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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) . - n° 30 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 Projets : Université de Paris / Clerici, Christine Article en page(s) : n° 30 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] analyse harmonique [Termes IGN] champ de pesanteur terrestre [Termes IGN] harmonique sphérique [Termes IGN] implémentation (informatique) [Termes IGN] polyèdre [Termes 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 Affiliation des auteurs : Géodésie+Ext (mi2018-2019) 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]

Assessment of a numerical method for computing the spherical harmonic coefficients of the gravitational potential of a constant density polyhedron / Olivier Jamet (2010)  

Public contenu dans Gravity, Geoid and Earth Observation, IAG Commission 2 Gravity Field, Chania, Crete, Greece, 23-27 June 2008 / Stelios Mertikas (2010)   Titre : Assessment of a numerical method for computing the spherical harmonic coefficients of the gravitational potential of a constant density polyhedron Type de document : Article/Communication Auteurs : Olivier Jamet , Auteur ; Jérome Verdun , Auteur ; Dimitrios Tsoulis, Auteur ; Nicolas Gonindard, Auteur Editeur : Berlin, Heidelberg, Vienne, New York, ... : Springer Année de publication : 2010 Collection : International Association of Geodesy Symposia, ISSN 0939-9585 num. 135 Conférence : IAG 2008 Commission 2, Gravity, Geoid and Earth Observation GGEO 23/06/2008 27/06/2008 Chania Crète - Grèce Proceedings Springer Importance : pp 437 - 443 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Termes IGN] géodésie physique [Termes IGN] harmonique sphérique [Termes IGN] modèle de géopotentiel [Termes IGN] polyèdre Résumé : (auteur) This study focuses on the assessment of a linear algorithm for computing the spherical harmonic coefficients of the gravitational potential of a constant density polyhedron. The ability to compute such an expansion would favor several applications, in particular in the field of the interpretation and assessment of GOCE gravitational models. The studied algorithm is the only known method that would achieve this computation at a computational cost depending linearly on the number of computed coefficients. We show that although this methods suffers from severe divergence issues, it could be applied to retrieve band-limited estimates of the potential generated by a constant density polyhedron. Numéro de notice : C2008-016 Affiliation des auteurs : LAREG+Ext (1991-2011) Thématique : MATHEMATIQUE/POSITIONNEMENT Nature : Communication nature-HAL : ComAvecCL&ActesPubliésIntl DOI : 10.1007/978-3-642-10634-7_58 Date de publication en ligne : 26/10/2010 En ligne : https://doi.org/10.1007/978-3-642-10634-7_58 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=90744

Recursive algorithms for the computation of the potential harmonic coefficients of a constant density polyhedron / Dimitrios Tsoulis in Journal of geodesy, vol 83 n° 10 (October 2009)  

Public [article]  inJournal of geodesy > vol 83 n° 10 (October 2009) . - pp 925 - 942 Titre : Recursive algorithms for the computation of the potential harmonic coefficients of a constant density polyhedron Type de document : Article/Communication Auteurs : Dimitrios Tsoulis, Auteur ; Olivier Jamet , Auteur ; Jérome Verdun , Auteur ; Nicolas Gonindard, Auteur Année de publication : 2009 Projets : 3-projet - voir note / Clerici, Christine Article en page(s) : pp 925 - 942 Note générale : Bibliographie The present research has been carried out in the frame of France-Greek bilateral cooperation PHC Platon, project number 15063 VE. Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] harmonique sphérique [Termes IGN] polyèdre [Termes IGN] potentiel de pesanteur terrestre Résumé : (Auteur) The gravitational potential of a constant density general polyhedron can be expressed both in terms of a closed analytical expression and as a series expansion involving the corresponding spherical harmonic coefficients. The latter can be obtained from two independent algorithms, which differ not only in their algorithmic architecture but in their efficiency and overall performance, especially when computing the coefficients of higher degree and order. In the present paper a comparative study of all these three approaches is carried out focusing on the numerical implementation of the recursive relations appearing in the two algorithms for the computation of the polyhedral potential harmonic coefficients. The performed numerical investigations show that the linear algorithm proposed by Jamet and Thomas (Proceedings of the second international GOCE user workshop, ‘GOCE, The Geoid and Oceanography’, ESA-ESRIN, Frascati, Italy, 8–10 March 2004, ESA SP-569, 2004), but so far not implemented, achieves a reasonable accuracy at a computational expense that opens to practical applications, for instance in the field of satellite gravimetry/gradiometry interpretation. The convergence behavior of the linear recursion algorithm is studied thoroughly and a computational procedure is proposed that enables the stable computation of potential harmonic coefficients up to degree 60 when referring to an arbitrarily shaped polyhedral body. Numéro de notice : A2009-429 Affiliation des auteurs : LAREG+Ext (1991-2011) Autre URL associée : vers HAL Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-009-0310-9 Date de publication en ligne : 10/03/2009 En ligne : http://dx.doi.org/10.1007/s00190-009-0310-9 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=30060 [article]

