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Bestimmung von Modellparametern der Erde durch Analyse ihrer Drehbewegung / H. Fröhlich (1994)
Titre : Bestimmung von Modellparametern der Erde durch Analyse ihrer Drehbewegung Titre original : [Estimation des paramètres de modèle de la Terre au travers de l'analyse de sa rotation] Type de document : Thèse/HDR Auteurs : H. Fröhlich, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1994 Collection : DGK - C Sous-collection : Dissertationen num. 420 Importance : 102 p. Format : 21 x 30 cm Note générale : Bibliographie Langues : Allemand (ger) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] correction différentielle
[Termes IGN] linéarisation
[Termes IGN] modèle mathématique
[Termes IGN] problème des valeurs limites
[Termes IGN] rotation de la Terre
[Termes IGN] théorème de LiouvilleIndex. décimale : 30.40 Géodésie physique Résumé : (Auteur) The rotation of the Earth is modeled by means of the linearized EULER-LIOUVlLLE equation. The different components described physically or by indices are combined in a joint model of the excitation function. Pa-rameters are estimated by differential correction. Parts of the excitation function not explicitly considered in the model can be derived from the residuals. The linearized EULER-LIOUVlLLE equation is solved as a bound-ary value problem; the formulas according to the method of infinitely many variables are derived. Results of the estimation of parameters are discussed by using their accuracies and amount and temporal course of the residuals. Numéro de notice : 28067 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Thèse étrangère Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=63414 Réservation
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Code-barres Cote Support Localisation Section Disponibilité 2806701 30.40 Livre Centre de documentation Géodésie Disponible Effects of Non-Linearity in the Geodetic Boundary Value Problems / B. Heck (1993)
Titre : Effects of Non-Linearity in the Geodetic Boundary Value Problems Type de document : Monographie Auteurs : B. Heck, Auteur ; Kurt Seitz, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1993 Collection : DGK - A Sous-collection : Theoretische Geodäsie num. 109 Importance : 74 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-3-7696-8191-8 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] analyse harmonique
[Termes IGN] champ de pesanteur terrestre
[Termes IGN] problème des valeurs limitesIndex. décimale : 30.40 Géodésie physique Résumé : (Auteur) The geodetic boundary value problem (GBVP) aims at the determination of the (external) gravity po-tential of the earth from (continuous) observations given on the earth's surface which acts as boundary surface. Essentially, three versions of the GBVP have to be distinguished: the fixed problem involving the assumption of a boundary surface with completely known geometry, and the vectorial and scalar formulations of the free GBVP where either the spatial or the vertical components of the position vector of the boundary surface occur as additional unknown functions. The number of prescribed boundary data types depends on the version of the GBVP; in order to obtain unique solutions, one observable only, e.g. the modulus of the gravity vector, is sufficient in the case of the free GBVP while two (resp. four) observables are necessary for the scalar (resp. vectorial) free problems.
Practical solutions of the GBVP are achieved by linearizing the boundary conditions, neglecting second and higher order terms. Due to this procedure the solutions of the GBVP are biased. In the present report the impact of the linearization errors on the (reduced) boundary conditions, the resolved po-tential function and - for the free problems - the geometry of the boundary surface is evaluated in the space and frequency domain. Numerical results have been obtained following two alternative concepts, a harmonic analysis and a synthesis approach. Both procedures rely on a representation of the gravi-tational potential of the earth by a truncated spherical harmonic expansion. The synthesis approach proved to be not feasible for degrees of expansion above N = 36 and had to be given up in favour of the harmonic analysis concept which was able to handle series representations up to degree N = 180.
