Comparison of methods for high-degree spherical harmonic analysis of a function given on a spheroid
19/09/2016 | 17:30 | Session 2: Global gravity field modelling
Author(s): Sten Claessens
A comparison is made between two analytical methods for the computation of a truncated series of solid spherical harmonic coefficients from data on a spheroid (i.e. an oblate ellipsoid of revolution). The two methods are: 1) the spheroidal harmonics method that relies on the Hotine-Jekeli transformation, and 2) the surface harmonics method that uses a transformation between surface and solid spherical harmonic coefficients. The latter method has been improved by a two-step procedure to extend the viability of the transformation well beyond degree and order 520. The methods are each tested numerically and then compared both numerically and conceptually. Both methods are shown to achieve sub-micrometre precision in terms of height anomalies for a high-degree model. However, both methods result in spherical harmonic models that are different by a significant amount in both height anomalies and gravity disturbances due to the different coordinate system used. While the spheroidal harmonics method requires the use of an ellipsoidal coordinate system, the surface harmonics method uses only spherical polar coordinates. The spheroidal harmonics method is numerically more efficient, but the surface harmonics method can more easily be extended to cases where (a linear combination of) normal derivatives of the function under consideration are given on the surface of the spheroid. The latter therefore provides a solution to many types of ellipsoidal boundary-value problems in the spectral domain.