Exemplaires(1)

Code-barres	Cote	Support	Localisation	Section	Disponibilité
266-09091	SL	Revue	Centre de documentation	Revues en salle	Disponible

Analytical and numerical methods in gravity field modelling of ideal and real masses / Dimitrios Tsoulis (1999)

Public Titre : Analytical and numerical methods in gravity field modelling of ideal and real masses Type de document : Thèse/HDR Auteurs : Dimitrios Tsoulis, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1999 Collection : DGK - C, ISSN 0065-5325 num. 510 Importance : 133 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-3-7696-9548-9 Note générale : Bibliographie Thèse allemande Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] analyse de variance [Termes IGN] champ de pesanteur terrestre [Termes IGN] International Terrestrial Reference Frame [Termes IGN] matrice de covariance [Termes IGN] modèle mathématique [Termes IGN] variance Index. décimale : 30.40 Géodésie physique Résumé : (Auteur) Based on Newton's law of gravitation, one can compute at arbitrary points in space the gravitational potential of a given mass distribution, as well as its first and second order derivatives. For a number of ideal bodies the solution of these computations can be given in closed analytical form or as series expansion. In particular for points situated outside the symmetry axes of ideal bodies the analytical solutions are very tedious. Expressions of this type find application especially for gravitational experiments in the laboratory or inside of satellites. For more complicated mass distributions, for example for a topographic terrain model, finite discretization of the masses into elementary blocks or twodimensional Fourier representation are employed. In order to avoid singularities a combination method for this latter case is proposed, where a biner part is computed by numerical integration and Fourier expansion is applied to the outer area. Note de contenu : 1 Introduction 2 Terrestrial Reference Systems 2.1 General Remarks on TRS 2.2 Datum Determination 2.3 Datum Transformation 2.4 Reference Frame Noise and STransformation 3 International Terrestrial Reference Frame 3.1 Historical Background 3.4 Mathematical Model 3.5 Stochastic Model 3.6 Normal Equations 3.7 Variance Component Estimation used in ITRF 3.8 Minimum Position Variance Investigation 3.9 Introduction of a Unique Reference Frame Noise 3.10 Combination Steps in the ITRF 4 Connection to ITRF 4.1 Connection to ITRF some Ideas and Concepts 4.2 Connecting by SevenParameter Transformation 4.3 Datum Information contained in aNetwork Solution 4.4 Spectral Analysis 4.5 Seven Parameter Transformation necessary? 5 Data and DataQuality Measures 5.1 Variance covariance Analysis 5.2 Data Analysis The Concepts 6 Data Analysis 6.1 Data Analysis 6.2 Influence on the Variance Component Estimation 6.3 Influence on the Seven Transformation Parameters 6.4 Influence on Transformed Point Positions 6.5 Final Transformation Concept 7 Conclusion Numéro de notice : 56580 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Thèse étrangère Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=52105

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Code-barres	Cote	Support	Localisation	Section	Disponibilité
56580-01	30.40	Livre	Centre de documentation	Géodésie	Disponible
56580-02	30.40	Livre	Centre de documentation	Géodésie	Disponible