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Studies on the use of the boundary element method in physical geodesy / Rüdiger Lehmann (1997)
Titre : Studies on the use of the boundary element method in physical geodesy Type de document : Monographie Auteurs : Rüdiger Lehmann, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1997 Collection : DGK - A Sous-collection : Theoretische Geodäsie num. 113 Importance : 103 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-3-7696-8194-9 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] discrétisation
[Termes IGN] équation intégrale
[Termes IGN] problème des valeurs limites
[Termes IGN] surface de référence
[Termes IGN] Terre (planète)Index. décimale : 30.40 Géodésie physique Résumé : (Auteur) This report investigates various aspects of the application of the boundary element method in physical geodesy. Mainly the increasing accuracy requirements for the high resolution gravity field and geoid deter-mination have induced the further development of classical methods for the solution of geodetic boundary value problems, but also new techniques were established. The boundary element method permits the nu-merical solution of linearized geodetic boundary value problems, formulated as geodetic boundary integral equations. Previous geodetic investigations have focused on the strongly singular boundary integral equations in a local scale, which were solved successfully by means of Galerkin discretization methods with piecewise constant trial functions.
We extend these results in various directions : We consider the closed surface of the Earth as the bound-ary surface. Additionally, we solve a hypersingular boundary integral equation, and also piecewise linear trial/test functions are applied. Modern numerical cubature methods for the different types of integrals are tested and implemented. For the solution of the resulting linear system of equations, we apply highly efficient generalized CG methods.
A very important aspect of this report is the application of modern parallel computers. Problems of imple-mentation of the boundary element method on such types of computers are in the focus of current research in engineering sciences. Some new problems arise, concerning the parallelization of data structures and algo-rithms, and their solutions are discussed comprehensively. The performance of the parallelization is tested on a MIMD computer with distributed memory of type IBM SP.
Final numerical investigations make the pros and cons of the applied solution methods clearer.Numéro de notice : 28249 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Monographie Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=63595 Réservation
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Code-barres Cote Support Localisation Section Disponibilité 28249-01 30.40 Livre Centre de documentation Géodésie Disponible 28249-02 30.40 Livre Centre de documentation Géodésie Disponible Systèmes de référence et de coordonnées. Fascicule 4 Géoïde et altitudes / Françoise Duquenne (1997)
Titre : Systèmes de référence et de coordonnées. Fascicule 4 Géoïde et altitudes Type de document : Guide/Manuel Auteurs : Françoise Duquenne , Auteur Editeur : Paris : Institut Géographique National - IGN (1940-2007) Année de publication : 1997 Importance : 25 p. Format : 21 x 30 cm Langues : Français (fre) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] altitude
[Termes IGN] géoïdeIndex. décimale : 30.40 Géodésie physique Numéro de notice : 66132 Affiliation des auteurs : IGN (1940-2011) Thématique : POSITIONNEMENT Nature : Manuel de cours IGN Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=49078 Réservation
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Code-barres Cote Support Localisation Section Disponibilité 66132-01 30.40 Livre Centre de documentation Géodésie Disponible 66132-02 30.40 Livre Centre de documentation Géodésie Disponible Analyse und Numerik überbestimmter Randwertprobleme in der Physikalischen Geodäsie / M. Hirsch (1996)
Titre : Analyse und Numerik überbestimmter Randwertprobleme in der Physikalischen Geodäsie Titre original : [Analyse et problème de valeur aux limites numériques surdéterminées en géodésie physique] Type de document : Thèse/HDR Auteurs : M. Hirsch, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1996 Collection : DGK - C Sous-collection : Dissertationen num. 453 Importance : 154 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 3-7696-9596-1 Note générale : Bibliographie Langues : Allemand (ger) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] Aristoteles
[Termes IGN] modèle mathématique
[Termes IGN] problème des valeurs limitesIndex. décimale : 30.40 Géodésie physique Résumé : (Auteur)The determination of the Earth gravity field is a primary objective of geodesy. In order to solve this task, gravity values must be available in global covering and high density; till now this condition is only insufficiently fulfilled. Therefore, great expectations are focused on new developed observation technologies realizing high precision measurements of gravity or gravitational field signals on moved platforms (airplanes, satellites). These processes promise strongly improved qualitative and quantitative information about the gravity field. Moreover, they are much more effective than traditional methods.
This study deals with suitable mathematical modelling of two of these new measurement methods: airborne gravimetry and satellite gradiometry. In particular, the combination between already available gravity information and new observations in a consistent model is investigated. Overdetermined boundary value problems are used for a mathematical description of this task. In contrast to the classical geodetic boundary value problem, the solution of these problems is not uniquely determinable. The sought quantities rather have to be estimated in function spaces. For this reason, the well known BLUE principle was expanded in order to apply it in infinite dimensional spaces. The direct parameter estimation in the overdetermined boundary value problem is not possible, since the equation types are different while the BLUE principle requires an identical equation type. Therefore, a transformation into a homogenous system of integral equations using the theory of pseudodifferential operators (PDO) has to be performed.
