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A line integral approach for the computation of the potential harmonic coefficients of a constant density polyhedron / Olivier Jamet in Journal of geodesy, Vol 94 n°3 (March 2020)  

Public [article]  inJournal of geodesy > Vol 94 n°3 (March 2020) Titre : A line integral approach for the computation of the potential harmonic coefficients of a constant density polyhedron Type de document : Article/Communication Auteurs : Olivier Jamet , Auteur ; Dimitrios Tsoulis, Auteur Année de publication : 2020 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes descripteurs IGN] analyse harmonique [Termes descripteurs IGN] champ de pesanteur terrestre [Termes descripteurs IGN] harmonique sphérique [Termes descripteurs IGN] implémentation (informatique) [Termes descripteurs IGN] polyèdre [Termes descripteurs IGN] potentiel de pesanteur terrestre Résumé : (auteur) A novel approach for the computation of the spherical harmonic coefficients of the gravity field of a constant density polyhedron is presented. The proposed method is based on the expression of these coefficients as the volume integral of solid harmonics. It is well known that the divergence theorem leads to an expression of these volume integrals as surface integrals. We show that these surface integrals can be expressed as the sum of line integrals along the edges of the polyhedron. In contrast to previous approaches, the values of the spherical harmonic coefficients at a given degree and order result directly from the computation of the line integrals. The performed numerical implementation revealed the stability of the proposed algorithm up to degree 360 for a prismatic test source. Numéro de notice : A2020-154 Thématique : MATHEMATIQUE/POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-020-01358-8 date de publication en ligne : 17/02/2020 En ligne : https://doi.org/10.1007/s00190-020-01358-8 Format de la ressource électronique : url article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=94803 [article]

Toward a global horizontal and vertical elastic load deformation model derived from GRACE and GNSS station position time series / Kristel Chanard in Journal of geophysical research : Solid Earth, vol 123 n° 4 (April 2018)  

Public [article]  inJournal of geophysical research : Solid Earth > vol 123 n° 4 (April 2018) . - pp Titre : Toward a global horizontal and vertical elastic load deformation model derived from GRACE and GNSS station position time series Type de document : Article/Communication Auteurs : Kristel Chanard , Auteur ; Luce Fleitout, Auteur ; Eric Calais, Auteur ; Paul Rebischung , Auteur ; Jean-Philippe Avouac, Auteur Année de publication : 2018 Article en page(s) : pp Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes descripteurs IGN] coordonnées GNSS [Termes descripteurs IGN] déformation horizontale de la croute terrestre [Termes descripteurs IGN] déformation verticale de la croute terrestre [Termes descripteurs IGN] données GRACE [Termes descripteurs IGN] Earth Gravity Model 2008 [Termes descripteurs IGN] erreur systématique [Termes descripteurs IGN] harmonique sphérique [Termes descripteurs IGN] modèle de déformation tectonique [Termes descripteurs IGN] mouvement du géocentre [Termes descripteurs IGN] série temporelle Résumé : (Auteur) We model surface displacements induced by variations in continental water, atmospheric pressure, and non‐tidal oceanic loading, derived from the Gravity and Recovery Climate Experiment (GRACE) for spherical harmonic degrees two and higher. As they are not observable by GRACE, we use at first the degree‐1 spherical harmonic coefficients from (Swenson2008estimating). We compare the predicted displacements with the position time series of 689 globally distributed continuous Global Navigation Satellite System (GNSS) stations. While GNSS vertical displacements are well explained by the model at a global scale, horizontal displacements are systematically underpredicted and out‐of‐phase with GNSS station position time series. We then re‐estimate the degree‐1 deformation field from a comparison between our GRACE‐derived model, with no a priori degree‐1 loads, and the GNSS observations. We show that this approach reconciles GRACE‐derived loading displacements and GNSS station position time series at a global scale, particularly in the horizontal components. Assuming that they reflect surface loading deformation only, our degree‐1 estimates can be translated into geocenter motion time series. We also address and assess the impact of systematic errors in GNSS station position time series at the Global Positioning System (GPS) draconitic period and its harmonics on the comparison between GNSS and GRACE‐derived annual displacements. Our results confirm that surface mass redistributions observed by GRACE, combined with an elastic spherical and layered Earth model, can be used to provide first order corrections for loading deformation observed in both horizontal and vertical components of GNSS station position time series. Numéro de notice : A2018-055 Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1002/2017JB015245 date de publication en ligne : 21/02/2018 En ligne : https://doi.org/10.1002/2017JB015245 Format de la ressource électronique : URL Article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=89382 [article]

