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A generalized theory of the figure of the Earth : formulae / Chengli Huang in Journal of geodesy, vol 93 n° 3 (March 2019)  

Public [article]  inJournal of geodesy > vol 93 n° 3 (March 2019) . - pp 297 - 317 Titre : A generalized theory of the figure of the Earth : formulae Type de document : Article/Communication Auteurs : Chengli Huang, Auteur ; Yu Liu, Auteur ; Chenjun Liu, Auteur ; Mian Zhang, Auteur Année de publication : 2019 Article en page(s) : pp 297 - 317 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie [Termes descripteurs IGN] croute terrestre [Termes descripteurs IGN] ellipticité (géométrie) [Termes descripteurs IGN] équation de Clairaut [Termes descripteurs IGN] figure de la Terre [Termes descripteurs IGN] surface de référence Résumé : (Auteur) Traditionally a laterally homogeneous and spherical base Earth model (e.g., the PREM model) is considered as input when computing the Earth’s equipotential surfaces, which are then resulted to be in symmetric shape. However, the Earth, known with a complex distribution of interior material and density, especially in the upper mantle and the crust, cannot be treated as a symmetric sphere. Recently, a CRUST1.0 model of crust layer is published and well accepted. But the effect caused by the asymmetric crust (and mantle) on equilibrium figures of the Earth cannot be analyzed by the traditional theories. A generalized theory of the figure of the Earth to third-order precision is firstly proposed in this paper, as well as the iterative calculation strategy to solve the complex equation system. In order to validate this generalized theory, the degeneration of this generalized theory with the PREM model is made and is compared with traditional theories, and it is shown that the result of this generalized theory, after degeneration, is consistent very well with traditional theory. Meanwhile, the effect (including both the direct and indirect effects) of the crust layer, from the CRUST1.0 model, on the figures of equipotential surfaces of the Earth’s interior, as well as their effects on the global dynamics flattening, will be presented as an application of this theory in accompanying paper. Numéro de notice : A2019-150 Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-018-1159-6 date de publication en ligne : 15/06/2018 En ligne : https://doi.org/10.1007/s00190-018-1159-6 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=92488 [article]

A generalized theory of the figure of the Earth : on the global dynamical flattening / Chenjun Liu in Journal of geodesy, vol 93 n° 3 (March 2019)  

Public [article]  inJournal of geodesy > vol 93 n° 3 (March 2019) . - pp 319 - 331 Titre : A generalized theory of the figure of the Earth : on the global dynamical flattening Type de document : Article/Communication Auteurs : Chenjun Liu, Auteur ; Chengli Huang, Auteur ; Yu Liu, Auteur ; Mian Zhang, Auteur Année de publication : 2019 Article en page(s) : pp 319 - 331 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie [Termes descripteurs IGN] aplatissement [Termes descripteurs IGN] croute terrestre [Termes descripteurs IGN] isostasie [Termes descripteurs IGN] manteau terrestre [Termes descripteurs IGN] moment d'inertie [Termes descripteurs IGN] noyau terrestre [Termes descripteurs IGN] rotation de la Terre Résumé : (Auteur) A generalized theory of the figures of the Earth’s interior to a third-order precision of ellipticity is proposed in accompanying paper in which all the odd degree and nonzero order spherical harmonic terms are included. As both the direct and indirect contributions of the asymmetric crust are included, this theory makes a significant improvement for calculating the asymmetric equilibrium figures of the real Earth comparing with the traditional theories which can only deal with the ideal symmetric Earth. The principal moments of inertia (PMOI: A, B, C) and global dynamical flattening (H) are important quantities in studying the rotating Earth. Precession and gravity observations give observation value of H (Hobs≈1/305.4559) with very high precision, while its theoretical calculated value (Htheory≈1/308.5) from traditional theories and a starting symmetric Earth model (like PREM model) is about 1% less than Hobs. Using the new theory in accompanying paper and replacing the homogeneous outermost crust and oceanic layers in PREM with CRUST1.0 model, we recalculate the equilibrium figures of the Earth’s interior and finally get new values of PMOI and Htheory (≈1/304.7167) whose consistency with Hobs are significantly improved to 0.24%. Furthermore, the asymmetric figures of some interesting boundaries, like inner core boundary, core-mantle boundary, are also given as by-products of this work as these boundaries’ figures are key input for studies of their topographic effect on global rotation and geodynamics, like nutation, normal modes, especially like free core nutation. Numéro de notice : A2019-151 Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-018-1163-x date de publication en ligne : 22/06/2018 En ligne : https://doi.org/10.1007/s00190-018-1163-x Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=92490 [article]

Geodesic equations and their numerical solution in Cartesian coordinates on a triaxial ellipsoid / Georgios Panou in Journal of geodetic science, vol 9 n° 1 (January 2019)  