Starting from a general formulation of the overdetermined boundary value problem, two special problems are studied; a linear fixed problem to model the local determination of the gravity field by means of airborne gravimetry, and a nonlinear free boundary value problem, describing the global determination of the gravitational field by means of satellite gradiometry. The solution of the nonlinear problem is based upon an imbedding technique by Hormander. Using this imbedding technique the problem can be decomposed into a sequence of linear boundary value problems with the same structure.
In order to be able to solve the problems with an uniform procedure, the problems are transformed in systems of PDO-equations and interpreted as an analogy to the Gauss-Markov-Model. Inversion-free solution formulae are derived for optimal estimation of the sought potential in the space and frequency domains. Using assumptions about stochastic properties of measurement noise, error formulae, describing expected accuracy of the solution, can be obtained.
In order to verify derived solutions, numerical studies are carried out, which can be divided into the following two parts:
In the first part, an overdetermined boundary value problem in local formulation is investigated. This problem is applied for modelling the stabilized downward continuation of airborne gravimeter data. Using three numerical experiments, the possibility of achieving the stabilization of continuation process without a smoothing of the measurements can be proved. This means that the overdetermined boundary value problem is an alternative to the usually applied Tikhonov's regularization, also in numerical case.
The second part discusses the numerical studies of an overdetermined boundary value problem, which has been formulated to determine the global gravitational field in high resolution. First, the numerical experiments are described. This description explains the simulation of the satellite gradiometry mission ARISTOTELES, the data reduction to given boundary surfaces and the error modelling. In the sequel, the successful numerical verification of the derived estimation formulae is covered. A detailed graphical representation illustrates the accuracy potential of the satellite gradiometry data. Further on, analyses of the influence of the polar data gaps and of the aliasing effect are carried out. The obtained results are compared with the results of other authors.Numéro de notice : 28036 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Thèse étrangère Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=63383 Réservation
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Code-barres Cote Support Localisation Section Disponibilité 28036-01 30.40 Livre Centre de documentation Géodésie Disponible 28036-02 30.40 Livre Centre de documentation Géodésie Disponible Borehole data and stochastic gravimetric inversion / G. Strykowski (1996)
Titre : Borehole data and stochastic gravimetric inversion Type de document : Monographie Auteurs : G. Strykowski, Auteur ; National survey and cadastre of danemark, Auteur Editeur : Copenhague : Kort & Matrikelstyrelsen Année de publication : 1996 Collection : Publications 4 Series, ISSN 0905-1279 num. 3 Importance : 220 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-87-7866-013-8 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] géophysique
[Termes IGN] gravimétrieIndex. décimale : 30.40 Géodésie physique Numéro de notice : 66655 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Monographie Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=61631 Réservation
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Code-barres Cote Support Localisation Section Disponibilité 66655-01 30.40 Livre Centre de documentation Géodésie Disponible CCD-Astrometrie von Objekten des geostationären Ringes / M. Ploner (1996)
Titre : CCD-Astrometrie von Objekten des geostationären Ringes Titre original : [Astrométrie CCD des objets de l'anneau géostationnaire] Type de document : Rapport Auteurs : M. Ploner, Auteur Editeur : Vienne [Autriche] : Technische Universität Wien Année de publication : 1996 Collection : Geowissenschaftliche Mitteilungen, ISSN 1811-8380 num. 46 Importance : 133 p. Format : 21 x 30 cm Note générale : Bibliographie Langues : Allemand (ger) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] astrométrie
[Termes IGN] campagne d'observations
[Termes IGN] chambre DTC
[Termes IGN] champ de pesanteur terrestre
[Termes IGN] orbitographie
[Termes IGN] Pascal
[Termes IGN] satellite géostationnaire
[Termes IGN] satellite météorologique
[Termes IGN] transformation de coordonnéesIndex. décimale : 30.40 Géodésie physique Résumé : (Auteur) The motions of artificial satellites are influenced by gravitational and non-gravitational perturbations. Of special interest among the gravitational perturbations is the anisotropy of the earth's gravitational field. Orbits of geostationary satellites are extremely sensitive to perturbations caused by the earth's equatorial ellipticity, which is described by the coefficients C22 and S22 in the harmonic series expansion of the geopotential. These coefficients cause resonant perturbations, which lead to a librating motion of geostationary objects around two defined points of the earth's equator. These points are located at longitude east 75' and longitude west 105' of Greenwich. The period of the librating motion varies between 1000 and 2000 days, changes in the semi-major axis can reach up to 35 km. On the other hand, these large variations allow for a very exact calculation of the above mentioned terms by means of observing geostationary satellites over a period of only a few weeks. Meteosat satellites are extremely useful for this type of study, because in contrast to communication satellites, orbit manoeuvres are carried out only every 2 or 3 months.
