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Untersuchungen zur Lösung der fixen gravimetrischen Randwertprobleme mittels sphäroidaler und Greenscher Funktionen / C.T. Nguyen (1993)

Public Titre : Untersuchungen zur Lösung der fixen gravimetrischen Randwertprobleme mittels sphäroidaler und Greenscher Funktionen Titre original : [Etudes sur la résolution du problème des valeurs aux limites fixes à l'aide des fonctions sphéroïdales et des fonctions de Green] Type de document : Thèse/HDR Auteurs : C.T. Nguyen, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1993 Collection : DGK - C Sous-collection : Dissertationen num. 399 Importance : 107 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-3-7696-9444-4 Note générale : Bibliographie Langues : Allemand (ger) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] champ de pesanteur terrestre [Termes IGN] espace de Hilbert [Termes IGN] fonction harmonique [Termes IGN] géodésie différentielle [Termes IGN] géoïde [Termes IGN] gravimétrie [Termes IGN] identité de Green [Termes IGN] problème des valeurs limites [Termes IGN] sphère des fixes [Termes IGN] sphèroïde Index. décimale : 30.40 Géodésie physique Résumé : (Auteur) Studies for solving the fixed gravimetric boundary value problems by means of spheroidal and Green's functions. In the present study the fixed gravimetric boundary value problems are considered for the exterior as well as for the interior domain of the earth. First of all existence and uniqueness of the solution are studied. For the solution theory the oblique Green's functions and the separable harmonic basis functions are generally discussed. The oblique derivative boundary operator is represented on the topography. A permissible reference density and the normal gravity field are derived from the equipotential earth spheroid. Based upon this the boundary value problems are solved by means of the spheroidal and Green's functions. The solutions are subsequently represented in the Hilbert space with reproducing kernel and the integral formulae on the earth spheroid are investigated with respect to the numerical aspects. The appendices give an overview of the special functions and the explicit representation of the infinite sums used in this study. Numéro de notice : 61575 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Thèse étrangère Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=60953

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Geodetic boundary value problems 3 / K. Arnold (1989)

Public Titre : Geodetic boundary value problems 3 Type de document : Monographie Auteurs : K. Arnold, Auteur Editeur : Postdam : Zentralinstitut für Physik der Erde ZPE Année de publication : 1989 Collection : Veröffentlichungen des Zentralinstituts für Physik der Erde, ISSN 0514-8790 num. 97 Importance : 200 p. Format : 21 x 30 cm Note générale : Bibliographie Langues : Anglais (eng) Allemand (ger) Russe (rus) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] identité de Green [Termes IGN] intégrale de Stokes [Termes IGN] problème des valeurs limites Index. décimale : 30.42 Gravimétrie Résumé : (Auteur) The author extends and completes his investigations about the solution of the boundary value problem of Molodenskij found by means of the identity of Green during the last 30 years. These derivations are developed here in a clear, comprehensive and systematic order. It is the inversion of the fundamental equation of physical geodesy which is treated here. The mapping between the telluroid and the Earth's surface happens by vertical point shifts. The final result allows the calculation of the height anomalies exact to 1 cm ; thus, it is usefull for the determination of the decimeter- and centimeter- geoid. The solution has the shape of a closed expression. It does not imply series developments which have a dubious convergence or which do not allow to evaluate the amount of the residual term of it. All the here introduced series developments have a quick, clear and guaranteed convergence. Iteration procedures are avoided. The final result expresses the height anomalies or the perturbation potential at the Earth's surface in terms of the free-air anomalies of the gravity at the Earth's surface. The main term of the solution is the Stokes integral which has the Faye - anomalies in the integrand. These anomalies consist in the sum of the free-air anomalies and the plane terrain reduction of the gravity. Further, these Faye - anomalies are supplemented by a small and smoothed term which can be disregarded in most cases, which has positive and negative amounts, and which implies the vertical gradient of the refined Bouguer - anomalies. Further on, this main term has to be supplemented by the addition of 3 or 4 relative small terms. only one of them can reach about 50 em in extreme cases. The final solution of the boundary value problem has a shape which is distinguished by the special property of the additives that a clear separation between the terms linear and quadratic in the heights takes place. The terms quadratic in the heights can be neglected for test points situated in plane countries or in low mountain ranges. Only for test points situated in high mountains, the terms quadratic in the heights can be of interest. Even in this case, these terms have only relative small amounts. and the integration area can be restricted on the near surroundings of the test point, to a distance of not more than some tens of kilometers. The final solution of the boundary value problem is convenient for routine applications, and it meets all theoretical requirements. The physical boundary values are not subsided downwards from the surface to the sphere, but the geometrical terms come upwards from the sphere to the surface. Numéro de notice : 39875C Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Monographie Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=57742

Voir aussi

• Geodetic boundary value problems 2 / K. Arnold (1986)
• Geodetic boundary value problems 1 / K. Arnold (1987)
• Geodetic boundary value problems 4 / K. Arnold (1990)

