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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)  

Public [article]  inJournal of geodesy > vol 92 n° 1 (January 2018) . - pp 1 - 19 Titre : Numerical solution to the oblique derivative boundary value problem on non-uniform grids above the Earth topography Type de document : Article/Communication Auteurs : Matej Medl’a, Auteur ; Karol Mikula, Auteur ; Robert Cunderlik, Auteur ; Marek Macák, Auteur Année de publication : 2018 Article en page(s) : pp 1 - 19 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] champ de pesanteur local [Termes IGN] discrétisation [Termes IGN] équation de Laplace [Termes IGN] méthode des éléments finis [Termes IGN] problème des valeurs limites Résumé : (Auteur) The paper presents a numerical solution of the oblique derivative boundary value problem on and above the Earth’s topography using the finite volume method (FVM). It introduces a novel method for constructing non-uniform hexahedron 3D grids above the Earth’s surface. It is based on an evolution of a surface, which approximates the Earth’s topography, by mean curvature. To obtain optimal shapes of non-uniform 3D grid, the proposed evolution is accompanied by a tangential redistribution of grid nodes. Afterwards, the Laplace equation is discretized using FVM developed for such a non-uniform grid. The oblique derivative boundary condition is treated as a stationary advection equation, and we derive a new upwind type discretization suitable for non-uniform 3D grids. The discretization of the Laplace equation together with the discretization of the oblique derivative boundary condition leads to a linear system of equations. The solution of this system gives the disturbing potential in the whole computational domain including the Earth’s surface. Numerical experiments aim to show properties and demonstrate efficiency of the developed FVM approach. The first experiments study an experimental order of convergence of the method. Then, a reconstruction of the harmonic function on the Earth’s topography, which is generated from the EGM2008 or EIGEN-6C4 global geopotential model, is presented. The obtained FVM solutions show that refining of the computational grid leads to more precise results. The last experiment deals with local gravity field modelling in Slovakia using terrestrial gravity data. The GNSS-levelling test shows accuracy of the obtained local quasigeoid model. Numéro de notice : A2018-011 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-017-1040-z Date de publication en ligne : 30/05/2017 En ligne : https://doi.org/10.1007/s00190-017-1040-z Format de la ressource électronique : URL Article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=89054 [article]

A conventional value for the geoid reference potential W0 / L. Sánchez in Journal of geodesy, vol 90 n° 9 (September 2016)  

