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Fast calculation of gravitational effects using tesseroids with a polynomial density of arbitrary degree in depth / Fang Ouyang in Journal of geodesy, vol 96 n° 12 (December 2022)  

Public [article]  inJournal of geodesy > vol 96 n° 12 (December 2022) . - n° 97 Titre : Fast calculation of gravitational effects using tesseroids with a polynomial density of arbitrary degree in depth Type de document : Article/Communication Auteurs : Fang Ouyang, Auteur ; Long-wei Chen, Auteur ; Zhi-gang Shao, Auteur Année de publication : 2022 Article en page(s) : n° 97 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] champ de gravitation [Termes IGN] coordonnées sphériques [Termes IGN] discrétisation [Termes IGN] intégrale de Newton [Termes IGN] inversion [Termes IGN] quadrature [Termes IGN] tesseroid [Termes IGN] transformation rapide de Fourier Résumé : (auteur) Fast and accurate calculation of gravitational effects on a regional or global scale with complex density environment is a critical issue in gravitational forward modelling. Most existing significant developments with tessroid-based modelling are limited to homogeneous density models or polynomial ones of a limited order. Moreover, the total gravitational effects of tesseroids are often calculated by pure summation in these methods, which makes the calculation extremely time-consuming. A new efficient and accurate method based on tesseroids with a polynomial density up to an arbitrary order in depth is developed for 3D large-scale gravitational forward modelling. The method divides the source region into a number of tesseroids, and the density in each tesseroid is assumed to be a polynomial function of arbitrary degree. To guarantee the computational accuracy and efficiency, two key points are involved: (1) the volume Newton’s integral is decomposed into a one-dimensional integral with a polynomial density in the radial direction, for which a simple analytical recursive formula is derived for efficient calculation, and a surface integral over the horizontal directions evaluated by the Gauss–Legendre quadrature (GLQ) combined with a 2D adaptive discretization strategy; (2) a fast and flexible discrete convolution algorithm based on 1D fast Fourier transform (FFT) and a general Toepritz form of weight coefficient matrices is adopted in the longitudinal dimension to speed up the computation of the cumulative contributions from all tesseroids. Numerical examples show that the gravitational fields predicted by the new method have a good agreement with the corresponding analytical solutions for spherical shell models with both polynomial and non-polynomial density variations in depth. Compared with the 3D GLQ methods, the new algorithm is computationally more accurate and efficient. The calculation time is significantly reduced by 3 orders of magnitude as compared with the traditional 3D GLQ methods. Application of the new algorithm in the global crustal CRUST1.0 model further verifies its reliability and practicability in real cases. The proposed method will provide a powerful numerical tool for large-scale gravity modelling and also an efficient forward engine for inversion and continuation problems. Numéro de notice : A2022-896 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article DOI : 10.1007/s00190-022-01688-9 Date de publication en ligne : 05/12/2022 En ligne : https://doi.org/10.1007/s00190-022-01688-9 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=102248 [article]

New algorithms for spherical harmonic analysis of area mean values over blocks delineated by equiangular and Gaussian grids / Rong Sun in Journal of geodesy, vol 95 n° 5 (May 2021)  

Public [article]  inJournal of geodesy > vol 95 n° 5 (May 2021) . - n° 47 Titre : New algorithms for spherical harmonic analysis of area mean values over blocks delineated by equiangular and Gaussian grids Type de document : Article/Communication Auteurs : Rong Sun, Auteur Année de publication : 2021 Article en page(s) : n° 47 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] analyse harmonique [Termes IGN] grille [Termes IGN] matrice [Termes IGN] méthode des moindres carrés [Termes IGN] quadrature [Termes IGN] transformation polynomiale Résumé : (auteur) Spherical harmonic analysis is widely used in all aspects of geoscience. Exact quadrature methods are available for the spherical harmonic analysis of band-limited point values at the grid points of equiangular and Gaussian grids. However, no similarly exact quadrature methods are available for the spherical harmonic analysis of area mean values over the blocks delineated by these grids. In this study, new algorithms appropriate for the exact spherical harmonic analysis of the band-limited area mean values over the blocks delineated by equiangular and Gaussian grids are proposed. For band-limited data, precision that is between that of the least-squares estimation method and of the approximate quadrature methods can be achieved by using the new algorithms. Regarding the computational complexity, fewer operations are needed by the new methods as compared to those needed by the least-squares estimation method and the approximate quadrature methods in the preparation stage when the maximum degree of the spherical harmonic analysis is very large. Simulation experiments are performed to compare the ability to recover the spherical harmonic coefficients by using the least-squares estimation method, the approximate quadrature methods and these new algorithms from aliased data with aliasing components of realistic magnitudes. The results suggest that these new algorithms, with time complexity one order less than that of the least-squares estimation method in the solving stage, perform roughly the same as the least-squares estimation method in recovering spherical harmonic coefficients from the aliased data. Numéro de notice : A2021-488 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE/POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-021-01495-8 Date de publication en ligne : 07/04/2021 En ligne : https://doi.org/10.1007/s00190-021-01495-8 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=97507 [article]

Cours d'analyse mathématique / E. Goursat (1933)

Public Titre : Cours d'analyse mathématique : dérivées et différentielles intégrales définies : développement Type de document : Guide/Manuel Auteurs : E. Goursat, Auteur Editeur : Paris : Gauthier-Villars Année de publication : 1933 Importance : 674 p. Format : 16 x 24 cm Langues : Français (fre) Descripteur : [Vedettes matières IGN] Analyse mathématique [Termes IGN] Alembert, Jean d' [Termes IGN] asymptote [Termes IGN] Cauchy, Augustin-Louis [Termes IGN] convergence [Termes IGN] courbe [Termes IGN] Dupin (Charles) [Termes IGN] Frenet Frédéric [Termes IGN] intégrale [Termes IGN] intégrale curviligne [Termes IGN] Legendre, Adrien-Marie [Termes IGN] projection conforme [Termes IGN] projection sphérique [Termes IGN] quadrature [Termes IGN] série de Fourier [Termes IGN] série de Taylor [Termes IGN] théorème de Taylor [Termes IGN] variable Numéro de notice : 26546 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Manuel de cours Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=47199

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Code-barres	Cote	Support	Localisation	Section	Disponibilité
26546-01	123.30	Livre	Centre de documentation	En réserve L-101	Fonds ancien - consultable sur RdV Exclu du prêt