The numerical investigations have revealed significant differences between the three formulations of the GBVP with respect to the impact of second-order non-linear effects. The smallest orders of magnitude show up in the fixed GBVP, amounting up to 15.10-8ms-2 in the boundary condition and 0.04 m2s-2 in the potential function. In contrast, the second-order effects in the vectorial free GBVP have magnitudes up to 3.10-5 ms-2 in the (reduced) boundary condition and 2 m2s-2 in the solution of the potential; the effects in the vertical component of the position correction vector amount up to 0.4 m, while the effects on the horizontal components have magnitudes up to 3 metres. The scalar free GBVP takes a mediate position between the fixed and the vectorial free GBVP, the non-linear terms in the (reduced) boundary condition amounting up to 1.10-6ms-2,0.1 m2s-2 in the potential, and 3 mm in
the vertical position correction.
From a practical point of view the bias in the solution is negligible in the case of the fixed GBVP, mostly tolerable for the scalar free GBVP, but inadmissibly large for the vectorial free GBVP, compared with the present-day observational accuracies. Due to its practical significance the results concerning the scalar free GBVP deserve most attention.Numéro de notice : 28245 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Monographie Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=63591 Réservation
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Code-barres Cote Support Localisation Section Disponibilité 28245-01 30.40 Livre Centre de documentation Géodésie Disponible Untersuchungen zur Lösung der fixen gravimetrischen Randwertprobleme mittels sphäroidaler und Greenscher Funktionen / C.T. Nguyen (1993)
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] sphèroïdeIndex. 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 Réservation
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Code-barres Cote Support Localisation Section Disponibilité 61575-01 30.40 Livre Centre de documentation Géodésie Disponible Untersuchungen zur Lösung der fixen gravimetrischen Randwertprobleme mittels sphäroidaler und Greenscher Funktionen / N. Thong (1993)
Titre : Untersuchungen zur Lösung der fixen gravimetrischen Randwertprobleme mittels sphäroidaler und Greenscher Funktionen Titre original : Studies for solving the fixed gravimetric boundary value problems by means of spheroidal and Green's functions Type de document : Thèse/HDR Auteurs : N. Thong, 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] analyse harmonique
[Termes IGN] champ de pesanteur terrestre
[Termes IGN] espace de Hilbert
[Termes IGN] fonction de Green
[Termes IGN] problème des valeurs limites
[Termes IGN] sphèroïdeIndex. 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 topogaphy.
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 : 28081 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Thèse étrangère Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=63428 Réservation
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Code-barres Cote Support Localisation Section Disponibilité 28081-01 30.40 Livre Centre de documentation Géodésie Disponible 28081-02 30.40 Livre Centre de documentation Géodésie Disponible Lösung des fixen geodätischen Randwertproblems mit Hilfe der Randelementmethode / R. Klees (1992)
Titre : Lösung des fixen geodätischen Randwertproblems mit Hilfe der Randelementmethode Titre original : [Solution du problème géodésique de valeurs aux limites à l'aide de la méthode des éléments résiduels] Type de document : Thèse/HDR Auteurs : R. Klees, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1992 Collection : DGK - C Sous-collection : Dissertationen num. 382 Importance : 314 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-3-7696-9428-4 Note générale : Bibliographie Langues : Allemand (ger) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] discrétisation
[Termes IGN] équation intégrale
[Termes IGN] linéarisation
[Termes IGN] problème des valeurs limitesIndex. décimale : 30.40 Géodésie physique Résumé : (Auteur)The présent study deals with thé numerical solution of thé fixed geodetic boundary value problem (bvp) using thé boundary élément method. Assuming a continuous covering of thé Earth's surface with gravity values thé mathematical formulation leads to a nonlinear outer bvp for thé Laplace-operator in three dimensional euclidean space.
