Thursday 25 August 2005

G2
1330-1500 hours

381
New analytic approaches to the construction of a spherical harmonic geopotential model
Claessens, Sten¹, Featherstone, Will¹
1 Western Australian Centre for Geodesy, Curtin University of Technology, Perth, Western Australia
Author email: claesses@vesta.curtin.edu.au
The computation of spherical harmonic geopotential coefficients from gravity anomalies is a fundamental stage in all modern geoid computation. For the evaluation of low-degree coefficients, a numerical least-squares adjustment is usually applied, but because of the large computational burden of this numerical method, analytical formulas are normally used for higher degrees. Various analytic methods to compute spherical harmonic geopotential coefficients from terrestrial data differ in the way the ellipticity of the Earth is taken into account. None of the existing methods is exact, and all show theoretical and numerical inaccuracies, especially in the high degrees of the spectrum (>360). In this paper, three approaches to compute geopotential coefficients are investigated: 1) computation of coefficients on a bounding sphere from upward-continued surface data, 2) computation from surface data on the ellipsoid using Green's second identity, and 3) direct evaluation of the ellipsoidal boundary condition in spherical harmonics. The first two approaches have been proposed earlier (e.g. Petrovskaya, J.Geod. 2001; Sjöberg, J.Geod. 2003), but here they are extended upon to significantly increase their accuracy. The third approach is completely new and arguably conceptually the simplest, since it follows the same line of derivation as the well-known spherical approximation. All solutions are based on a recently derived general relation among spherical harmonics, and all have in common that the coefficients are computed from a weighted summation over spherically approximated coefficients. There are, however, numerical differences in accuracy and efficiency between the different approaches, and these will also be presented. Moreover, the numerical performance of all three methods will be compared to Jekeli's ellipsoidal harmonic approach (manu.geod., 1988).

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