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Titre : Regional gravity field modelling with radial basis functions Type de document : Thèse/HDR Auteurs : Tobias Wittwer, Auteur Editeur : Delft : Netherlands Geodetic Commission NGC Année de publication : 2009 Collection : Netherlands Geodetic Commission Publications on Geodesy, ISSN 0165-1706 num. 72 Importance : 190 p. Format : 17 x 24 cm ISBN/ISSN/EAN : 978-90-6132-315-0 Note générale : Bibliographie
Document téléchargeable sur le site de NCG : voir lien dans la noticeLangues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] Antarctique
[Termes IGN] Canada
[Termes IGN] champ de pesanteur local
[Termes IGN] données GOCE
[Termes IGN] données GRACE
[Termes IGN] factorisation de Cholesky
[Termes IGN] filtre de Wiener
[Termes IGN] fonction de base radiale
[Termes IGN] Groenland
[Termes IGN] harmonique sphérique
[Termes IGN] levé gravimétrique
[Termes IGN] modèle de géopotentiel
[Termes IGN] modèle mathématiqueIndex. décimale : 30.42 Gravimétrie Résumé : (Auteur) Terrestrial gravimetry, airborne gravimetry, and the recent dedicated satellite gravity missions Challenging Minisatellite Payload (CHAMP), Gravity Recovery and Climate Experiment (GRACE), and Gravity and Ocean Circulation Explorer (GOCE) provide us with high-quality, high-resolution gravity data, which are used in many application areas such as
1. the computation of global static gravity fields, in support of precise orbit determination of many Earth observation satellites;
2. the quantification and interpretation of mass transport in the Earth system such as the shrinking of ice sheets, the shifting of ocean currents, and water storage variations;
3. the computation of high resolution regional and local gravity fields in support of height system realisation and the modelling of reservoirs and geophysical features.
Traditionally, for each data set (satellite, airborne, terrestrial) dedicated data processing schemes have been developed using different estimation principles, parametrisations, etc. The optimal combination of different data sets would benefit of a methodology that can be used for any type of data. Elements of this methodology comprise a uniform parametrisation, estimation principle, data weighting scheme, regularisation, and error propagation.
In the framework of this thesis, such a methodology is developed. It uses radial basis functions (RBFs) as parametrisation. They have parameters that allow us to tune their approximation properties as function of the data coverage and distribution and the signal variations. This makes them equally well suited for global and local parametrisation. Moreover, there exists an analytical relationship between a spherical harmonic representation and a radial basis function representation, which allows the latter to be transformed into the former, without any approximation error. Among others, this has the advantage that one can make use of existing processing tools, such as spectral analysis.
Although radial basis functions are not new in gravity field modelling, there are many important issues which have not yet been addressed or require further research. The main research question underlying this thesis is: "Are radial basis functions a suitable parametrisation for global and regional models of the mean and time-variable gravity field, and if so, how do they perform compared with spherical harmonic solutions?" Directly related to this is the question: "Are there situations where radial basis functions models outperform spherical harmonic solutions?" The answer to both questions is positive as will be shown in this thesis.
There are two important aspects that determine the quality of a gravity field model based on radial basis functions: 1) the spatial distribution of the radial basis functions, i.e. the basis function network design, and 2) the choice of the bandwidths of the radial basis functions. For both problems, semi-automatic algorithms have been developed. Data-adaptive network design and local refinement avoid respectively over- and under-parametrisation by fine-tuning the basis function network based on the data. The basis function bandwidth is determined by optimising the fit to the data including control data.
The computation of regional gravity fields constitutes a considerable numerical workload, especially since the methodology presented here does not use an iterative normal equation solver (e.g., the preconditioned conjugate gradient method). Instead, a Cholesky solver is used, which requires the assembly of the complete normal equation system. For this purpose the program is numerically optimised and fully parallelised for hybrid high performance computer architectures. This guarantees optimal performance on all types of parallel computers and handles the memory requirements.