In the course of this project, the Zeiss BNIK 75 ballistic camera of the Graz-Lustbühel satellite observation centre was adapted for CCD observations. Instead of the automatic plate-changing device, the CCD camera SITe 1024B (1024*1024 pixel, pixel size 24µm, backside illuminated, 1 pixel = 6.6") was mounted. Thanks to a special shuttering technique, the epoch registration of the observations can be carried out with an accuracy of a few microseconds. After installing the hardware, a two-month observation campaign of the satellites Meteosat 5 and Meteosat 6 as well as the Russian satellites Gorizont 11 and Statsionar-raduga 8 was carried out. Whereas, due to orbital manoeuvres, the orbits of the Meteosat satellites are very close to the theoretical geostationary orbit, the latter mentioned satellites have not been controlled for a quite long time. Inevitably this causes an increasing motion leading away from their geostationary orbit. They also are marked by heavy tumbling movements.
The astrometric evaluation of the observations was carried out with the help of the program CCD. Its development was - besides the hardware installation - one of the main tasks of this project. This Windows application, which is written in Borland Pascal 7.0, permits the use of different polynomes for the transformation of the measured coordinates into tangent coordinates and makes use of various fit algorithms (Gaussian, Laplace and Cauchy distributions) for the calculation of the object coordinates. Usually the star tracker is switched off when observations of geostationary satellites are carried out. Therefore special attention has to be paid to the determination of the starting and final point of star trails. The reference stars can be selected from the PPM and the GSC catalogue. The calculated coordinates of the measured objects either refer to the true date and equinox or to the mean date and equinox (J2000.0).
The orbit integration program ORBDET of the Astronomical Institute of the University of Berne was used for the calculation of the osculating orbital elements and the direct solar radiation pressure of all satellites. The residuals of the two Meteosat satellites did not show any remaining signals. The average deviation of a single observation was 0.5" for these extremely faint objects, which corresponds to less than 1/10 of the pixel size. This high accuracy was a consequence of calculating the satellite coordinates by fitting a two-dimensional Gaussian distribution. The situation concerning Gorizont 11 and Statsionar-raduga 8 is different. Significant signals were found in the residuals, which can be explained by extreme difficulties in establishing an appropriate model for the direct solar radiation pressure. While Meteosat satellites have a simple cylindrical shape, the Russian satellites are marked by large solar panels. The establishment of a model for the direct solar radiation pressure is further complicated because of the heavy tumbling movements.
Finally, the geopotential coefficients C22 and S22 were calculated from observations of the satellites Meteosat 5 and 6. The results show an extremely low deviation from the corresponding numbers of the well-known gravity model JGM-3). By combining this data with observations made by the satellite observation centre Zimmerwald (Switzerland), the accuracy of the coefficients C22 and S22 could be further increased. The calculations result in the following values for the two normalized coefficients :
C22 = 2.43923E-06 ± 3.9OE-10
S22 = -1.4003IE-06 ± 9.77E-11
The results show that CCD observations of geostationary satellites can contribute considerably to the determination of the above mentioned parameters. A further increase in accuracy is to be expected by the use of the Hipparcos star catalogue, which is going to be available in summer 1997.Numéro de notice : 55044 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Rapport d'étude technique Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=59754 Réservation
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Code-barres Cote Support Localisation Section Disponibilité 55044-01 30.40 Livre Centre de documentation Géodésie Disponible Évaluation des nouveaux modèles géopotentiels GSFC-DMA / Claude Boucher (1996)PermalinkTailored numerical solution strategies for the global determination of the Earth's gravity field / W.D. Schuh (1996)PermalinkZur Bahndynamik niedrigfliegender Satelliten / M. Scheinert (1996)PermalinkPolar motion derived from DORIS technique / Pascal Willis (12/05/1995)PermalinkModellierung stochastisch korrelierter Signalanteile in geodätischen Beobachtungen, angewendet insbesondere auf die Bestimmung des Schwerefeldes aus der Kombination von kinematischen und dynamischen Messungen / K. Neumayer (1995)PermalinkRegionale Gravitationsfeldbestimmung mit zukünftigen Satellitenmissionen (SST und Gradiometrie) / M. Thalhammer (1995)PermalinkBestimmung von Modellparametern der Erde durch Analyse ihrer Drehbewegung / H. Fröhlich (1994)PermalinkParameterschätzung in dynamischen Systemen für die Satelliten-Altimetrie / G. Hückelheim (1994)PermalinkZur Bestimmung des Erdschwerefeldes unter Verwendung des Maximum-Entropie-Prinzips / Rüdiger Lehmann (1994)PermalinkEffects of Non-Linearity in the Geodetic Boundary Value Problems / B. Heck (1993)Permalink