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Wavelet frames:An alternative to spherical harmonic representation of potential fields / Aude Chambodut in Geophysical journal international, vol 163 n° 3 (December 2005)  

Public [article]  inGeophysical journal international > vol 163 n° 3 (December 2005) . - pp 875 - 899 Titre : Wavelet frames:An alternative to spherical harmonic representation of potential fields Type de document : Article/Communication Auteurs : Aude Chambodut, Auteur ; Isabelle Panet , Auteur ; Mioara Mandea, Auteur ; Michel Diament , Auteur ; Matthias Holschneider, Auteur ; Olivier Jamet , Auteur Année de publication : 2005 Article en page(s) : pp 875 - 899 Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] champ de pesanteur terrestre [Termes IGN] champ magnétique [Termes IGN] harmonique sphérique [Termes IGN] ondelette d'Abel-Poisson Résumé : (auteur) Potential fields are classically represented on the sphere using spherical harmonics. However, this decomposition leads to numerical difficulties when data to be modelled are irregularly distributed or cover a regional zone. To overcome this drawback, we develop a new representation of the magnetic and the gravity fields based on wavelet frames. In this paper, we first describe how to build wavelet frames on the sphere. The chosen frames are based on the Poisson multipole wavelets, which are of special interest for geophysical modelling, since their scaling parameter is linked to the multipole depth (Holschneider et al.). The implementation of wavelet frames results from a discretization of the continuous wavelet transform in space and scale. We also build different frames using two kinds of spherical meshes and various scale sequences. We then validate the mathematical method through simple fits of scalar functions on the sphere, named ‘scalar models’. Moreover, we propose magnetic and gravity models, referred to as ‘vectorial models’, taking into account geophysical constraints. We then discuss the representation of the Earth’s magnetic and gravity fields from data regularly or irregularly distributed. Comparisons of the obtained wavelet models with the initial spherical harmonic models point out the advantages of wavelet modelling when the used magnetic or gravity data are sparsely distributed or cover just a very local zone. Numéro de notice : A2005-615 Affiliation des auteurs : LAREG+Ext (1991-2011) Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1111/j.1365-246X.2005.02754.x Date de publication en ligne : 01/12/2005 En ligne : https://doi.org/10.1111/j.1365-246X.2005.02754.x Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=102897 [article]