The modelling of satellite data with radial basis functions is investigated using real data of the GRACE satellites collected over the period 2003-2006. An optimal Wiener filter has been developed for radial basis functions in line with the optimal Wiener filter approach previously developed at DEOS for spherical harmonic representations. Monthly GRACE gravity models computed using radial basis function are compared to spherical harmonic models, and validated using independent data provided by the Ice Cloud and Land Elevation Satellite (ICESat), radar altimetry satellites, and the global hydrological model PCR-GLOBWB. Two applications were considered: 1) mass variations over Greenland and Antarctica and 2) water storage variations in river basins. The results show that the radial basis function approach yields solutions that are of at least the same quality as global models using spherical harmonics. There is evidence that radial basis functions may provide better spatial resolution and more realistic amplitudes in particular in high-latitude areas. For instance, it will be shown that radial basis function solutions detected signal that could not be seen in spherical harmonic solutions.
Two test areas are used for regional gravity field modelling using real terrestrial data: An area in the northeastern USA and a larger area in eastern Canada. The results show that the data-adaptivity and local refinement algorithms developed in the framework of this thesis provide good solutions of constant quality regardless of the initially chosen grid spacing. The models are compared to the official regional geoid models GEOID03 and CGG05, respectively. In both cases, rms errors of several centimetres remain, which are attributed to different input data and processing strategies.
The combination of satellite and terrestrial data is tested using simulated global and regional data sets. It is shown that a joint inversion of the two data sets yields combined solutions which are significantly better than a solution using the traditional remove-restore approach. The addition of satellite data with the corresponding stochastic model compensates the reduced quality of the terrestrial data at long wavelengths.
The examples show that the regional modelling methodology presented here is a very flexible approach that can be applied to all types of gravity data and data distributions, regardless of application, data source, and area size. The quality of the solutions is at least equal to the solutions developed for the stand-alone inversion of individual data sets, while radial basis functions offer numerical benefits. As a result, this approach is already used for marine geoid modelling, and recommended for the modelling of airborne gravity data and data of the GOCE satellite, and for the joint inversion of satellite, airborne and ground-based gravity data.Note de contenu : Nomenclature
