On the regularization of regional gravity field solutions in spherical radial base functions

authored by: Majid Naeimi, Jakob Flury, Phillip Brieden
Abstract: Regional refinement of the gravity field models from satellite data using spherical radial base functions (SRBF) is an ill-posed problem. This is mainly due to the regional confinement of the data and the base functions, which leads to severe instabilities in the solutions. Here, this ill-posedness as well as the related regularization process are investigated. We compare three methods for the choice of the regularization parameter, which have been frequently used in gravity modelling. These methods are (1) the variance component estimation (VCE), (2) the generalized cross validation (GCV) and (3) the L-curve criterion. A particular emphasis is put on the impact of the SRBF type on the regularization parameter. To do this, we include two types of SRBF which are often used for regional gravity field modelling. These are the Shannon SRBF or the reproducing kernel and the Spline SRBF. The investigations are performed on two months of the real GOCE ultrasensitive gravity gradients over Central Africa and Amazon. The solutions are validated against a state-of-the-art global gravity solution. We conclude that if a proper regularization method is applied, both SRBF deliver more or less the same accuracy. We show that when the Shannon wavelet is used, the L-curve method gives the best results, while with the Spline kernel, the GCV outperforms the other two methods. Moreover, we observe that the estimated coefficients for the Spline kernel cannot be spatially interpreted. In contrast, the coefficients obtained for the Shannon wavelet reflect the energy of the recovered gravity field with a correlation factor of above 95 per cent. Therefore, when combined with the L-curve method, the Shannon SRBF is advantageous for regional gravity field estimation, since it is one of the simplest band-limited SRBF. In addition, it delivers promising solutions and the estimated coefficients represent the characteristics of the gravity field within the target region.
Organisation(s): Institute of Geodesy
Quest: Centre for Quantum Engineering and Space-Time Research
Type: Article
Journal: Geophysical journal international
Volume: 202
Pages: 1041-1053
No. of pages: 13
ISSN: 0956-540X
Publication date: 01.08.2015
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Geophysics, Geochemistry and Petrology
Electronic version(s): https://doi.org/10.1093/gji/ggv210 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{50ce0084a94e4cfe951de2d85502a403,
title = "On the regularization of regional gravity field solutions in spherical radial base functions",
abstract = "Regional refinement of the gravity field models from satellite data using spherical radial base functions (SRBF) is an ill-posed problem. This is mainly due to the regional confinement of the data and the base functions, which leads to severe instabilities in the solutions. Here, this ill-posedness as well as the related regularization process are investigated. We compare three methods for the choice of the regularization parameter, which have been frequently used in gravity modelling. These methods are (1) the variance component estimation (VCE), (2) the generalized cross validation (GCV) and (3) the L-curve criterion. A particular emphasis is put on the impact of the SRBF type on the regularization parameter. To do this, we include two types of SRBF which are often used for regional gravity field modelling. These are the Shannon SRBF or the reproducing kernel and the Spline SRBF. The investigations are performed on two months of the real GOCE ultrasensitive gravity gradients over Central Africa and Amazon. The solutions are validated against a state-of-the-art global gravity solution. We conclude that if a proper regularization method is applied, both SRBF deliver more or less the same accuracy. We show that when the Shannon wavelet is used, the L-curve method gives the best results, while with the Spline kernel, the GCV outperforms the other two methods. Moreover, we observe that the estimated coefficients for the Spline kernel cannot be spatially interpreted. In contrast, the coefficients obtained for the Shannon wavelet reflect the energy of the recovered gravity field with a correlation factor of above 95 per cent. Therefore, when combined with the L-curve method, the Shannon SRBF is advantageous for regional gravity field estimation, since it is one of the simplest band-limited SRBF. In addition, it delivers promising solutions and the estimated coefficients represent the characteristics of the gravity field within the target region.",
keywords = "Geopotential theory, Inverse theory, Numerical solutions, Satellite gravity, Spatial analysis",
author = "Majid Naeimi and Jakob Flury and Phillip Brieden",
note = "The authors would like to thank the DFG Sonderforschungsbereich (SFB 1128: geo-Q) Relativistic Geodesy and Gravimetry with Quantum Sensors for financial support. Part of this work is also supported by the centre for Quantum Engineering and Space Time research (QUEST) at University of Hannover, Germany. Special thanks go to Professor Reiner Rummel for his valuable comments on this study. We wish to thank the two anonymous reviewers for their constructive remarks which helped us to improve the quality of this work. ",
year = "2015",
month = aug,
day = "1",
doi = "10.1093/gji/ggv210",
language = "English",
volume = "202",
pages = "1041--1053",
journal = "Geophysical journal international",
issn = "0956-540X",
publisher = "Oxford University Press",
number = "2",
}