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Vertical and horizontal spheroidal boundary-value problems / Michal Šprlák in Journal of geodesy, vol 92 n° 7 (July 2018)  

Public [article]  inJournal of geodesy > vol 92 n° 7 (July 2018) . - pp 811 - 826 Titre : Vertical and horizontal spheroidal boundary-value problems Type de document : Article/Communication Auteurs : Michal Šprlák, Auteur ; Natthachet Tangdamrongsub, Auteur Année de publication : 2018 Article en page(s) : pp 811 - 826 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes descripteurs IGN] analyse harmonique [Termes descripteurs IGN] gradient de gravitation [Termes descripteurs IGN] problème des valeurs limites [Termes descripteurs IGN] sphèroïde Résumé : (Auteur) Vertical and horizontal spheroidal boundary-value problems (BVPs), i.e., determination of the external gravitational potential from the components of the gravitational gradient on the spheroid, are discussed in this article. The gravitational gradient is decomposed into the series of the vertical and horizontal vector spheroidal harmonics, before being orthogonalized in a weighted sense by two different approaches. The vertical and horizontal spheroidal BVPs are then formulated and solved in the spectral and spatial domains. Both orthogonalization methods provide the same analytical solutions for the vertical spheroidal BVP, and give distinct, but equivalent, analytical solutions for the horizontal spheroidal BVP. A closed-loop simulation is performed to test the correctness of the analytical solutions, and we investigate analytical properties of the sub-integral kernels. The systematic treatment of the spheroidal BVPs and the resulting mathematical equations extend the theoretical apparatus of geodesy and of the potential theory. Numéro de notice : A2018-455 Thématique : MATHEMATIQUE/POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-017-1096-9 date de publication en ligne : 07/12/2017 En ligne : https://doi.org/10.1007/s00190-017-1096-9 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=91046 [article]

Alternative validation method of satellite gradiometric data by integral transform of satellite altimetry data / Michal Šprlák in Journal of geodesy, vol 89 n° 8 (August 2015)  

Public [article]  inJournal of geodesy > vol 89 n° 8 (August 2015) . - pp 757 - 773 Titre : Alternative validation method of satellite gradiometric data by integral transform of satellite altimetry data Type de document : Article/Communication Auteurs : Michal Šprlák, Auteur ; Eliška Hamáčková, Auteur ; Pavel Novák, Auteur Année de publication : 2015 Article en page(s) : pp 757 - 773 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes descripteurs IGN] altimétrie satellitaire par radar [Termes descripteurs IGN] champ de gravitation [Termes descripteurs IGN] données GOCE [Termes descripteurs IGN] équation intégrale [Termes descripteurs IGN] gradient de gravitation [Termes descripteurs IGN] gradiométrie [Termes descripteurs IGN] potentiel de pesanteur terrestre Résumé : (auteur) Integral transforms of the disturbing gravitational potential derived from satellite altimetry onto satellite gradiometric data are formulated, investigated and applied in this article. First, corresponding differential operators, that relate the disturbing gravitational potential to the six components of the disturbing gradiometric tensor in the spherical local north-oriented frame, are applied to the spherical Abel-Poisson integral equation. This yields six new integral equations for which respective kernel functions are given in both spectral and spatial forms. Second, truncation error formulas for each of the integral transforms are provided in the spectral form. Also expressions for the corresponding truncation error coefficients are derived. Third, practical estimators for evaluation of the disturbing gravitational gradients are formulated, and their correctness and expected accuracy are investigated. Finally, the practical estimators are applied for validation of a sample of the gradiometric data provided by the GOCE satellite mission. Obtained results demonstrate applicability of the new apparatus as an alternative validation method of the satellite gravitational gradients. Numéro de notice : A2015-375 Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern En ligne : http://link.springer.com/article/10.1007/s00190-015-0813-5/fulltext.html Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=76853 [article]