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Titre : Regional gravity field modeling using airborne gravimetry data Type de document : Thèse/HDR Auteurs : Bas Alberts, Auteur Editeur : Delft : Netherlands Geodetic Commission NGC Année de publication : 2009 Collection : Netherlands Geodetic Commission Publications on Geodesy, ISSN 0165-1706 num. 70 Importance : 180 p. Format : 17 x 24 cm ISBN/ISSN/EAN : 978-90-6132-312-9 Note générale : Bibliographie
Document en téléchargement sur le site de NCG : lien dans la noticeLangues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] champ de pesanteur local
[Termes IGN] Chili
[Termes IGN] espace de Hilbert
[Termes IGN] gravimétrie aérienne
[Termes IGN] gravimétrie en mer
[Termes IGN] levé gravimétrique
[Termes IGN] méthode des moindres carrés
[Termes IGN] modèle de géopotentiel local
[Termes IGN] Nord, mer du
[Termes IGN] Ontario (Canada)
[Termes IGN] pondération
[Termes IGN] processus
[Termes IGN] traitement automatique de donnéesIndex. décimale : 30.42 Gravimétrie Résumé : (Auteur) Airborne gravimetry is the most efficient technique to provide accurate high-resolution gravity data in regions that lack good data coverage and that are difficult to access otherwise. With current airborne gravimetry systems gravity can be obtained at a spatial resolution of 2 km with an accuracy of 1-2' mGal. It is therefore an ideal technique to complement ongoing satellite gravity missions and establish the basis for many applications of regional gravity field modelling.
Gravity field determination using airborne gravity data can be divided in two major steps. The first step comprises the preprocessing of raw in-flight gravity sensor measurements to obtain gravity disturbances at flight level and the second step consists of the inversion of these observations into gravity functionals at ground level. The preprocessing of airborne gravity data consists of several independent steps such as low-pass filtering, a cross-over adjustment to minimize misfits at cross-overs of intersecting lines, and gridding. Each of these steps may introduce errors that accumulate in the course of processing, which can limit the accuracy and the resolution of the resulting gravity field.
For the inversion of the airborne gravity data at flight level into gravity functionals at the Earth's surface, several approaches can be used. Methods that have been successfully applied to airborne gravity data are integral methods and least-squares collocation, but both methods have some disadvantages. Integral methods require that the data are available in a much larger area than for which the gravity functionals are computed. A large cap size is required to reduce edge effects that result from missing data outside the target area. Least-squares collocation suffers much less from these errors and can yield accurate results, provided that the auto-covariance function gives a good representation of data in- and outside the area. However, the number of base functions equals the number of observations, which makes least-squares collocation numerically less efficient.
In this thesis a new methodology for processing airborne gravity data is proposed. It combines separate preprocessing steps with the estimation of gravity field parameters in one algorithm. Importantly, the concept of low-pass filtering is replaced by a frequency-dependent data weighting to handle the strong colored noise in the data. Frequencies at which the noise level is high get a lower weight than frequencies at which the noise level is low. Furthermore, bias parameters are estimated jointly with gravity field parameters instead of applying a cross-over adjustment. To parameterize the gravity potential a spectral representation is used, which means that the estimation results in a set of coefficients. These coefficients are used to compute gravity functional at any location on the Earth's surface within the survey area. The advantage of the developed approach is that it requires a minimum of preprocessing and that all data can be used as obtained at the locations where they are observed.
The performance of the developed methodology is tested using simulated data and data acquired in airborne gravimetry surveys. The goal of the simulations is to test the approach in a controlled environment and to make optimal choices for the processing of real data. For the numerical studies with simulated data, the new methodology outperforms the more traditional approaches for airborne gravity data processing. For the application of the developed methodology to real data, three data sets are used. The first data set comprises airborne gravity measurements over the Skagerrak area, obtained as part of a joint project between several European institutions in 1996. This survey provided accurate airborne gravity data, and because good surface gravity data are available within the area, the data set is very useful to test the performance of the approach. The second data set was obtained by the GeoForschungsZentrum Potsdam during a survey off the coast of Chile in 2002. This data set, which has a lower accuracy than the first data set, is used to investigate the estimation of non-gravitational parameters such as biases and scaling factors. The final data set that is used consists of airborne gravity data acquired by Sander Geophysics Limited in 2003. The survey area is located near Timmins, Ontario and is much smaller than the area of the other data sets. The small size of the area and the high accuracy of the data make it a challenging data set for regional gravity modeling.