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Code-barres	Cote	Support	Localisation	Section	Disponibilité
39875-01C	30.42	Livre	Centre de documentation	Géodésie	Disponible
39875-02C	30.42	Livre	Centre de documentation	Géodésie	Disponible

The role of the geoid in high precision geodesy and oceanography / Chris Rizos (1982)

Public Titre : The role of the geoid in high precision geodesy and oceanography Type de document : Monographie Auteurs : Chris Rizos, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1982 Collection : DGK - A Sous-collection : Theoretische Geodäsie num. 096 Importance : 64 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-3-7696-8178-9 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] données altimétriques [Termes IGN] géodésie physique [Termes IGN] géoïde terrestre [Termes IGN] identité de Green [Termes IGN] océanographie dynamique [Termes IGN] océanographie spatiale [Termes IGN] potentiel de pesanteur terrestre [Termes IGN] relief de la surface de la mer Index. décimale : 30.40 Géodésie physique Résumé : (Auteur) The principal role played by the geoid in classical geodesy has been as a datum for levelling. The most obvious level surface of the earth's gravity field that could act as a vertical datum to which all elevations on land may be referred is that "corresponding" to mean sea level (MSL). It has therefore been conventional to define the geoid as that level surface that was the directly observable elevation datum afforded by the mean level of the oceans (more precisely; a coastal estimate). As a corollary, it was assumed that different height systems based on local MSL were related to such a unique geop. This procedure is adequate for geodetic considerations to precisions of 1 part in a million (± 6 m in position). It has, however, long been recognised by physical oceanographers that the MSL surface does not lie along a unique equipotential surface of the earth's gravity field. Direct analogy with the solid earth has resulted in departures of sea level from an equipotential surface being referred to as Sea Surface Topography (SST). The total range of SST is estimated at 3-4 m, with a time varying component approximately one quarter the magnitude of the stationary part. Consequently in aiming at the higher precision of 1 part in 108 (< ± 10 cm in position) a number of factors have to be reassessed. These include the fundamental definitions, the basis and constants of the vertical reference system, the definition, accuracy and limitations of the data available. In such a reassessment it is apparent that SST is a factor which needs to be taken into account in many respects. It can be treated as a nuisance factor in high precision definitions and determinations of the geoid (or any other vertical reference surface) or as an important parameter to be estimated in support of oceanographic studies. This report will attempt to confront some of the following questions: (1) How is the geometry of the Molodenskii Boundary Value Problem (BVP) affected by the existence of SST? (2) Is it possible to formulate in practice, a solution of the free BVP to ± 10 cm precision from surface gravity data that can no longer) be considered refer-enced to a unique vertical datum surface? (3) With 70% of the earth's surface now "fixed" using satellite altimetry data, are high precision solutions to the BVP from surface gravity data irrelevant? (4) What is the role of concepts such as the geoid and geodetic techniques such as altimetry in ocean dynamical studies? Numéro de notice : 28237 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Monographie Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=63583

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28237-01	30.40	Livre	Centre de documentation	Géodésie	Disponible

Simulation studies on the computation of the gravity vector in space from surface data considering the topography of the Earth / K. Katsambalos (1981)

Public Titre : Simulation studies on the computation of the gravity vector in space from surface data considering the topography of the Earth Type de document : Rapport Auteurs : K. Katsambalos, Auteur Editeur : Colombus (Ohio) : Ohio State University Année de publication : 1981 Collection : Reports of the Department of Geodetic Science num. 314 Format : 21 x 27 cm Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] champ de pesanteur terrestre [Termes IGN] identité de Green [Termes IGN] méthode des moindres carrés [Termes IGN] simulation [Termes IGN] surface topographique Index. décimale : 30.40 Géodésie physique Numéro de notice : 56991 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Rapport de recherche Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=60140

Exemplaires(2)

Code-barres	Cote	Support	Localisation	Section	Disponibilité
56991-01	30.40	Livre	Centre de documentation	Géodésie	Disponible
56991-02	30.40	Livre	Centre de documentation	Géodésie	Disponible

Physical geodesy / W. Heiskanen (1967)

Public Titre : Physical geodesy Type de document : Guide/Manuel Auteurs : W. Heiskanen, Auteur ; Helmut Moritz, Auteur Editeur : Londres [etc.] : Freeman (W.H.) Année de publication : 1967 Autre Editeur : Michigan : University Microfilms International Importance : 364 p. Format : 17 x 22 cm ISBN/ISSN/EAN : 1-800-521-0600 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] altitude [Termes IGN] anomalie de pesanteur [Termes IGN] champ de pesanteur terrestre [Termes IGN] ellipsoïde (géodésie) [Termes IGN] ellipsoïde de référence [Termes IGN] figure de la Terre [Termes IGN] fonction harmonique [Termes IGN] géodésie physique [Termes IGN] géoïde [Termes IGN] gravimétrie [Termes IGN] identité de Green [Termes IGN] potentiel de pesanteur terrestre [Termes IGN] système de coordonnées [Termes IGN] système de référence céleste [Termes IGN] système de référence mondial Index. décimale : 30.40 Géodésie physique Numéro de notice : 23793 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Manuel de cours Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=47147