Spherical harmonic analysis of a harmonic function given on a spheroid
MetadataShow full item record
A new analytical method for the computation of a truncated series of solid spherical harmonic coefficients (HCs) from data on a spheroid (i.e. an oblate ellipsoid of revolution) is derived, using a transformation between surface and solid spherical HCs. A two-step procedure is derived to extend this transformation beyond degree and order (d/o) 520. The method is compared to the Hotine-Jekeli transformation in a numerical study based on the EGM2008 global gravity model. Both methods are shown to achieve submicrometre precision in terms of height anomalies for a model to d/o 2239. However, both methods result in spherical harmonic models that are different by up to 7.6 mm in height anomalies and 2.5 mGal in gravity disturbances due to the different coordinate system used. While the Hotine-Jekeli transformation requires the use of an ellipsoidal coordinate system, the new method uses only spherical polar coordinates. The Hotine-Jekeli transformation is numerically more efficient, but the new 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. It therefore provides a solution to many types of ellipsoidal boundary-value problems in the spectral domain.
This article has been accepted for publication in Geophysical Journal International©2016. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.
Showing items related by title, author, creator and subject.
Claessens, Sten; Hirt, C. (2015)A surface spherical harmonic expansion of gravity anomalies with respect to a geodetic reference ellipsoid can be used to model the global gravity field and reveal its spectral properties. In this paper, a direct and ...
Ellipsoidal topographic potential: New solutions for spectral forward gravity modeling of topography with respect to a reference ellipsoidClaessens, Sten; Hirt, Christian (2013)Forward gravity modeling in the spectral domain traditionally relies on spherical approximation. However, this level of approximation is insufficient for some present day high-accuracy applications. Here we present two ...
Claessens, Sten; Featherstone, Will (2008)We present a variant of the Meissl scheme to relate surface spherical harmonic coefficients of the disturbing potential of the Earth's gravity field on the surface of the geodetic ellipsoid to surface spherical harmonic ...