The theoretical part starts in section 1 with some of thé most important mathematical foundations we need such as properties of boundary surfaces embedded in R3, strongly singular surface intégrais, some aspects of thé theory of pseudodifferential operators and singular intégral operators forming thé theoretical frame for thé whole convergence analysis and finally some détails from thé theory of (bivariate) spline functions. Section 2 contains thé mathematical formulation of thé fixed geodetic bvp and gives a short overview over known geodetic literatures concerning this problem. Local existence and uniqueness assertions both in Hôlder and Sobolev spaces are given based on thé implicit function theorem of Hildebrandt and Graves. Besides, thé convergence of a perturbation expansion is shown based on an idea of Jorge (1987) leading to a constructive method for thé solution of thé nonlinear problem in Hôlder spaces. In both cases thé nonlinear problem is transformed into a séries of linear ones which can be classified as oblique bvps. Under thé assumption of their regularity thé Fredholm alternative is valid not only in thé case of Hôlder spaces but also in Sobolev spaces so that uniqueness implies existence. The uniqueness can be proved in both cases using thé generalized maximum principle of Hopf. The very restrictive requirement F e C3 in thé case of Sobolev spaces can be weakened under some suppositions so that F e G1*" is sufficient to apply thé maximum principle. Therefore thé nonlinear fixed bvp can be solved iteratively where in each step a classi-cal oblique bvp arises being thé subject of thé next sections.
Both direct and indirect methods are discussed in section 4 to transform thé oblique boundary value prob-lem into an intégral équation leading to équations of différent types like strongly singular or hypersingular équations of thé second kind depending on thé methods used. It is shown that thé strongly singular intégral équation resulting from thé représentation of thé unknown disturbing potential as single layer potential is thé most appropriate one especially from thé numerical point of view. The principal symbol of this intégral operator is determined and it is proved that our intégral operator is strongly elliptic if and only if thé oblique direction is never tangential to thé Earth's surface, i.e. thé strong ellipticity is not automatically fulfilled by our intégral operator but has to be demanded explicitly.
For thé transformation of thé intégral équation into a finite dimensional lirfear System différent discreti-zation methods are disussed in section 5 like allocation, Galerkin and least squares. It is shown that GalerkinBubnov discretization is thé best compromise between thé numerical effort, thé properties of thé boundary intégral operator to assure thé convergence of thé discretization procédure and thé order of convergence. For thé convergence of thé GalerkinBubnov method we need thé strong ellipticity of thé boundary intégral operator bringing on thé coerciveness in thé form of a Garding's inequality being thé starting point for thé whole convergence analysis. Section 6 contains thé définition of thé boundary élément method including thé pros and cons in relation to finite élément methods, thé définition of thé test and trial functions consisting of polynomial finite élément functions on thé boundary. Besides, thé coefficients of thé linear System for GalerkinBubnov discretization using piecewise constant test and trial functions are derived. In section 7 a nearly complète error analysis in Sobolev spaces is given, considering both discreti-zation and numerical cubature errors and giving thé state of thé art in estimating thé influence of surface approximation errors. Under thé assumption of strong ellipticity, being équivalent to thé positive definiteness of thé principal symbol of thé boundary intégral operator, it is shown that ail Galerkin methods are stable and converge. The asymptotic order of convergence is quasioptimal i.e. it has thé same order as thé best approximation of thé theoretical solution by our boundary élément trial functions. For piecewise constant functions a convergence of thé order 0(h2) for h-iO is proved if we measure thé error in thé Sobolev norm H''(F). This implies convergence of thé same order for thé potential in points away from thé boundary surface in any norm.
The numerical part mainly deals with thé development of efficient methods for thé approximation and représentation of parts of thé Earth's surface and of cubature formulas for calculating thé coefficients of thé linear System and thé potential in thé Earth's outer space. It is shown in section 9 that Overhauser splines and bicubic BSplines are very suitable for thé approximation and représentation of thé boundary surface and superior to many other methods. For 1 1 km2 boundary éléments this leads to mean approximation errors of approximately 810 m where larger errors are possible depending on thé roughness of thé real topography. For thé représentation of thé surface normal field it is also shown that Overhauser splines are thé most appropriate approximation especially for finer grids.
