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Local multi-polar expansions in potential field modeling / B. Minchev in Earth, Planets and Space, vol 61 n° 10 (October 2009)
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[article]
Titre : Local multi-polar expansions in potential field modeling Type de document : Article/Communication Auteurs : B. Minchev, Auteur ; Aude Chambodut, Auteur ; Matthias Holschneider, Auteur ; Isabelle Panet , Auteur ; Eckehard Schöll, Auteur ; Mioara Mandea, Auteur ; Guillaume Ramillien, Auteur
Année de publication : 2009 Projets : 1-Pas de projet / Article en page(s) : pp 1127 - 1141 Note générale : bibliographie
This work was supported by the Deutsche Forschungsgemeinschaft(DFG) within the framework of the projects BMBF/DFG “GEOTECHNOLOGIEN” and the DFG project KO 2870/3-1.Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] champ de pesanteur terrestre
[Termes IGN] données CHAMP
[Termes IGN] données géophysiques
[Termes IGN] harmonique sphérique
[Termes IGN] problème inverseRésumé : (auteur) The satellite era brings new challenges in the development and the implementation of potential field models. Major aspects are, therefore, the exploitation of existing space- and ground-based gravity and magnetic data for the long-term. Moreover, a continuous and near real-time global monitoring of the Earth system, allows for a consistent integration and assimilation of these data into complex models of the Earth’s gravity and magnetic fields, which have to consider the constantly increasing amount of available data. In this paper we propose how to speed up the computation of the normal equation in potential filed modeling by using local multi-polar approximations of the modeling functions. The basic idea is to take advantage of the rather smooth behavior of the internal fields at the satellite altitude and to replace the full available gravity or magnetic data by a collection of local moments. We also investigate what are the optimal values for the free parameters of our method. Results from numerical experiments with spherical harmonic models based on both scalar gravity potential and magnetic vector data are presented and discussed. The new developed method clearly shows that very large datasets can be used in potential field modeling in a fast and more economic manner. Numéro de notice : A2009-605 Affiliation des auteurs : LAREG+Ext (1991-2011) Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1186/BF03352965 Date de publication en ligne : 30/11/2009 En ligne : https://doi.org/10.1186/BF03352965 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=95757
in Earth, Planets and Space > vol 61 n° 10 (October 2009) . - pp 1127 - 1141[article]Recursive algorithms for the computation of the potential harmonic coefficients of a constant density polyhedron / Dimitrios Tsoulis in Journal of geodesy, vol 83 n° 10 (October 2009)
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Titre : Recursive algorithms for the computation of the potential harmonic coefficients of a constant density polyhedron Type de document : Article/Communication Auteurs : Dimitrios Tsoulis, Auteur ; Olivier Jamet , Auteur ; Jérome Verdun
, Auteur ; Nicolas Gonindard, Auteur
Année de publication : 2009 Projets : 3-projet - voir note / Article en page(s) : pp 925 - 942 Note générale : Bibliographie
The present research has been carried out in the frame of France-Greek bilateral cooperation PHC Platon, project number 15063 VE.Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] harmonique sphérique
[Termes IGN] polyèdre
[Termes IGN] potentiel de pesanteur terrestreRésumé : (Auteur) The gravitational potential of a constant density general polyhedron can be expressed both in terms of a closed analytical expression and as a series expansion involving the corresponding spherical harmonic coefficients. The latter can be obtained from two independent algorithms, which differ not only in their algorithmic architecture but in their efficiency and overall performance, especially when computing the coefficients of higher degree and order. In the present paper a comparative study of all these three approaches is carried out focusing on the numerical implementation of the recursive relations appearing in the two algorithms for the computation of the polyhedral potential harmonic coefficients. The performed numerical investigations show that the linear algorithm proposed by Jamet and Thomas (Proceedings of the second international GOCE user workshop, ‘GOCE, The Geoid and Oceanography’, ESA-ESRIN, Frascati, Italy, 8–10 March 2004, ESA SP-569, 2004), but so far not implemented, achieves a reasonable accuracy at a computational expense that opens to practical applications, for instance in the field of satellite gravimetry/gradiometry interpretation. The convergence behavior of the linear recursion algorithm is studied thoroughly and a computational procedure is proposed that enables the stable computation of potential harmonic coefficients up to degree 60 when referring to an arbitrarily shaped polyhedral body. Numéro de notice : A2009-429 Affiliation des auteurs : LAREG+Ext (1991-2011) Autre URL associée : vers HAL Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-009-0310-9 Date de publication en ligne : 10/03/2009 En ligne : http://dx.doi.org/10.1007/s00190-009-0310-9 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=30060
in Journal of geodesy > vol 83 n° 10 (October 2009) . - pp 925 - 942[article]Exemplaires(1)
Code-barres Cote Support Localisation Section Disponibilité 266-09091 SL Revue Centre de documentation Revues en salle Disponible Optima multi-step collocation: application to the space-wise approach for GOCE data analysis / M. Reguzzoni in Journal of geodesy, vol 83 n° 1 (January 2009)
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Titre : Optima multi-step collocation: application to the space-wise approach for GOCE data analysis Type de document : Article/Communication Auteurs : M. Reguzzoni, Auteur ; N. Tselfes, Auteur Année de publication : 2009 Article en page(s) : pp 13 - 29 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] analyse harmonique
[Termes IGN] champ de pesanteur terrestre
[Termes IGN] coefficient de géopotentiel
[Termes IGN] collocation
[Termes IGN] GOCE
[Termes IGN] harmonique sphérique
