Regionale Schwerefeldmodellierung durch Slepian- und Radiale Basisfunktionen

authored by: Markus Antoni, Wolfgang Keller, Matthias Weigelt
Abstract: The satellite missions CHAMP and GRACE have been launched in 2000 and 2002 respectively, to determine the static and the time variable gravity field of the Earth. Usually, the gravity field, which is derived from the observations of the missions, is modeled by a sum of spherical harmonics. It turns out, however, that these global base functions are not able to represent all the local details of the data. This study demonstrates two methods of modeling the residual signal by localizing base functions. On the one hand, the radial base functions are used, on the other hand the Slepian functions, which are generated by orthogonalization of spherical harmonics on a subspace of the sphere. If fall parameters of the radial base functions are estimated, the non-linear problem demands initial values. Additionally a line search is necessary to improve the convergence of the solution and a penalty method to fix the estimated parameters in a reasonable interval. The achieved accuracy and the numerical efforts are compared in a simulation for both systems of localizing functions.
External Organisation(s): University of Stuttgart
Type: Article
Journal: ZFV - Zeitschrift fur Geodasie, Geoinformation und Landmanagement
Volume: 133
Pages: 120-129
No. of pages: 10
ISSN: 1618-8950
Publication date: 2008
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Earth and Planetary Sciences(all)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{e6f3f3cbe2054c61b418898c7d29d5de,
title = "Regionale Schwerefeldmodellierung durch Slepian- und Radiale Basisfunktionen",
abstract = "The satellite missions CHAMP and GRACE have been launched in 2000 and 2002 respectively, to determine the static and the time variable gravity field of the Earth. Usually, the gravity field, which is derived from the observations of the missions, is modeled by a sum of spherical harmonics. It turns out, however, that these global base functions are not able to represent all the local details of the data. This study demonstrates two methods of modeling the residual signal by localizing base functions. On the one hand, the radial base functions are used, on the other hand the Slepian functions, which are generated by orthogonalization of spherical harmonics on a subspace of the sphere. If fall parameters of the radial base functions are estimated, the non-linear problem demands initial values. Additionally a line search is necessary to improve the convergence of the solution and a penalty method to fix the estimated parameters in a reasonable interval. The achieved accuracy and the numerical efforts are compared in a simulation for both systems of localizing functions.",
author = "Markus Antoni and Wolfgang Keller and Matthias Weigelt",
year = "2008",
language = "Deutsch",
volume = "133",
pages = "120--129",
journal = "ZFV - Zeitschrift fur Geodasie, Geoinformation und Landmanagement",
issn = "1618-8950",
publisher = "Wissner Verlag",
number = "2",
}