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Fourier-series representation and projection of spherical harmonic functions / H. Cheong in Journal of geodesy, vol 86 n° 11 (November 2012)  

Public [article]  inJournal of geodesy > vol 86 n° 11 (November 2012) . - pp 975 - 990 Titre : Fourier-series representation and projection of spherical harmonic functions Type de document : Article/Communication Auteurs : H. Cheong, Auteur ; J. Park, Auteur ; H. Kang, Auteur Année de publication : 2012 Article en page(s) : pp 975 - 990 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Statistiques [Termes IGN] harmonique sphérique [Termes IGN] relief sous-marin [Termes IGN] série de Fourier [Termes IGN] théorème de Legendre [Termes IGN] variance Résumé : (Auteur) Computations of Fourier coefficients and related integrals of the associated Legendre functions with a new method along with their application to spherical harmonics analysis and synthesis are presented. The method incorporates a stable three-step recursion equation that can be processed separately for each colatitudinal Fourier wavenumber. Recursion equations for the zonal and sectorial modes are derived in explicit single-term formulas to provide accurate initial condition. Stable computations of the Fourier coefficients as well as the integrals needed for the projection of Legendre functions are demonstrated for the ultra-high degree of 10,800 corresponding to the resolution of one arcmin. Fourier coefficients, computed in double precision, are found to be accurate to 15 significant digits, indicating that the normalized error is close to the machine round-off error. The orthonormality, evaluated with Fourier coefficients and related integrals, is shown to be accurate to O(10-15) for degrees and orders up to 10,800. The Legendre function of degree 10,800 and order 5,000, synthesized from Fourier coefficients, is accurate to the machine round-off error. Further extension of the method to even higher degrees seems to be realizable without significant deterioration of accuracy. The Fourier series is applied to the projection of Legendre functions to the high-resolution global relief data of the National Geophysical Data Center of the National Oceanic and Atmospheric Administration, and the spherical harmonic degree variance (power spectrum) of global relief data is discussed. Numéro de notice : A2012-576 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-012-0558-3 Date de publication en ligne : 11/04/2012 En ligne : https://doi.org/10.1007/s00190-012-0558-3 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=32022 [article]

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