In Section 10 thé problem of efficient cubatures is considered for calculating thé coefficients of thé linear System defined by single and double intégrais over boundary éléments where both regular, weakly singular, strongly singular and quasisingular intégrais arise. Several cubature formulas for thé différent types of intégrais are considered. Extensive analytical and numerical developments show their efficiency compared with other cubature formulas used in engineering sciences. A detailed analysis shows that thé highly prob-
lematic strongly singular intégrais can be calculated analytically and that thé resulting kernel has a loga-rithmic singularity over thé whole boundary of thé fini te élément.
A local solution is calculated for a région of size 100-100 km2 using 10000 boundary éléments. The GalerkinBubnov discretization with piecewise constant trial functions leads to a dense unsymmetric linear System of thé order 10000-10000 with approximately 108 coefficients. In order to achieve a relative accuracy of at least 10'3 - 10'4 for each coefficient setting up thé linear System takes about 1 CPU-hour. In section 11.2 an efficient direct équation solver is developed based on a LUfactorization using a spécial Gaussian élimination well adapted to thé architecture of thé pipeline computer Siemens/Fujitsu VP 400-EX resp. S400/10. It is shown that thé time for thé I/O opérations can be reduced by minimizing thé amount of data to be transferred and by speeding up thé I/Oopérations using spécial runtime options of thé operational System and asynchronous I/O so that CPUusage and I/O opérations are done in parallel. The test compu-tations show that thé linear System mentioned before can be solved in approximately 10.5 resp. 7 minutes corresponding to a performance of 1.1 resp. 1.6 GFLOPS. In section 11.4 thé well-conditioning of thé linear System is proved leading to a very small sensitivity against errors of thé input data; thé influence of round off errors is proved to be below 10-". The local solution is based on thé use of a degree and order 360 spherical harmonie expansion of thé gravitational potential as référence potential and thé neglect of thé outer zone. As a detailed analysis shows, this leads to large errors only near by thé boundary of thé local région and a drastic decrease of thé layer density errors with increasing distance from thé boundary so that only relative différences of thé order 10'3 10'5 occur in most parts of our local région.
In section 12 thé calculation of thé gravitational potential in points of thé Earth's outer space is considered. Efficient cubatures for thé numerical calculation of thé single layer potential are developed especially for points near by thé Earth's surface, and they are compared with other cubatures used in engineering sciences. The results show that such formulas can be found based on spécial parameter transformations smoothing out thé strong variation of thé integrand in points near by both thé Earth's surface and thé boundary of thé fmite élément. '
Section 13 contains some proposais for future work which has to be done in relation to thé numerical sol-ution of thé fixed geodetic bvp and thé boundary élément method.Numéro de notice : 28089 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Thèse étrangère Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=63436 Réservation
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Code-barres Cote Support Localisation Section Disponibilité 28089-01 30.40 Livre Centre de documentation Géodésie Disponible 28089-02 30.40 Livre Centre de documentation Géodésie Disponible Eine approximative Lösung der fixen gravimetrischen Randwertaufgabe im Innen- und Außenraum der Erde / J. Engels (1991)PermalinkGeodetic work in the Netherlands 1987-1990 / W. Baarda (1991)PermalinkOn the linearized boundary value problems of physical geodesy / B. Heck (1991)PermalinkThe geodetic boundary value problem in two dimensions and its iterative solution / M. Van Gelderen (1991)PermalinkGeodetic boundary value problems 4 / K. Arnold (1990)PermalinkThe role of the topography in gravity gradiometer reductions and in the solution of the geodetic boundary value problem using analytical downward continuation / Y.M. Wang (1990)PermalinkAdvanced physical geodesy / Helmut Moritz (1989)PermalinkGeodetic boundary value problems 3 / K. Arnold (1989)PermalinkA simulation study of the overdetermined geodetic boundary value problem using collocation / L. Tsaoussi (1989)PermalinkNumerical recipes / William H. Press (1988)Permalink