[Termes IGN] levé gravimétriqueRésumé : (Auteur) Collocation is widely used in physical geodesy. Its application requires to solve systems with a dimension equal to the number of observations, causing numerical problems when many observations are available. To overcome this drawback, tailored step-wise techniques are usually applied. An example of these step-wise techniques is the space-wise approach to the GOCE mission data processing. The original idea of this approach was to implement a two-step procedure, which consists of first predicting gridded values at satellite altitude by collocation and then deriving the geo-potential spherical harmonic coefficients by numerical integration. The idea was generalized to a multi-step iterative procedure by introducing a time-wise Wiener filter to reduce the highly correlated observation noise. Recent studies have shown how to optimize the original two-step procedure, while the theoretical optimization of the full multi-step procedure is investigated in this work. An iterative operator is derived so that the final estimated spherical harmonic coefficients are optimal with respect to the Wiener–Kolmogorov principle, as if they were estimated by a direct collocation. The logical scheme used to derive this optimal operator can be applied not only in the case of the space-wise approach but, in general, for any case of step-wise collocation. Several numerical tests based on simulated realistic GOCE data are performed. The results show that adding a pre-processing time-wise filter to the two-step procedure of data gridding and spherical harmonic analysis is useful, in the sense that the accuracy of the estimated geo-potential coefficients is improved. This happens because, in its practical implementation, the gridding is made by collocation over local patches of data, while the observation noise has a time-correlation so long that it cannot be treated inside the patch size. Therefore, the multi-step operator, which is in theory equivalent to the two-step operator and to the direct collocation, is in practice superior thanks to the time-wise filter that reduces the noise correlation before the gridding. The criteria for the choice of this filter are investigated numerically. Copyright Springer Numéro de notice : A2009-179 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-008-0225-x En ligne : https://doi.org/10.1007/s00190-008-0225-x Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=29809
in Journal of geodesy > vol 83 n° 1 (January 2009) . - pp 13 - 29[article]Exemplaires(2)
Code-barres Cote Support Localisation Section Disponibilité 266-09011 RAB Revue Centre de documentation En réserve L003 Disponible 266-09012 RAB Revue Centre de documentation En réserve L003 Disponible
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 Exemplaires(1)
Code-barres Cote Support Localisation Section Disponibilité 15511-01 30.42 Livre Centre de documentation Géodésie Disponible A study reference frame consistency in recent Earth gravitational models / Christopher Kotsakis in Journal of geodesy, vol 83 n° 1 (January 2009)
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Titre : A study reference frame consistency in recent Earth gravitational models Type de document : Article/Communication Auteurs : Christopher Kotsakis, Auteur Année de publication : 2009 Article en page(s) : pp 31 - 50 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] champ de pesanteur terrestre
[Termes IGN] cohérence des données
[Termes IGN] Earth Gravity Model 2008
[Termes IGN] GRACE
[Termes IGN] harmonique sphérique
[Termes IGN] levé gravimétrique
[Termes IGN] modèle de géopotentiel
[Termes IGN] repère de référenceRésumé : (Auteur) All gravity field functionals obtained from an Earth gravitational model (EGM) depend on the underlying terrestrial reference frame (TRF), with respect to which the EGM’s spherical harmonic coefficients refer to. In order to maintain a coherent framework for the comparison of current and future EGMs, it is thus important to investigate the consistency of their inherent TRFs, especially when their use is intended for high precision studies. Following the methodology described in an earlier paper by Kleusberg (1980), the similarity transformation parameters between the associated reference frames for several EGMs (including the most recent CHAMP/GRACE models at the time of writing this paper) are estimated in the present study. Specifically, the differences between the spherical harmonic coefficients for various pairs of EGMs are parameterized through a 3D-similarity spatial transformation model that relates their underlying TRFs. From the least-squares adjustment of such a parametric model, the origin, orientation and scale stability between the EGMs’ reference frames can be identified by estimating their corresponding translation, rotation and scale factor parameters. Various aspects of the estimation procedure and its results are highlighted in the paper, including data weighting schemes, the sensitivity of the results with respect to the selected harmonic spectral band, the correlation structure and precision level of the estimated transformation parameters, the effect of the estimated differences of the EGMs’ reference frames on their height anomaly signal, and the overall feasibility of Kleusberg’s formulae for the assessment of TRF inconsistencies among global geopotential models. Copyright Springer Numéro de notice : A2009-180 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-008-0227-8 En ligne : https://doi.org/10.1007/s00190-008-0227-8 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=29810
in Journal of geodesy > vol 83 n° 1 (January 2009) . - pp 31 - 50[article]Exemplaires(2)
Code-barres Cote Support Localisation Section Disponibilité 266-09011 RAB Revue Centre de documentation En réserve L003 Disponible 266-09012 RAB Revue Centre de documentation En réserve L003 Disponible PermalinkReprésentation du champ de pesanteur sur des repères d'ondelettes sphériques / Isabelle Panet in Bulletin d'information scientifique et technique de l'IGN, n° 75 (mars 2006)
PermalinkWavelet frames:An alternative to spherical harmonic representation of potential fields / Aude Chambodut in Geophysical journal international, vol 163 n° 3 (December 2005)
PermalinkPermalinkA linear algorithm for computing the spherical harmonic coefficients of the gravitational potential from a constant density polyhedron / Olivier Jamet (2004)
PermalinkDéveloppement en harmoniques sphériques de la contribution au potentiel de gravité d'un volume polyédrique représenté par sa surface externe / E. Thomas (2003)
PermalinkSpace gravity spectroscopy - The sensitivity analysis of GPS-tracked satellite missions (case study CHAMP) / C. Schäfer (2001)
PermalinkMapping and predicting the Earth's ionosphere using the Global Positioning System / Stefan Schaer (1999)
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