The computational experiments with real data show that the performance of the developed methodology is at the same level as traditional methods in terms of gravity field errors. However, it provides a more flexible and powerful approach to airborne gravity data processing. It requires a minimum of preprocessing and all observations are used in the determination of a regional gravity field. The frequency-dependent data weighting is successfully applied to each data set. The approach provides a statistically optimal solution and is a formalized way to handle colored noise. A noise model can be estimated from a posteriori least-squares residuals in an iterative way. The procedure is purely data-driven and, unlike low-pass filtering, does not depend on previous experience of the user. The developed methodology allows for the simultaneous estimation of non-gravitational parameters with the gravity field parameters. A testing procedure should be applied, however, to avoid insignificant estimations and high correlations. For the Chile data set a significant improvement of the estimated gravity field is obtained when bias and scale factors are estimated from the observations. The results of the computations with the real data sets show the high potential of using airborne gravimetry to obtain accurate gravity for geodetic and geophysical applications.Note de contenu : 1 Introduction
1.1 Background
1.2 Objectives
1.3 Outline
2 Airborne gravimetry
2.1 Historical overview
2.2 The principle of airborne gravimetry
2.3 Mathematical models
2.4 Applications and opportunities
3 Processing of airborne gravity data
3.1 Pre-processing
3.2 Inversion of airborne gravity data
3.3 Discussion
4 Combined data processing and inversion
4.1 Gravity field representation
4.2 Inversion methodology
4.3 Regularization and parameter choice rule
4.4 Frequency-dependent data weighting
4.5 Estimation of non-gravitational parameters
4.6 Edge effect reduction
4.7 Combination with prior information
5 Application to simulated data
5.1 Description of the data
5.2 Computations with noise-free data
5.3 Computations with data corrupted by white noise
5.4 Computations with data corrupted by colored noise
5.5 Bias and drift handling
5.6 Summary of the optimal solution strategy
6 Application to airborne gravimetric survey data
6.1 Skagerrak data set
6.2 Chile data set
6.3 Timmins, Ontario data set
6.4 Summary and discussion
7 Conclusions and recommendations
7.1 Conclusions .
7.2 Recommendations.
A Pre-processing of airborne gravity data
A.1 GPS processing
A..2 Gravity processing
B Coordinate transformation
C Least-squares collocation and Hilbert spaces
C.1 Definition of a Hilbert space and some properties
C.2 Reproducing kernel Hilbert spaces
C.3 Least-squares collocation
D Derivation of the ZOT regularization matrix
E Modification of the base functionsNuméro de notice : 15494 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Thèse étrangère DOI : sans En ligne : https://www.ncgeo.nl/downloads/70Alberts.pdf Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=62736 Réservation
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Code-barres Cote Support Localisation Section Disponibilité 15494-01 30.42 Livre Centre de documentation Géodésie 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 Réservation
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Code-barres Cote Support Localisation Section Disponibilité 15511-01 30.42 Livre Centre de documentation Géodésie Disponible The gravitational effect of ocean tide loading at high latitude coastal stations in Norway / D.I. Lysaker in Journal of geodesy, vol 82 n° 9 (September 2008)
[article]
Titre : The gravitational effect of ocean tide loading at high latitude coastal stations in Norway Type de document : Article/Communication Auteurs : D.I. Lysaker, Auteur ; K. Breili, Auteur ; Bjørn Ragnvald Pettersen, Auteur Année de publication : 2008 Article en page(s) : pp 569 - 583 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] analyse comparative
[Termes IGN] Arctique
[Termes IGN] champ de pesanteur local
[Termes IGN] champ de pesanteur terrestre
[Termes IGN] correction du signal
[Termes IGN] déformation de la croute terrestre
[Termes IGN] levé gravimétrique
[Termes IGN] littoral
[Termes IGN] Norvège
[Termes IGN] série temporelle
