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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]

The Iranian height datum offset from the GBVP solution and spirit-leveling/gravimetry data / Amir Ebadi in Journal of geodesy, vol 93 n° 8 (August 2019)  

Public [article]  inJournal of geodesy > vol 93 n° 8 (August 2019) . - pp 1207 - 1225 Titre : The Iranian height datum offset from the GBVP solution and spirit-leveling/gravimetry data Type de document : Article/Communication Auteurs : Amir Ebadi, Auteur ; Alireza A. Ardalan, Auteur ; Roohollah Karimi, Auteur Année de publication : 2019 Article en page(s) : pp 1207 - 1225 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] analyse de variance [Termes IGN] champ de pesanteur terrestre [Termes IGN] compensation par moindres carrés [Termes IGN] géoïde terrestre [Termes IGN] Iran [Termes IGN] levé gravimétrique [Termes IGN] modèle de géopotentiel [Termes IGN] potentiel de pesanteur terrestre [Termes IGN] problème des valeurs limites [Termes IGN] réseau altimétrique local [Termes IGN] réseau altimétrique national Résumé : (auteur) The gravity potential of the zero point of the Iranian height datum (IRHD) is determined as well as the IRHD offset from a global geoid. For this purpose, the geodetic boundary value problem (GBVP) solution based on the remove–compute–restore (RCR) technique is used. In the RCR technique, a global geopotential model (GGM) is required as a reference to remove and restore the long wavelengths of the gravity field. Since the GGMs do not have adequate accuracy over Iran, the IRHD offset is not precisely estimated by the GBVP solution. In this study, aiming to improve the latter, a combination solution based on the GBVP approach and spirit-leveling/gravimetry (LG) data, called the GBVP_LG solution, is proposed. To obtain the GBVP_LG solution, gravity potential obtained from the GBVP solution and the gravity potential differences derived from the LG data are used as two types of observations in a least-squares adjustment. The proper relative weight matrices are determined using the variance component estimation method. To evaluate the proposed method, the gravity potential differences between the start and end points of several check-lines in the leveling network derived from the GBVP and GBVP_LG solutions are compared with those of the LG data. The results show that the dependency of the GBVP_LG solution on the reference model used is much less than that of the GBVP solution. In addition, the results indicate that the GBVP_LG solution has a 42% improvement with respect to the GBVP solution in terms of root-mean-square error. As a result of the GBVP_LG solution, the gravity potential of the IRHD zero point is estimated equal to WIRHD0=62,636,855.89±0.16m2/s2. Therefore, the IRHD offset with respect to the geoid defined by W0=62,636,853.4m2/s2 is obtained equal to −25.4±1.6cm, which means that the IRHD is 25.4 cm below the geoid. Numéro de notice : A2019-385 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-019-01237-x Date de publication en ligne : 12/02/2019 En ligne : https://doi.org/10.1007/s00190-019-01237-x Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=93464 [article]

Error propagation for the Molodensky G1 term / Jack C. McCubbine in Journal of geodesy, vol 93 n°6 (June 2019)  

Public [article]  inJournal of geodesy > vol 93 n°6 (June 2019) . - pp 889 - 898 Titre : Error propagation for the Molodensky G1 term Type de document : Article/Communication Auteurs : Jack C. McCubbine, Auteur ; Will E. Featherstone, Auteur ; Nicholas J. Brown, Auteur Année de publication : 2019 Article en page(s) : pp 889 - 898 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] anomalie de pesanteur [Termes IGN] Australie [Termes IGN] géoïde gravimétrique [Termes IGN] géoïde local [Termes IGN] hauteur ellipsoïdale [Termes IGN] incertitude de position [Termes IGN] intégrale de Stokes [Termes IGN] modèle numérique de surface [Termes IGN] problème des valeurs limites [Termes IGN] propagation d'erreur [Termes IGN] quasi-géoïde [Termes IGN] transformation de coordonnées Résumé : (auteur) Molodensky G terms are used in the computation of the quasigeoid. We derive error propagation formulas that take into account uncertainties in both the free air gravity anomaly and a digital elevation model. These are applied to generate G1 terms and their errors on a 1″ × 1″ grid over Australia. We use these to produce Molodensky gravity anomaly and accompanying uncertainty grids. These uncertainties have average value of 2 mGal with maximum of 54 mGal. We further calculate a gravimetric quasigeoid model by the remove–compute–restore technique. These Molodensky gravity anomaly uncertainties lead to quasigeoid uncertainties with a mean of 4 mm and maximum of 80 mm when propagated through a deterministically modified Stokes’s integral over an integration cap radius of 0.5°. Numéro de notice : A2019-351 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE/POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-018-1211-6 Date de publication en ligne : 09/11/2018 En ligne : https://doi.org/10.1007/s00190-018-1211-6 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=93395 [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 IGN] constante [Termes IGN] coordonnées cartésiennes géocentriques [Termes IGN] coordonnées ellipsoïdales [Termes IGN] problème des valeurs limites [Termes 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 Affiliation des auteurs : non IGN 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]

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]

Numerical solution to the oblique derivative boundary value problem on non-uniform grids above the Earth topography / Matej Medl’a in Journal of geodesy, vol 92 n° 1 (January 2018)  

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Geodesic equations and their numerical solutions in geodetic and cartesian coordinates on an oblate spheroid / Georgios Panou in Journal of geodetic science, vol 7 n° 1 (February 2017)  

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Gravity forward modeling with a tesseroid-based rock-water-ice approach / Thomas Grombein (2017)  

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Global height system unification with GOCE: a simulation study on the indirect bias term in the GBVP approach / C. Gerlach in Journal of geodesy, vol 87 n° 1 (January 2013)  

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The combination of GNSS-levelling data and gravimetric (quasi-) geoid heights in the presence of noise / R. Klees in Journal of geodesy, vol 84 n° 12 (December 2010)  

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Can mean values of Helmert's gravity anomalies be continued downward directly? / Petr Vanicek in Geomatica, vol 64 n° 2 (June 2010)  

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A bias-free geodetic boundary value problem approach to height datum unification / Alireza A. Ardalan in Journal of geodesy, vol 84 n° 2 (February 2010)  

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Finite element method for solving geodetic boundary value problems / Z. Faskova in Journal of geodesy, vol 84 n° 2 (February 2010)  

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Détermination du géoïde gravimétrique au nord de l'Algérie : méthodes de Stokes-Helmert / N. Zekkour in Bulletin des sciences géographiques, n° 24 (Septembre 2009)

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Singularity free formulations of the geodetic boundary value problem in gravity-space / G. Austen in Journal of geodesy, vol 83 n° 7 (July 2009)  

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