Descripteur
Termes IGN > mathématiques > analyse numérique > analyse harmonique > fonction harmonique > harmonique sphérique
harmonique sphérique |
Documents disponibles dans cette catégorie (95)
![](./images/expand_all.gif)
![](./images/collapse_all.gif)
![Tris disponibles](./images/orderby_az.gif)
Etendre la recherche sur niveau(x) vers le bas
Tailored numerical solution strategies for the global determination of the Earth's gravity field / W.D. Schuh (1996)
Titre : Tailored numerical solution strategies for the global determination of the Earth's gravity field : study of the complementary use of the gradiometry and Global Positioning System (GPS) for the Earth's gravity field Type de document : Rapport Auteurs : W.D. Schuh, Auteur Editeur : Graz : Technische Universität Graz Année de publication : 1996 Collection : Mitteilungen der geodätischen Institute num. 81 Importance : 156 p. Format : 21 x 30 cm Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] champ de pesanteur terrestre
[Termes IGN] compensation par moindres carrés
[Termes IGN] équation linéaire
[Termes IGN] harmonique sphérique
[Termes IGN] matrice de covariance
[Termes IGN] modèle stochastique
[Termes IGN] potentiel de pesanteur terrestre
[Termes IGN] problème des valeurs limitesIndex. décimale : 30.40 Géodésie physique Numéro de notice : 18259 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Rapport d'étude technique Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=41459 Exemplaires(1)
Code-barres Cote Support Localisation Section Disponibilité 18259-01 30.40 Livre Centre de documentation Géodésie Disponible Estimation of sea dynamic topography, ocean tides, and secular changes from Topex altimeter data / Y.M. Wang (1994)
Titre : Estimation of sea dynamic topography, ocean tides, and secular changes from Topex altimeter data Type de document : Monographie Auteurs : Y.M. Wang, Auteur ; R.H. Rapp, Auteur Editeur : Colombus (Ohio) : Ohio State University Année de publication : 1994 Collection : Department of Geodetic Science and Surveying Reports num. 430 Importance : 86 p. Format : 21 x 27 cm Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie spatiale
[Termes IGN] données altimétriques
[Termes IGN] fonction harmonique
[Termes IGN] harmonique sphérique
[Termes IGN] hauteurs de mer
[Termes IGN] marée océanique
[Termes IGN] perturbation séculaire
[Termes IGN] TOPEX
[Termes IGN] valeur efficaceIndex. décimale : 30.52 Marégraphie et niveau moyen des mers Résumé : (Auteur) Sea surface dynamic topography (SSDT) has been determined from the separation of the Topex sea surface height and the geoid undulations implied by the JGM-2/OSU91A merged potential coefficient model. The SSDT was initially analyzed to determine annual and semiannual variations in the ocean surface, corrections to the M2, S2, K1, 01 constituents of the Cartwright/Ray tide model, and bias and bias rate terms. All correction terms were represented by spherical series to degree 8 (for most testing purposes) and to degree 15 for final runs. The most complete analysis was done with Topex cycles 4 to 58. From this solution we found that the root mean square annual signal was ±4.5 cm in the Northern Hemisphere and ±3.5 cm in the Southern Hemisphere with an overall amplitude of ±4.0 cm. Large 'annual signals were associated with features such as the Kurishio Current (±10 cm), Gulf Stream (±7 cm) and the Falkland Current (±6 cm). The tide correction terms were ±2.9 CM (MA ±1.5 CM (S2), +0.8 CM (01), ±1.4 cm. (K1). The improvement in the tide model was proven through comparisons at the 104/95 tide gauge data set provided by C. Le Provost.
The bias rate value was determined at each normal point and then averaged to determine a mean rate of 4.8 mm/yr. - After removing an altimeter drift rate of 2.0 mm/yr the net rate is 2.8 mm/yr., This rate could be a combination of sea level change and effects associated with the various correction terms applied to the data.
The second main theme of the report relates to the representation of SSDT in spherical harmonics (SH) and orthonormal (ON) functions. Procedures were implemented to estimate either SH or ON coefficients. It was found that the estimation of SH coefficients was more stable than the ON estimation. For those applications on which spectral information of SSDT is needed a SH model can be transformed into an ON model. It was found that the lower degree SH coefficients are quite sensitive to the -bias correction applied to the sea surface height data. This sensitivity does not occur in ON coefficient estimation. For the analysis with data from cycles 4 to 58 a bias term of 55 cm. was applied to the data. This value leads to a zero value for the degree zero term in the ON expansion. An SH expansion to degree 24 was computed using a priori degree variance computed from 10 selected cycles of Topex data. The SH expansion was transformed to an ON expansion and both coefficient sets are given in the report. The degree 2,0 coefficient in the SH representation was -37.8 cm quite comparable with other altimeter based solutions.
