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Construction of spherical harmonic series for the potential derivatives of arbitrary orders in the geocentric Earth-fixed reference frame / M. Petrovskaya in Journal of geodesy, vol 84 n° 3 (March 2010)  

Public [article]  inJournal of geodesy > vol 84 n° 3 (March 2010) . - pp 165 - 178 Titre : Construction of spherical harmonic series for the potential derivatives of arbitrary orders in the geocentric Earth-fixed reference frame Type de document : Article/Communication Auteurs : M. Petrovskaya, Auteur ; A. Vershkov, Auteur Année de publication : 2010 Article en page(s) : pp 165 - 178 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] champ de pesanteur local [Termes IGN] coordonnées cartésiennes géocentriques [Termes IGN] déviation de la verticale [Termes IGN] Earth Gravity Model 2008 [Termes IGN] harmonique sphérique [Termes IGN] repère de référence [Termes IGN] trièdre local [Termes IGN] variance Résumé : (Auteur) The derivatives of the Earth gravitational potential are considered in the global Cartesian Earth-fixed reference frame. Spherical harmonic series are constructed for the potential derivatives of the first and second orders on the basis of a general expression of Cunningham (Celest Mech 2:207–216, 1970) for arbitrary order derivatives of a spherical harmonic. A common structure of the series for the potential and its first- and second-order derivatives allows to develop a general procedure for constructing similar series for the potential derivatives of arbitrary orders. The coefficients of the derivatives are defined by means of recurrence relations in which a coefficient of a certain order derivative is a linear function of two coefficients of a preceding order derivative. The coefficients of the second-order derivatives are also presented as explicit functions of three coefficients of the potential. On the basis of the geopotential model EGM2008, the spherical harmonic coefficients are calculated for the first-, second-, and some third-order derivatives of the disturbing potential T, representing the full potential V, after eliminating from it the zero- and first-degree harmonics. The coefficients of two lowest degrees in the series for the derivatives of T are presented. The corresponding degree variances are estimated. The obtained results can be applied for solving various problems of satellite geodesy and celestial mechanics. Copyright Springer Numéro de notice : A2010-155 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-009-0353-y Date de publication en ligne : 10/11/2009 En ligne : https://doi.org/10.1007/s00190-009-0353-y Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=30350 [article]

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Prediction of vertical deflections from high-degree spherical harmonic synthesis and residual terrain model data / C. Hirt in Journal of geodesy, vol 84 n° 3 (March 2010)  

Public [article]  inJournal of geodesy > vol 84 n° 3 (March 2010) . - pp 179 - 190 Titre : Prediction of vertical deflections from high-degree spherical harmonic synthesis and residual terrain model data Type de document : Article/Communication Auteurs : C. Hirt, Auteur Année de publication : 2010 Article en page(s) : pp 179 - 190 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] Allemagne [Termes IGN] Alpes centrales [Termes IGN] champ de pesanteur terrestre [Termes IGN] déviation de la verticale [Termes IGN] Earth Gravity Model 2008 [Termes IGN] harmonique sphérique [Termes IGN] MNS SRTM [Termes IGN] modèle de géopotentiel [Termes IGN] modèle de géopotentiel local [Termes IGN] modèle numérique de terrain [Termes IGN] Suisse [Termes IGN] valeur efficace Résumé : (Auteur) This study demonstrates that in mountainous areas the use of residual terrain model (RTM) data significantly improves the accuracy of vertical deflections obtained from high-degree spherical harmonic synthesis. The new Earth gravitational model EGM2008 is used to compute vertical deflections up to a spherical harmonic degree of 2,160. RTM data can be constructed as difference between high-resolution Shuttle Radar Topography Mission (SRTM) elevation data and the terrain model DTM2006.0 (a spherical harmonic terrain model that complements EGM2008) providing the long-wavelength reference surface. Because these RTM elevations imply most of the gravity field signal beyond spherical harmonic degree of 2,160, they can be used to augment EGM2008 vertical deflection predictions in the very high spherical harmonic degrees. In two mountainous test areas—the German and the Swiss Alps—the combined use of EGM2008 and RTM data was successfully tested at 223 stations with high-precision astrogeodetic vertical deflections from recent zenith camera observations (accuracy of about 0.1 arc seconds) available. The comparison of EGM2008 vertical deflections with the ground-truth astrogeodetic observations shows root mean square (RMS) values (from differences) of 3.5 arc seconds for È and 3.2 arc seconds for È , respectively. Using a combination of EGM2008 and RTM data for the prediction of vertical deflections considerably reduces the RMS values to the level of 0.8 arc seconds for both vertical deflection components, which is a significant improvement of about 75%. Density anomalies of the real topography with respect to the residual model topography are one factor limiting the accuracy of the approach. The proposed technique for vertical deflection predictions is based on three publicly available data sets: (1) EGM2008, (2) DTM2006.0 and (3) SRTM elevation data. This allows replication of the approach for improving the accuracy of EGM2008 vertical deflection predictions in regions with a rough topography or for improved validation of EGM2008 and future high-degree spherical harmonic models by means of independent ground truth data. Numéro de notice : A2010-156 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-009-0354-x Date de publication en ligne : 12/11/2009 En ligne : https://doi.org/10.1007/s00190-009-0354-x Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=30351 [article]

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