Representation of Regional Gravity Fields by Radial Base Functions

authored by: M. Antoni, W. Keller, M. Weigelt
Abstract: The research aims at an investigation of the optimal choice of local base functions, to derive a regional solution of the gravity field. Therefore, the representation of the gravity field is separated into a global and a residual signal, which includes the regional details. To detect these details, a superposition of localizing radial base functions is used. The base functions are developed from one mother function, and modified by four parameters. These arguments can be separated into two coordinates, one scale factor and a shape parameter. The observations of a few residual gravity fields are simulated by orbit integration and the energy-balance technique, in order to test the current approach. After selecting a region of interest, the parameters of the base functions are estimated. In order to get the optimal positions, two searching algorithms are compared. In the first algorithm the scale factors are estimated, while the positions and shape parameters are fixed. This method requires no initial values, because of the linear, but ill-posed and maybe ill-conditioned problem, but usually a regularization is necessary. The second algorithm searches possible positions for one base function in each step, until a termination condition is fulfilled, and improves the positions and scale factors in one adjustment. The results in the second case are better and faster for the test fields, but they depend on the initial values, the number of iterations and an assumption of an approximate constant orbit height.
Organisation(s): Geodetic Institute
External Organisation(s): University of Stuttgart
Type: Conference contribution
Pages: 293-299
No. of pages: 7
Publication date: 2009
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computers in Earth Sciences, Geophysics
Electronic version(s): https://doi.org/10.1007/978-3-540-85426-5_34 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@inproceedings{673f0807ac024af88a5c9ec7b699f29a,
title = "Representation of Regional Gravity Fields by Radial Base Functions",
abstract = "The research aims at an investigation of the optimal choice of local base functions, to derive a regional solution of the gravity field. Therefore, the representation of the gravity field is separated into a global and a residual signal, which includes the regional details. To detect these details, a superposition of localizing radial base functions is used. The base functions are developed from one mother function, and modified by four parameters. These arguments can be separated into two coordinates, one scale factor and a shape parameter. The observations of a few residual gravity fields are simulated by orbit integration and the energy-balance technique, in order to test the current approach. After selecting a region of interest, the parameters of the base functions are estimated. In order to get the optimal positions, two searching algorithms are compared. In the first algorithm the scale factors are estimated, while the positions and shape parameters are fixed. This method requires no initial values, because of the linear, but ill-posed and maybe ill-conditioned problem, but usually a regularization is necessary. The second algorithm searches possible positions for one base function in each step, until a termination condition is fulfilled, and improves the positions and scale factors in one adjustment. The results in the second case are better and faster for the test fields, but they depend on the initial values, the number of iterations and an assumption of an approximate constant orbit height.",
keywords = "Energy-balance technique, Local base function, Radial base function, Regional gravity field, Searching algorithms",
author = "M. Antoni and W. Keller and M. Weigelt",
year = "2009",
doi = "10.1007/978-3-540-85426-5_34",
language = "English",
isbn = "9783540854258",
series = "International Association of Geodesy Symposia",
pages = "293--299",
booktitle = "Observing our Changing Earth - Proceedings of the 2007 IAG General Assembly",
note = "24th General Assembly of the International Union of Geodesy and Geophysics, IUGG 2007 ; Conference date: 02-07-2007 Through 13-07-2007",
}