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On determination of the geoid from measured gradients of the Earth's gravity field potential / Pavel Novák in Earth-Science Reviews, vol 221 (October 2021)  

Public [article]  inEarth-Science Reviews > vol 221 (October 2021) . - n° 103773 Titre : On determination of the geoid from measured gradients of the Earth's gravity field potential Type de document : Article/Communication Auteurs : Pavel Novák, Auteur ; Michal Šprlák, Auteur ; Martin Pitoňák, Auteur Année de publication : 2021 Article en page(s) : n° 103773 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] champ de pesanteur terrestre [Termes IGN] géoïde terrestre [Termes IGN] gradient de gravitation [Termes IGN] modèle mathématique [Termes IGN] modèle stochastique [Termes IGN] précision centimétrique [Termes IGN] problème des valeurs limites Résumé : (auteur) The geoid is an equipotential surface of the static Earth's gravity field which plays a fundamental role in definition of physical heights related to the mean sea level (orthometric heights) in geodesy and which represents a reference surface in many geoscientific studies. Its determination with the cm-level accuracy or better, in particular over dry land, belongs to major tasks of modern geodesy. Traditional data and underlined theory have significantly been affected in recent years by rapid advances in observation techniques. This study reviews gradients of the disturbing gravity potential, both currently available and foreseen, and systematically discusses mathematical models for geoid determination based on gradient data. Fundamentals required for geoid definition and its estimation from measured potential gradients are shortly reviewed at the beginning of the text. Then particular mathematical models based on solutions to boundary-value problems of the potential theory, which include both integral transforms and integral equations, are formulated. Properties of respective integral kernel functions are demonstrated and discussed. With the new mathematical models introduced, new research topics are opened which must be resolved in order to allow for their full-fledged applicability in geoid modelling. Stochastic modelling is also discussed which estimates gradient spatial resolution and accuracy required for geoid modelling with the cm-level accuracy. Results of stochastic modelling suggest that the cm-geoid can be estimated using available gradient data if related problems, namely reduction of gradient data for gravitational effects of all masses outside the geoid and their downward continuation, are solved at the same level of accuracy. Numéro de notice : A2021-944 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article DOI : 10.1016/j.earscirev.2021.103773 Date de publication en ligne : 14/09/2021 En ligne : https://doi.org/10.1016/j.earscirev.2021.103773 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=99756 [article]

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 IGN] analyse harmonique [Termes IGN] gradient de gravitation [Termes IGN] problème des valeurs limites [Termes 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 Affiliation des auteurs : non IGN 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 IGN] altimétrie satellitaire par radar [Termes IGN] champ de gravitation [Termes IGN] données GOCE [Termes IGN] équation intégrale [Termes IGN] gradient de gravitation [Termes IGN] gradiométrie [Termes 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 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-015-0813-5 Date de publication en ligne : 24/04/2015 En ligne : http://dx.doi.org/10.1007/s00190-015-0813-5 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=76853 [article]