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Analyse und Numerik überbestimmter Randwertprobleme in der Physikalischen Geodäsie / M. Hirsch (1996)

Public 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 limites Index. 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

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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

Zur Bahndynamik niedrigfliegender Satelliten / M. Scheinert (1996)

Public Titre : Zur Bahndynamik niedrigfliegender Satelliten Titre original : [Sur l'orbite dynamique des satellites à basse altitude] Type de document : Thèse/HDR Auteurs : M. Scheinert, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1996 Collection : DGK - C Sous-collection : Dissertationen num. 435 Importance : 140 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-3-7696-9478-9 Note générale : Bibliographie Langues : Allemand (ger) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] Aristoteles [Termes IGN] champ de pesanteur terrestre [Termes IGN] données GPS [Termes IGN] équation de Hill [Termes IGN] équation différentielle [Termes IGN] gradiométrie [Termes IGN] orbite [Termes IGN] orbite circulaire [Termes IGN] poursuite de satellite [Termes IGN] système linéaire Index. décimale : 30.40 Géodésie physique Résumé : (Auteur) The satellite missions ARISTOTELES and STEP, under discussion for some years, would give the chance to determine the gravitational field of the Earth with high accuracy and up to the short-wave domain. This is due to the expected highly sensitive observations of gravitational gradients fend tracking information obtained by GPS. The goal of the hereby presented dissertation is to investigate especially the potentiality of the GPS tracking data to solve the coefficients of the long-wave domain in particular. The theory of Hill's equations forms an excellent tool to analyse the orbit perturbations of the satellites moving in nearly polar, nearly circular orbits of very low altitude. The derivation of the linear perturbation theory is dealt with in detail. Special attention is given to the formulation of differential equations and their analytical and numerical solution. On the basis of the linear theory numerical simulations were carried out which proofed the impossibility to solve the long-wave domain completely from tracking data of only one of the discussed satellites. But the orbit analysis allows to set up a so-called Tailored Model in each case which may support and complete the processing of the gradiometry data. Further applications of a Tailored Model, gained from an orbit analysis of ARISTOTELES or STEP, resp., are possible, e.g. in the fields of satellite altimetry or of the development of global Earth's gravity models which uses data of satellites in many different orbits. Numéro de notice : 28054 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Thèse étrangère Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=63401

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Code-barres	Cote	Support	Localisation	Section	Disponibilité
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28054-02	30.40	Livre	Centre de documentation	Géodésie	Disponible

From Mars to Greenland / Oscar L. Colombo (1992)

Public Titre : From Mars to Greenland : charting gravity with space and airborne instruments, fields tide methods results, International Association of Geodesy symposium Type de document : Actes de congrès Auteurs : Oscar L. Colombo, Éditeur scientifique Editeur : Berlin, Heidelberg, Vienne, New York, ... : Springer Année de publication : 1992 Collection : International Association of Geodesy Symposia, ISSN 0939-9585 num. 11 Conférence : IAG 1991, 20th general assembly and symposium, From Mars to Greenland : charting gravity with space and airborne instruments, fields tide methods results 11/08/1991 24/08/1991 Vienne Autriche Importance : 358 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-3-540-97857-2 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] altimétrie [Termes IGN] Aristoteles [Termes IGN] atmosphère terrestre [Termes IGN] géodésie spatiale [Termes IGN] Global Positioning System [Termes IGN] gravimètre supraconducteur [Termes IGN] Groenland [Termes IGN] Mars (planète) [Termes IGN] orbite [Termes IGN] pesanteur terrestre [Termes IGN] satellite artificiel Numéro de notice : 67653 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Actes Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=37147

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Code-barres	Cote	Support	Localisation	Section	Disponibilité
67653-01	CG.91	Livre	Centre de documentation	En réserve M-103	Disponible