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Zur Bestimmung des Erdschwerefeldes unter Verwendung des Maximum-Entropie-Prinzips / Rüdiger Lehmann (1994)

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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 :	Rüdiger 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 IGN] Baltique, mer [Termes IGN] champ de pesanteur local [Termes IGN] distribution de Gauss [Termes IGN] entropie [Termes IGN] harmonique sphérique [Termes IGN] levé gravimétrique [Termes IGN] méthode de Monte-Carlo [Termes IGN] problème inverse [Termes IGN] système non linéaire
Index. décimale :	30.40 Géodésie physique
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 :	https://documentation.ensg.eu/index.php?lvl=notice_display&id=63410

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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

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