1 Introduction
1.1 Background
1.2 Motivation
1.2.1 Regional modelling from satellite data
1.2.2 Regional modelling from terrestrial data
1.2.3 Combined modelling of satellite and terrestrial data
1.2.4 Radial basis functions
1.3 Prior research on radial basis functions
1.4 Research objectives
1.5 Outline of thesis
2 Radial basis functions
2.1 Gravity field representations
2.1.1 Spherical harmonics
2.1.2 Radial basis functions
2.2 RBF types and behaviour in the spectral domain
2.3 Behaviour in the spatial domain
2.4 Relation of RBFs to a spherical harmonic representation
2.5 Choice of RBF characteristics
2.5.1 Choice of the kernel
2.5.2 Bandwidth selection
2.6 RBF network design
2.6.1 Grids
2.6.2 Adaptation to data
2.6.3 Local refinement
2.7 Multi-scale modelling
2.7.1 Introduction
2.7.2 Methodology
2.7.3 Filtering
3 Mathematical model and estimation principle
3.1 Functional model
3.2 Stochastic model
3.3 Least-squares estimation and regularisation
3.4 Solution strategies
3.4.1 Cholesky factorisation
3.4.2 Conjugate gradients
3.5 Variance component estimation .
3.5.1 Normal equations
3.5.2 Variance component estimation
3.5.3 Stochastic trace estimation
4 Numerical aspects
4.1 Numerical optimisation
4.1.1 Constant expressions in "do"-loops
4.1.2 Computation of the design matrix
4.1.3 Normalisation of coordinates
4.1.4 Normalisation of basis functions
4.2 Fast synthesis
4.3 Parallelisation
4.3.1 Problem description
4.3.2 Parallel computer architectures .
4.3.3 Parallelisation for shared memory computers
4.3.4 Parallelisation for distributed memory computers
4.3.5 Hybrid parallelisation
4.3.6 Results of parallelisation
4.4 Summary and conclusions
5 Gravity field modelling from satellite data
5.1 Functional model
5.1.1 Three-point range combination approach
5.1.2 Residual accelerations
5.1.3 Equivalent water heights
5.1.4 Trend and signal amplitude estimation
5.2 Stochastic model
5.3 Optimal filtering
5.3.1 Introduction
5.3.2 Signal covariance matrix computation
5.3.3 Noise level estimation
5.4 RBF network design
5.4.1 Grid choice
5.4.2 Data-adaptivity and local refinement
5.4.3 Parametrised area
5.5 Bandwidth selection
5.6 Results.
5.6.1 Comparison of unfiltered RBF and spherical harmonic solution
5.6.2 Models used for comparison
5.6.3 Recovery of ice mass loss in Greenland and Antarctica
5.6.4 Recovery of terrestrial water storage variations
5.7 Summary and conclusions
6 Local gravity field modelling from terrestrial data
6.1 Functional model
6.1.1 Functional model for gravity disturbances
6.1.2 Functional model for gravity anomalies
6.1.3 Functional model for height anomalies
6.2 RBF network design
6.2.1 Grid choice
6.2.2 Data-adaptivity and local refinement
6.2.3 Parametrised area
6.3 Bandwidth selection
6.4 Results
6.4.1 Northeastern USA
6.4.2 Canada
6.5 Summary and conclusions
7 Combined modelling of satellite and terrestrial data
7.1 Combination strategies
7.1.1 Remove-restore approach
7.1.2 High-pass filtering
7.1.3 Direct combination
7.1.4 Combination with satellite-only solution
7.2 RBF network design and bandwidth selection
7.3 Results
7.3.1 Global test
7.3.2 Regional test
7.4 Summary and conclusions
8 Summary, conclusions and recommendations
8.1 Summary and conclusions
8.2 Recommendations for further researchNuméro de notice : 15511 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Thèse étrangère Note de thèse : PhD thesis En ligne : https://www.ncgeo.nl/index.php/en/publicatiesgb/publications-on-geodesy/item/258 [...] Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=62744 Réservation
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Code-barres Cote Support Localisation Section Disponibilité 15511-01 30.42 Livre Centre de documentation Géodésie Disponible A data-driven approach to local gravity field modelling using spherical radial basis functions / R. Klees in Journal of geodesy, vol 82 n° 8 (August 2008)
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Titre : A data-driven approach to local gravity field modelling using spherical radial basis functions Type de document : Article/Communication Auteurs : R. Klees, Auteur ; Robert Tenzer, Auteur ; I. Prutkin, Auteur ; Tobias Wittwer, Auteur Année de publication : 2008 Article en page(s) : pp 457 - 471 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] anomalie de pesanteur
[Termes IGN] champ de pesanteur local
[Termes IGN] fonction de base radiale
[Termes IGN] hauteur ellipsoïdale
[Termes IGN] nivellement par GPS
[Termes IGN] Pays-Bas
[Termes IGN] problème des valeurs limitesRésumé : (Auteur) We propose a methodology for local gravity field modelling from gravity data using spherical radial basis functions. The methodology comprises two steps: in step 1, gravity data (gravity anomalies and/or gravity disturbances) are used to estimate the disturbing potential using least-squares techniques. The latter is represented as a linear combination of spherical radial basis functions (SRBFs). A data-adaptive strategy is used to select the optimal number, location, and depths of the SRBFs using generalized cross validation. Variance component estimation is used to determine the optimal regularization parameter and to properly weight the different data sets. In the second step, the gravimetric height anomalies are combined with observed differences between global positioning system (GPS) ellipsoidal heights and normal heights. The data combination is written as the solution of a Cauchy boundary-value problem for the Laplace equation. This allows removal of the non-uniqueness of the problem of local gravity field modelling from terrestrial gravity data. At the same time, existing systematic distortions in the gravimetric and geometric height anomalies are also absorbed into the combination. The approach is used to compute a height reference surface for the Netherlands. The solution is compared with NLGEO2004, the official Dutch height reference surface, which has been computed using the same data but a Stokes-based approach with kernel modification and a geometric six-parameter “corrector surface” to fit the gravimetric solution to the GPS-levelling points. A direct comparison of both height reference surfaces shows an RMS difference of 0.6 cm; the maximum difference is 2.1 cm. A test at independent GPS-levelling control points, confirms that our solution is in no way inferior to NLGEO2004. Copyright Springer Numéro de notice : A2008-319 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-007-0196-3 En ligne : https://doi.org/10.1007/s00190-007-0196-3 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=29312
in Journal of geodesy > vol 82 n° 8 (August 2008) . - pp 457 - 471[article]Réservation
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Code-barres Cote Support Localisation Section Disponibilité 266-08071 RAB Revue Centre de documentation En réserve L003 Disponible 266-08072 RAB Revue Centre de documentation En réserve L003 Disponible