[Termes IGN] surcharge océaniqueRésumé : (Auteur) Gravity measurements close to the ocean are strongly affected by ocean tide loading (OTL). The gravitational OTL effect consists of three parts, i.e. a change in gravity caused by direct attraction from the variable water-masses, by displacement of the observing point due to the load, and by redistribution of masses due to crustal deformation. We compare the OTL gravitational effect of several global models to observed time-series of gravity to identify the best model for four arctic observation sites. We also investigate if the global models are sufficient for correcting gravity observations. The NAO99b model fits the observations best at three stations. At two stations (Tromsø and Bodø) the global models explain the variability in the observations well. At the other two (Honningsvåg and Andøya), a significant periodic signal remains after the OTL correction has been applied. We separate two of the gravitational effects, the direct attraction and the change in gravity due to displacement, to study the local effects. Simple geometric models of the water load and independent measurements from local tide-gauges are used to calculate these effects. This leads to improved correspondence with the OTL signal, hence demonstrating the importance of careful modelling of local effects for correction of gravity observations in coastal stations. Copyright Springer Numéro de notice : A2008-351 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-007-0207-4 En ligne : https://doi.org/10.1007/s00190-007-0207-4 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=29344
in Journal of geodesy > vol 82 n° 9 (September 2008) . - pp 569 - 583[article]Réservation
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Code-barres Cote Support Localisation Section Disponibilité 266-08081 RAB Revue Centre de documentation En réserve L003 Disponible 266-08082 RAB Revue Centre de documentation En réserve L003 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)
[article]
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 Astronomical-topographic levelling using high-precision astrogeodetic vertical deflections and Digital Terrain Model data / C. Hirt in Journal of geodesy, vol 82 n° 4-5 (April - May 2008)
[article]
Titre : Astronomical-topographic levelling using high-precision astrogeodetic vertical deflections and Digital Terrain Model data Type de document : Article/Communication Auteurs : C. Hirt, Auteur ; J. Flury, Auteur Année de publication : 2008 Article en page(s) : pp 231 - 248 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Nivellement
[Termes IGN] Alpes
[Termes IGN] champ de pesanteur local
[Termes IGN] collocation par moindres carrés
[Termes IGN] déviation de la verticale
[Termes IGN] modèle numérique de terrain
[Termes IGN] nivellement indirectRésumé : (Auteur) At the beginning of the twenty-first century, a technological change took place in geodetic astronomy by the development of Digital Zenith Camera Systems (DZCS). Such instruments provide vertical deflection data at an angular accuracy level of 0.?1 and better. Recently, DZCS have been employed for the collection of dense sets of astrogeodetic vertical deflection data in several test areas in Germany with high-resolution digital terrain model (DTM) data (10–50 m resolution) available. These considerable advancements motivate a new analysis of the method of astronomical-topographic levelling, which uses DTM data for the interpolation between the astrogeodetic stations. We present and analyse a least-squares collocation technique that uses DTM data for the accurate interpolation of vertical deflection data. The combination of both data sets allows a precise determination of the gravity field along profiles, even in regions with a rugged topography. The accuracy of the method is studied with particular attention on the density of astrogeodetic stations. The error propagation rule of astronomical levelling is empirically derived. It accounts for the signal omission that increases with the station spacing. In a test area located in the German Alps, the method was successfully applied to the determination of a quasigeoid profile of 23 km length. For a station spacing from a few 100 m to about 2 km, the accuracy of the quasigeoid was found to be about 1–2 mm, which corresponds to a relative accuracy of about 0.05-0.1 ppm. Application examples are given, such as the local and regional validation of gravity field models computed from gravimetric data and the economic gravity field determination in geodetically less covered regions. Copyright Springer Numéro de notice : A2008-168 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-007-0173-x En ligne : https://doi.org/10.1007/s00190-007-0173-x Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=29163
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