The analysis of the ON coefficient indicated an rms value of SSDT equal to ±61 cm. The ON- power spectrum, in conjunction with the geoid undulation accuracy of the JGM-2 model in the ocean areas, indicated the two values are approximately equal near degree 13. This suggests that SSDT estimates above degree 13 may be unreliable. This statement was consistent with the inconsistency of geostrophic flow patterns implied, by the SSDT expansions at the higher degrees. Even at the lower (e.g. 13) degree the flow patterns showed only moderate agreement with known circulation patterns.Numéro de notice : 12110 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Monographie Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=54539 Exemplaires(1)
Code-barres Cote Support Localisation Section Disponibilité 12110-01 30.52 Livre Centre de documentation Géodésie Disponible Zur Bestimmung des Erdschwerefeldes unter Verwendung des Maximum-Entropie-Prinzips / Rüdiger 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 : 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 linéaireIndex. 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 Exemplaires(2)
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
Titre : Spherical harmonic analysis of satellite gradiometry Type de document : Rapport Auteurs : Reiner Rummel, Auteur ; Fernando Sanso, Auteur ; Martin Van Gelderen, Auteur ; Radboud Koop, Auteur ; E.J.O. Schrama, Auteur ; Maria Antonia Brovelli, Auteur ; F. Miggliaccio, Auteur ; F. Sacerdote, Auteur Editeur : Delft : Netherlands Geodetic Commission NGC Année de publication : 1993 Collection : Netherlands Geodetic Commission Publications on Geodesy Sous-collection : New series num. 39 Importance : 122 p. Format : 20 x 28 cm ISBN/ISSN/EAN : 978-90-6132-247-4 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie spatiale
[Termes IGN] analyse harmonique
[Termes IGN] gradiométrie
[Termes IGN] harmonique sphérique
[Termes IGN] méthode des moindres carrés
[Termes IGN] poursuite de satelliteIndex. décimale : 30.60 Géodésie spatiale Résumé : (auteur) In 1988 the European Space Agency started with a series of studies with the goal to prepare the geodetic user community for a dedicated gravity field mission and stimulate cooperation among various groups. Thereby it was left open whether the planned mission should be based on the principle of satellite-to-satellite tracking, on satellite gradiometry or on a combination of these two methods. In the course of these studies it turned out that the group of the dipartimento di ingegneria idraulica, ambientale e del rilevamento of the politecnico di Milano and that of the faculty of geodetic engineering of the Delft University of Technology worked much along the same line. At various occasions very exciting and stimulating exchange of ideas took place between these two groups. In 1991 it was therefore decided to publish the main line of their development in gradiometry analysis, the so-called timewise and spacewise approach, in a joint report. Compared with the benefit it would have been rather cumbersome to try to homogenize the adopted style of presentation and notation of the two groups. Thus little effort was spent on this aspect. We hope that this does not hamper reading. Numéro de notice : 61103 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Rapport de recherche DOI : sans En ligne : https://www.ncgeo.nl/downloads/39Rummel.pdf Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=60878 Exemplaires(2)
Code-barres Cote Support Localisation Section Disponibilité 61103-01 30.60 Livre Centre de documentation Géodésie Disponible 61103-02 30.60 Livre Centre de documentation Géodésie Disponible Neue Verfahren zur Kombination heterogener Daten bei der Bestimmung des Erdschwerefeldes / B. Middel (1992)
Titre : Neue Verfahren zur Kombination heterogener Daten bei der Bestimmung des Erdschwerefeldes Titre original : [Nouveaux procédés pour la combinaison de données hétérogènes lors de la détermination du champ de pesanteur terrestre] Type de document : Thèse/HDR Auteurs : B. Middel, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1992 Collection : DGK - C Sous-collection : Dissertationen num. 395 Importance : 124 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-3-7696-9441-3 Note générale : Bibliographie Langues : Allemand (ger) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] champ de pesanteur terrestre
[Termes IGN] collocation
[Termes IGN] erreur systématique
[Termes IGN] harmonique sphérique
[Termes IGN] méthode robuste
[Termes IGN] potentiel de pesanteur terrestreIndex. décimale : 30.40 Géodésie physique Résumé : (Auteur)New techniques for the combination of heterogenous data when determing the Earth's gravity field
A fundamental problem for the modulation of the Earth's gravity field is the combination of very different pieces of information in an adequate way.
Within this thesis a concept for the solution of this task is developed in which the idea of robust collocation, based on a Random Effects Model, is generalized. With the predictors multi hom-BLUP and mixed BLUP two approaches are presented where the influence of possible systematic errors in the data set, being interpreted as stochastic prior information, can be reduced. In order to judge the different combination solutions a statistic test strategy is developed.
These new techniques are numerically tested by means of an expansion of the Earth's gravitational potential in spherical harmonics based on terrestrial gravity data and satellite orbit information. Due to the robustification very homogenous combination solutions can be obtained by the use of the predictors developed within this thesis; they turn out to be superior when compared with the traditional approaches.Numéro de notice : 28082 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Thèse étrangère Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=63429 Exemplaires(1)
Code-barres Cote Support Localisation Section Disponibilité 28082-01 30.40 Livre Centre de documentation Géodésie Disponible Eine approximative Lösung der fixen gravimetrischen Randwertaufgabe im Innen- und Außenraum der Erde / J. Engels (1991)
PermalinkFGI studies on satellite gravity gradiometry, 2. 2 Geopotential recovery at 0.5-degree resolution from global satellite gradiometry data sets / Martin Vermeer (1990)
PermalinkPermalinkPermalinkPermalinkPermalinkPermalinkPermalinkUntersuchungen zur Approximation des äußeren Gravitationsfeldes der Erde durch Punktmassen mit optimierten Positionen / F. Barthelmes (1986)
PermalinkPermalink