Transformation between surface spherical harmonic expansion of arbitrary high degree and order and double Fourier series on sphere / Toshio Fukushima in Journal of geodesy, vol 92 n° 2 (February 2018)  

Public [article]  inJournal of geodesy > vol 92 n° 2 (February 2018) . - pp 123 - 130 Titre : Transformation between surface spherical harmonic expansion of arbitrary high degree and order and double Fourier series on sphere Type de document : Article/Communication Auteurs : Toshio Fukushima, Auteur Année de publication : 2018 Article en page(s) : pp 123 - 130 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie [Termes descripteurs IGN] harmonique sphérique [Termes descripteurs IGN] série de Fourier [Termes descripteurs IGN] transformation géométrique [Termes descripteurs IGN] transformation inverse Résumé : (Auteur) In order to accelerate the spherical harmonic synthesis and/or analysis of arbitrary function on the unit sphere, we developed a pair of procedures to transform between a truncated spherical harmonic expansion and the corresponding two-dimensional Fourier series. First, we obtained an analytic expression of the sine/cosine series coefficient of the 4π fully normalized associated Legendre function in terms of the rectangle values of the Wigner d function. Then, we elaborated the existing method to transform the coefficients of the surface spherical harmonic expansion to those of the double Fourier series so as to be capable with arbitrary high degree and order. Next, we created a new method to transform inversely a given double Fourier series to the corresponding surface spherical harmonic expansion. The key of the new method is a couple of new recurrence formulas to compute the inverse transformation coefficients: a decreasing-order, fixed-degree, and fixed-wavenumber three-term formula for general terms, and an increasing-degree-and-order and fixed-wavenumber two-term formula for diagonal terms. Meanwhile, the two seed values are analytically prepared. Both of the forward and inverse transformation procedures are confirmed to be sufficiently accurate and applicable to an extremely high degree/order/wavenumber as 230≈109. The developed procedures will be useful not only in the synthesis and analysis of the spherical harmonic expansion of arbitrary high degree and order, but also in the evaluation of the derivatives and integrals of the spherical harmonic expansion. Numéro de notice : A2018-057 Thématique : MATHEMATIQUE/POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-017-1049-3 En ligne : https://doi.org/10.1007/s00190-017-1049-3 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=89390 [article]

Contribution of mass density heterogeneities to the quasigeoid-to-geoid separation / Robert Tenzer in Journal of geodesy, vol 90 n° 1 (January 2016)  

Public [article]  inJournal of geodesy > vol 90 n° 1 (January 2016) . - pp 65-80 Titre : Contribution of mass density heterogeneities to the quasigeoid-to-geoid separation Type de document : Article/Communication Auteurs : Robert Tenzer, Auteur ; Christian Hirt, Auteur ; Pavel Novák, Auteur ; et al., Auteur Année de publication : 2016 Article en page(s) : pp 65-80 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes descripteurs IGN] anomalie de pesanteur [Termes descripteurs IGN] champ de pesanteur terrestre [Termes descripteurs IGN] harmonique sphérique [Termes descripteurs IGN] masse de la Terre [Termes descripteurs IGN] modèle de densité [Termes descripteurs IGN] quasi-géoïde [Termes descripteurs IGN] topographie Résumé : (auteur) The geoid-to-quasigeoid separation is often computed only approximately as a function of the simple planar Bouguer gravity anomaly and the height of the computation point while disregarding the contributions of terrain geometry and anomalous topographic density as well as the sub-geoid masses. In this study we demonstrate that these contributions are significant and, therefore, should be taken into consideration when investigating the relation between the normal and orthometric heights particularly in the mountainous, polar and geologically complex regions. These contributions are evaluated by applying the spectral expressions for gravimetric forward modelling and using the EIGEN-6C4 gravity model, the Earth2014 datasets of terrain, ice thickness and inland bathymetry and the CRUST1.0 sediment and (consolidated) crustal density data. Since the global crustal density models currently available (e.g. CRUST1.0) have a limited accuracy and resolution, the comparison of individual density contributions is—for consistency—realized with a limited spectral resolution up to a spherical harmonic degree 360 (or 180). The results reveal that the topographic contribution globally varies between −0.33 and 0.57 m, with maxima in Himalaya and Tibet. The contribution of ice considerably modifies the geoid-to-quasigeoid separation over large parts of Antarctica and Greenland, where it reaches ∼0.2 m. The contributions of sediments and bedrock are less pronounced, with the values typically varying only within a few centimetres. These results, however, have still possibly large uncertainties due to the lack of information on the actual sediment and bedrock density. The contribution of lakes is mostly negligible; its maxima over the Laurentian Great Lakes and the Baikal Lake reach only several millimetres. The contribution of the sub-geoid masses is significant. It is everywhere negative and reaches extreme values of −4.43 m. According to our estimates, the geoid-to-quasigeoid separation globally varies within −4.19 and 0.26 m while the corresponding values computed according to a classical definition are only negative and reach extreme values of −3.5 m. A comparison of these results reveals that inaccuracies caused by disregarding the terrain geometry and mass density heterogeneities distributed within the topography and below the geoid surface can reach ±2 m or more in the mountainous regions. Numéro de notice : A2016-019 Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern En ligne : http://link.springer.com/article/10.1007/s00190-015-0858-5/fulltext.html Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=79466 [article]

