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Spherical harmonic synthesis of area-mean potential values on irregular surfaces / Blažej Bucha in Journal of geodesy, vol 96 n° 10 (October 2022)  

Public [article]  inJournal of geodesy > vol 96 n° 10 (October 2022) . - n° 68 Titre : Spherical harmonic synthesis of area-mean potential values on irregular surfaces Type de document : Article/Communication Auteurs : Blažej Bucha, Auteur Année de publication : 2022 Article en page(s) : n° 68 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] champ de gravitation [Termes IGN] convergence [Termes IGN] harmonique sphérique [Termes IGN] surface hétérogène [Termes IGN] transformation de Legendre [Termes IGN] transformation rapide de Fourier Résumé : (auteur) We present a method to integrate external solid spherical harmonic expansions at geographical grids residing on undulated surfaces. It can be used to evaluate area-mean potential values on planetary surfaces that vary within grid cells. This is in contrast with available methods, which assume cells with a constant spherical radius only. When formulating the technique, we took advantage of 2D spherical Fourier methods to improve the computational speed. The price to be paid are high memory requirements, even with moderate maximum harmonic degrees such as 100 (both of the potential and of the irregular surface). In numerical experiments, we validate the method against independent area-mean potential values to prove its correctness. A study of the series behavior below the sphere of convergence shows that the series may diverge on planetary topographies, similarly as it is with its point-value counterpart. The method can be utilized in numerical studies of the change of boundary method, one of the pivotal concepts of recent high-degree models such as EGM2008. A numerical implementation is made available through CHarm, a C library to work with spherical harmonics up to high degrees. CHarm is accessible via https://github.com/blazej-bucha/charm. Numéro de notice : A2022-736 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-022-01658-1 Date de publication en ligne : 27/09/2022 En ligne : https://doi.org/10.1007/s00190-022-01658-1 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=101708 [article]

Gravitational field modelling near irregularly shaped bodies using spherical harmonics: a case study for the asteroid (101955) Bennu / Blažej Bucha in Journal of geodesy, vol 95 n° 5 (May 2021)  

Public [article]  inJournal of geodesy > vol 95 n° 5 (May 2021) . - n° 56 Titre : Gravitational field modelling near irregularly shaped bodies using spherical harmonics: a case study for the asteroid (101955) Bennu Type de document : Article/Communication Auteurs : Blažej Bucha, Auteur ; Fernando Sanso, Auteur Année de publication : 2021 Article en page(s) : n° 56 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] astéroïde [Termes IGN] champ de gravitation [Termes IGN] champ de pesanteur terrestre [Termes IGN] convergence [Termes IGN] harmonique sphérique [Termes IGN] intégrale de Newton Résumé : (auteur) We apply three spherical-harmonic-based techniques to deliver external gravitational field models of the asteroid (101955) Bennu within its circumscribing sphere. This region is known to be peculiar for external spherical harmonic expansions, because it may lead to a divergent series. The studied approaches are (i) spectral gravity forward modelling via external spherical harmonics, (ii) the least-squares estimation from surface gravitational data using external spherical harmonics and (iii) the combination of internal and external series expansions. While the first method diverges beyond any reasonable doubts, we show that the other two methods may ensure relative accuracy from ∼10−6 to 10−8 in the vicinity of Bennu. This is possible even with the second method, despite the fact that it relies on a single series of external spherical harmonics. Our main motivation was to study conceptual differences between spherical harmonic coefficients from satellite data (analogy to the first method) and from surface gravitational data (the second method). Such coefficients are available through the popular spherical-harmonic-based models of the Earth’s gravitational field and often are combined together. We show that the coefficients from terrestrial data may lead to a divergence effect of partial sums, though excellent accuracy can be achieved when such model is used in full. Under (presently) extreme but realistic conditions, the divergence effect of partial sums may affect many near-surface geoscientific applications, such as the geoid/quasigeoid computation or residual terrain modelling. Computer codes (Fortran, MATLAB) and data produced within the study are made freely available at http://edisk.cvt.stuba.sk/~xbuchab/. Numéro de notice : A2021-347 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-021-01493-w Date de publication en ligne : 22/04/2021 En ligne : https://doi.org/10.1007/s00190-021-01493-w Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=97591 [article]