Public [article]  inJournal of geodetic science > vol 9 n° 1 (January 2019) . - pp 1 - 12 Titre : Geodesic equations and their numerical solution in Cartesian coordinates on a triaxial ellipsoid Type de document : Article/Communication Auteurs : Georgios Panou, Auteur ; Romylos Korakitis, Auteur Année de publication : 2019 Article en page(s) : pp 1 - 12 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie [Termes descripteurs IGN] constante [Termes descripteurs IGN] coordonnées cartésiennes géocentriques [Termes descripteurs IGN] coordonnées ellipsoïdales [Termes descripteurs IGN] problème des valeurs limites [Termes descripteurs IGN] transformation de coordonnées Résumé : (auteur) In this work, the geodesic equations and their numerical solution in Cartesian coordinates on an oblate spheroid, presented by Panou and Korakitis (2017), are generalized on a triaxial ellipsoid. A new exact analytical method and a new numerical method of converting Cartesian to ellipsoidal coordinates of a point on a triaxial ellipsoid are presented. An extensive test set for the coordinate conversion is used, in order to evaluate the performance of the two methods. The direct geodesic problem on a triaxial ellipsoid is described as an initial value problem and is solved numerically in Cartesian coordinates. The solution provides the Cartesian coordinates and the angle between the line of constant λ and the geodesic, at any point along the geodesic. Also, the Liouville constant is computed at any point along the geodesic, allowing to check the precision of the method. An extensive data set of geodesics is used, in order to demonstrate the validity of the numerical method for the geodesic problem. We conclude that a complete, stable and precise solution of the problem is accomplished. Numéro de notice : A2019-407 Thématique : POSITIONNEMENT Nature : Article DOI : 10.1515/jogs-2019-0001 En ligne : https://doi.org/10.1515/jogs-2019-0001 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=93524 [article]

A factor model approach for the joint segmentation with between-series correlation / Xavier Collilieux (17/07/2018)  

Public contenu dans ArXiv / Université Cornell (Etats-Unis) (1991)   Titre : A factor model approach for the joint segmentation with between-series correlation Type de document : Article/Communication Auteurs : Xavier Collilieux , Auteur ; Emilie Lebarbier, Auteur ; Stéphane Robin, Auteur Mention d'édition : v2 Editeur : Ithaca [New York - Etats-Unis] : ArXiv - Université Cornell Année de publication : 17/07/2018 Importance : 27 p. Format : 21 x 30 cm Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie [Termes descripteurs IGN] corrélation [Termes descripteurs IGN] données géodésiques [Termes descripteurs IGN] programmation dynamique [Termes descripteurs IGN] R (langage) [Termes descripteurs IGN] segmentation [Termes descripteurs IGN] série temporelle Résumé : (auteur) We consider the segmentation of set of correlated time-series, the correlation being allowed to take an arbitrary form but being the same at each time-position. We show that encoding the dependency in a factor model enables us to use the dynamic programming algorithm for the inference of the breakpoints, which remains one the most efficient algorithm. We propose a model selection procedure to determine both the number of breakpoints and the number of factors. This proposed method is implemented in the FASeg R package, which is available on the CRAN. We demonstrate the performances of our procedure through simulation experiments and an application to geodesic data is presented. Numéro de notice : P2018-0 Thématique : MATHEMATIQUE/POSITIONNEMENT Nature : Preprint nature-HAL : Préprint DOI : sans date de publication en ligne : 17/07/2018 En ligne : https://arxiv.org/abs/1505.05660 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=91388

Voronoi tessellation on the ellipsoidal earth for vector data / Christos Kastrisios in International journal of geographical information science IJGIS, vol 32 n° 7-8 (July - August 2018)  

Public [article]  inInternational journal of geographical information science IJGIS > vol 32 n° 7-8 (July - August 2018) . - pp 1541 - 1557 Titre : Voronoi tessellation on the ellipsoidal earth for vector data Type de document : Article/Communication Auteurs : Christos Kastrisios, Auteur ; Lysandros Tsoulos, Auteur Année de publication : 2018 Article en page(s) : pp 1541 - 1557 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie [Termes descripteurs IGN] diagramme de Voronoï [Termes descripteurs IGN] données vectorielles [Termes descripteurs IGN] ellipsoïde (géodésie) [Termes descripteurs IGN] entité géographique [Termes descripteurs IGN] frontière maritime [Termes descripteurs IGN] géomètrie algorithmique [Termes descripteurs IGN] Python (langage de programmation) [Termes descripteurs IGN] tessellation [Termes descripteurs IGN] triangulation de Delaunay Résumé : (auteur) Voronoi tessellation, and its dual the Delaunay triangulation, provide a cohesive framework for the study and interpretation of phenomena of geographical space in two and three dimensions. The planar and spherical solutions introduce errors in the positional accuracy of both Voronoi vertices and Voronoi edges due to errors in distance computations and the path connecting two locations with planar lines or great circle arcs instead of geodesics. For most geospatial applications the introduction of the above errors is insignificant or tolerable. However, for applications where the accuracy is of utmost importance, the ellipsoidal model of the Earth must be used. Characteristically, the introduction of any positional error in the delimitation of maritime zones and boundaries results in increased maritime space for one state at the expense of another. This is a situation that may, among others, have a serious impact on the financial activities and the relations of the states concerned. In the context of previous work on maritime delimitation we show that the Voronoi diagram constitutes the ideal solution for the development of an automated methodology addressing the problem in its entirety. Due to lack of a vector methodology for the generation of Voronoi diagram on the ellipsoid, the aforementioned solution was constrained by the accuracy of existing approaches. In order to fill this gap, in this paper we deal with the inherent attributes of the ellipsoidal model of the Earth, e.g. the fact that geodesics are open lines, and we elaborate on a methodology for the generation of the Voronoi diagram on the ellipsoid for a set of points in vector format. The resulting Voronoi diagram consists of vertices with positional accuracy that is only bounded by the user needs and edges that are comprised of geodesics densified with vertices equidistant to their generators. Finally, we present the implementation of the proposed algorithm in the Python programming language and the results of two case studies, one on the formation of closest service areas and one on maritime boundaries delimitation, with the positional accuracy set to 1 cm. Numéro de notice : A2018-282 Thématique : POSITIONNEMENT Nature : Article DOI : 10.1080/13658816.2018.1434890 date de publication en ligne : 15/02/2018 En ligne : https://doi.org/10.1080/13658816.2018.1434890 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=90366 [article]

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