On the ellipsoidal corrections to gravity anomalies computed using the inverse Stokes integral

<p>It is used to state that all geoid determination techniques should yield to the same geoid if the indirect effect is properly taken into account (Heiskanen and Moritz, 1967). The current study compares different geoid determination techniques for Austria. The used techniques are the gravimetric, astrogravimetric and astrogeodetic geoid determination techniques. The available data sets (gravity, deflections of the vertical, height, GPS) are described. The window remove-restore technique (Abd-Elmotaal and Kuehtreiber, 2003) has been used. The available gravity anomalies and the deflections of the vertical have been topographically-isostatically reduced using the Airy isostatic hypothesis. The reduced deflections have been used to interpolate deflections on a relatively dense grid covering the data window. These gridded reduced deflections have been used to compute an astrogeodetic geoid for Austria using least-squares collocation technique within the remove-restore scheme. The Vening Meinesz formula has been used to compute an astrogravimetric geoid for Austria. Another gravimetric geoid for Austria has been determined in the framework of the window remove-restore technique using Stokes integral with modified Stokes kernel. All computed geoids have been validated using GNSS/levelling derived geoid. A wide comparison among the derived geoids computed within the current investigation has been carried out.</p>

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

Journal of Applied Geodesy ◽

10.1515/jag-2014-0026 ◽

2015 ◽

Vol 9 (2) ◽

Cited By ~ 1

Author(s):

Zahra Ismail ◽

Olivier Jamet

Keyword(s):

Gravity Anomalies ◽

Real Data ◽

Mountain Areas ◽

General Behaviour ◽

Spherical Harmonic Degree ◽

Mountainous Regions ◽

Optimal Accuracy ◽

Stokes Integral ◽

Stokes Kernel ◽

Geoid Computation

AbstractGeoid determinations by the Remove-Compute-Restore (R-C-R) technique involves 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 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 also find 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.

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