii up to 6 •. This result tends to prove that a one centimetre accuracy cannot be reached in semi-mountainous and mountainous regions with the unmodified Stokes' kernel.

Mots clés: Integration radius; Stokes' integration; Remove-Compute-Restore; Geoid; GRAVSOFT 1; EGM2008; Gravity anomaly grid resolution

Domaines: Sciences de la Terre

Zahra Ismail, Olivier Jamet. Accuracy of unmodified Stokes’ integration in the R-C-R procedure for geoid computation. Journal of Applied Geodesy, 2015, 9 (2), ⟨10.1515/jag-2014-0026⟩. ⟨hal-02612190⟩