Public [article]  inJournal of geodesy > vol 90 n° 9 (September 2016) . - pp 815 - 835 Titre : A conventional value for the geoid reference potential W0 Type de document : Article/Communication Auteurs : L. Sánchez, Auteur ; Robert Cunderlik, Auteur ; N. Dayoub, Auteur ; et al., Auteur Année de publication : 2016 Article en page(s) : pp 815 - 835 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] champ de pesanteur terrestre [Termes IGN] données GOCE [Termes IGN] données GRACE [Termes IGN] force de gravitation [Termes IGN] géoïde terrestre [Termes IGN] potentiel de pesanteur terrestre [Termes IGN] surface de la mer [Termes IGN] télémétrie laser sur satellite Résumé : (auteur) W0 is defined as the potential value of a particular level surface of the Earth’s gravity field called the geoid. Since the most accepted definition of the geoid is understood to be the equipotential surface that coincides with the worldwide mean ocean surface, a usual approximation of W0 is the averaged potential value WS at the mean sea surface. In this way, the value of W0 depends not only on the Earth’s gravity field modelling, but also on the conventions defining the mean sea surface. W0 computations performed since 2005 demonstrate that current published estimations differ by up to −2.6 m2 s−2 (corresponding to a level difference of about 27 cm), which could be caused by the differences in the treatment of the input data. The main objective of this study is to perform a new W0 estimation relying on the newest gravity field and sea surface models and applying standardised data and procedures. This also includes a detailed description of the processing procedure to ensure the reproducibility of the results. The following aspects are analysed in this paper: (1) sensitivity of the W0 estimation to the Earth’s gravity field model (especially omission and commission errors and time-dependent Earth’s gravity field changes); (2) sensitivity of the W0 estimation to the mean sea surface model (e.g., geographical coverage, time-dependent sea surface variations, accuracy of the mean sea surface heights); (3) dependence of the W0 empirical estimation on the tide system; and (4) weighted computation of the W0 value based on the input data quality. Main conclusions indicate that the satellite-only component (n=200) of a static (quasi-stationary) global gravity model is sufficient for the computation of W0. This model should, however, be based on a combination of, at least, satellite laser ranging (SLR), GRACE and GOCE data. The mean sea surface modelling should be based on mean sea surface heights referring to a certain epoch and derived from a standardised multi-mission cross-calibration of several satellite altimeters. We suggest that the uncertainties caused by geographically correlated errors, including shallow waters in coastal areas and sea water ice content at polar regions should be considered in the computation of W0 by means of a weighed adjustment using the inverse of the input data variances as a weighting factor. This weighting factor should also include the improvement provided by SLR, GRACE and GOCE to the gravity field modelling. As a reference parameter, W0 should be time-independent (i.e., quasi-stationary) and it should remain fixed for a long-term period (e.g., 20 years). However, it should have a clear relationship with the mean sea surface level (as this is the convention for the realisation of the geoid). According to this, a suitable recommendation is to adopt a potential value obtained for a certain epoch as the reference value W0 and to monitor the changes of the mean potential value at the sea surface WS. When large differences appear between W0 and WS (e.g., >±2 m2 s−2), the adopted W0 may be replaced by an updated (best estimate) value. In this paper, the potential value obtained for the epoch 2010.0 (62,636,853.4 m2 s−2) is recommended as the present best estimate for the W0 value. It differs −2.6 m2 s−2 from the so-called IERS W0 value (62,636,856.0 m2 s−2), which corresponds to the best estimate available in 1998. Numéro de notice : A2016-655 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-016-0913-x En ligne : http://dx.doi.org/10.1007/s00190-016-0913-x Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=81857 [article]

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

Public [article]  inJournal of geodesy > vol 84 n° 2 (February 2010) . - pp 135 - 144 Titre : Finite element method for solving geodetic boundary value problems Type de document : Article/Communication Auteurs : Z. Faskova, Auteur ; Robert Cunderlik, Auteur ; Karol Mikula, Auteur Année de publication : 2010 Article en page(s) : pp 135 - 144 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] champ de pesanteur terrestre [Termes IGN] Earth Gravity Model 2008 [Termes IGN] géoïde [Termes IGN] méthode des éléments finis [Termes IGN] problème de Dirichlet [Termes IGN] problème des valeurs limites Résumé : (Auteur) The goal of this paper is to present the finite element scheme for solving the Earth potential problems in 3D domains above the Earth surface. To that goal we formulate the boundary-value problem (BVP) consisting of the Laplace equation outside the Earth accompanied by the Neumann as well as the Dirichlet boundary conditions (BC). The 3D computational domain consists of the bottom boundary in the form of a spherical approximation or real triangulation of the Earth’s surface on which surface gravity disturbances are given. We introduce additional upper (spherical) and side (planar and conical) boundaries where the Dirichlet BC is given. Solution of such elliptic BVP is understood in a weak sense, it always exists and is unique and can be efficiently found by the finite element method (FEM). We briefly present derivation of FEM for such type of problems including main discretization ideas. This method leads to a solution of the sparse symmetric linear systems which give the Earth’s potential solution in every discrete node of the 3D computational domain. In this point our method differs from other numerical approaches, e.g. boundary element method (BEM) where the potential is sought on a hypersurface only. We apply and test FEM in various situations. First, we compare the FEM solution with the known exact solution in case of homogeneous sphere. Then, we solve the geodetic BVP in continental scale using the DNSC08 data. We compare the results with the EGM2008 geopotential model. Finally, we study the precision of our solution by the GPS/levelling test in Slovakia where we use terrestrial gravimetric measurements as input data. All tests show qualitative and quantitative agreement with the given solutions. Copyright Springer Numéro de notice : A2010-108 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-009-0349-7 Date de publication en ligne : 13/10/2009 En ligne : https://doi.org/10.1007/s00190-009-0349-7 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=30304 [article]

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