A surface spherical harmonic expansion of gravity anomalies on the ellipsoid / S.J. Claessens in Journal of geodesy, vol 89 n° 10 (october 2015)  

Public [article]  inJournal of geodesy > vol 89 n° 10 (october 2015) . - pp 1035 - 1048 Titre : A surface spherical harmonic expansion of gravity anomalies on the ellipsoid Type de document : Article/Communication Auteurs : S.J. Claessens, Auteur ; C. Hirt, Auteur Année de publication : 2015 Article en page(s) : pp 1035 - 1048 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes descripteurs IGN] anomalie de pesanteur [Termes descripteurs IGN] ellipsoïde de référence [Termes descripteurs IGN] ellipsoïde GRS 1980 [Termes descripteurs IGN] harmonique sphérique [Termes descripteurs IGN] TRANSFORMATION Résumé : (auteur) A surface spherical harmonic expansion of gravity anomalies with respect to a geodetic reference ellipsoid can be used to model the global gravity field and reveal its spectral properties. In this paper, a direct and rigorous transformation between solid spherical harmonic coefficients of the Earth’s disturbing potential and surface spherical harmonic coefficients of gravity anomalies in ellipsoidal approximation with respect to a reference ellipsoid is derived. This transformation cannot rigorously be achieved by the Hotine–Jekeli transformation between spherical and ellipsoidal harmonic coefficients. The method derived here is used to create a surface spherical harmonic model of gravity anomalies with respect to the GRS80 ellipsoid from the EGM2008 global gravity model. Internal validation of the model shows a global RMS precision of Numéro de notice : A2015-881 Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern En ligne : http://link.springer.com/article/10.1007/s00190-015-0832-2/fulltext.html Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=79413 [article]

Reducing leakage error in GRACE-observed long-term ice mass change: a case study in West Antarctica / J. L. Chen in Journal of geodesy, vol 89 n° 9 (september 2015)  

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Accuracy of unmodified Stokes’ integration in the R-C-R procedure for geoid computation / Zahra Ismaïl in Journal of applied geodesy, vol 9 n° 2 (June 2015)  

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Regional vertical total electron content (VTEC) modeling together with satellite and receiver differential code biases (DCBs) using semi-parametric multivariate adaptive regression B-splines (SP-BMARS) / Murat Durmaz in Journal of geodesy, vol 89 n° 4 (April 2015)  

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SHPTS: towards a new method for generating precise global ionospheric TEC map based on spherical harmonic and generalized trigonometric series functions / Zishen Li in Journal of geodesy, vol 89 n° 4 (April 2015)  

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La mission Rosetta et le calcul de gravité / Julien Laurent-Varin in XYZ, n° 142 (mars - mai 2015)

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Empirical model of the gravitational field generated by the oceanic lithosphere / Robert Tenzer in Advances in space research, vol 55 n° 1 ([01/01/2015])  

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Reducing the draconitic errors in GNSS geodetic products / C.J. Rodriguez-Solano in Journal of geodesy, vol 88 n° 6 (June 2014)  

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Comparison among three harmonic analysis techniques on the sphere and the ellipsoid / Hussein Abd-Elmotaal in Journal of applied geodesy, vol 8 n° 1 (April 2014)  

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Evaluation of the third- and fourth-generation GOCE Earth gravity field models with Australian terrestrial gravity data in spherical harmonics / Moritz Rexer in Journal of geodesy, vol 88 n° 4 (April 2014)  

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Comparing seven candidate mission configurations for temporal gravity field retrieval through full-scale numerical simulation / Basem Elsaka in Journal of geodesy, vol 88 n° 1 (January 2014)  

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