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Auteur R. Lehmann
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Studies on the use of the boundary element method in physical geodesy / R. Lehmann (1997)
Titre : Studies on the use of the boundary element method in physical geodesy Type de document : Monographie Auteurs : R. 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 descripteurs IGN] discrétisation
[Termes descripteurs IGN] équation intégrale
[Termes descripteurs IGN] problème des valeurs limites
[Termes descripteurs IGN] surface de référence
[Termes descripteurs IGN] Terre (planète)
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 :
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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 DisponibleZur Bestimmung des Erdschwerefeldes unter Verwendung des Maximum-Entropie-Prinzips / R. Lehmann (1994)
Titre : Zur Bestimmung des Erdschwerefeldes unter Verwendung des Maximum-Entropie-Prinzips Titre original : [Sur la détermination du champ de pesanteur terrestre en utilisant le principe d'entropie maximale] Type de document : Thèse/HDR Auteurs : R. Lehmann, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1994 Collection : DGK - C Sous-collection : Dissertationen num. 425 Importance : 103 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-3-7696-9468-0 Note générale : Bibliographie Langues : Allemand (ger) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes descripteurs IGN] Baltique, mer
[Termes descripteurs IGN] champ de pesanteur local
[Termes descripteurs IGN] distribution de Gauss
[Termes descripteurs IGN] entropie
[Termes descripteurs IGN] harmonique sphérique
[Termes descripteurs IGN] levé gravimétrique
[Termes descripteurs IGN] méthode de Monte-Carlo
[Termes descripteurs IGN] problème inverse
[Termes descripteurs IGN] système non linéaire
Résumé : (Auteur) The thesis deals with the problem of determining the outer gravity field of the Earth based on a finite number of data affected by measurement errors. It is described as a discrete inverse problem in an informational framework suggested by Tarantola and Valette (1982). Based on a conjunction operation for different states of information, a very general solution scheme for such problems is provided. For the first time we give a complete axiomatic foundation of this operation.
The mainstay of this work is the application of the solution scheme to the problem of modelling the disturbing potential in the outer space of the Earth. It is necessary to extend the scheme to account for unknown variance components, namely the squares of the unavoidable modellization errors. The result is not immediately a spatial potential function, but a state of information for the value of the disturbing potential at any point in the outer space, being the result of the conjunction of the states of information available. The solution scheme does not suggest a certain type of model for the representation of the potential, e.g. spherical harmonics could be used. Here the method of point masses in free (optimized) positions serves as an illustrating example.
For the definition of the probability distributions used we exclusively rely on the maximum entropy principle. This gives the least informative state of information consistent with given constraints. In this context the problem of constructing probability distributions for mass anomalies inside the Earth subject to spectral constraints for the outer gravity field is treated. The solution is presented for point mass anomalies and a number of practically occuring spectral constraints, both on a sphere as well as in a tangential plane.
In general, the probability distributions finally obtained for the representation of the state of information on the disturbing potential cannot be expressed analytically, because a multidimensional integral is not analytically tractable. However, two special cases exist, where an analytical solution is possible. Then we obtain either a t-distribution or a normal distribution for the disturbing potential value, both very well suited for estimation. In the remaining cases the resulting probability distributions can only be described by means of characteristic parameters. First of all, we investigate both the expectation as well as the mode (maximum likelihood point). Again, as the multidimensional integrals involved have no analytical solution, both can in general not be computed directly. Without numerical integration only the joint mode over the space of model parameters, modellization error squares, and the disturbing potential can be computed. This is accomplished by solving a nonlinear equation system.
If any, only the method of Monte Carlo integration is powerful enough to provide numerical approximates for the multidimensional integrals to be evaluated. The crucial point here is the proper choice of the pseudorandom distributions. For truely large dimension numbers even expensively determined pseudorandom distributions fall short. In a simple synthetic simulation study we compute marginal probability distributions for model parameters, for the modellization errors as well as for the disturbing potential by means of the Monte Carlo integration technique. In a larger scale simulation example, modelled close to the real behaviour of the gravity field in the Gulf of Bothnia, we try to assess biases of the maximum likelihood estimate. The Monte Carlo integration as well as the average second order remainder assessment do not agree well. Here the only conclusion to be drawn is: The biases do not form the largest constituent of the posterior errors in the results.
Finally we compute a local gravity field based on real data on the Gulf of Bothnia. We process more than 11000 gravimetric and more than 900 altimetric data. The results are two maximum likelihood solutions for up to 750 point masses in free positions. The first is based exclusively on the gravimetric data. The predicted geoid fits the altimetrically surveyed sea surface within 11 cm, that is not much more than the actual error of the altimetry. The second solution also includes the altimetry. Unlike the original method of point masses in free positions, we are now able to handle problems with different types of data, different data accuracies, as well as inhomogeneous spatial data coverage. This indicates the power of the suggested approach.
Numéro de notice : 28063 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Thèse étrangère Permalink :
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Code-barres Cote Support Localisation Section Disponibilité 28063-01 30.40 Livre Centre de documentation Géodésie Disponible 28063-02 30.40 Livre Centre de documentation Géodésie Disponible