Wavelet analysis of potential fields

F. Moreau (1) , D. Gibert (1) , M. Holschneider (2, 3) , Ginette Saracco (1, 4, 5)

1 geophysique Interne
2 CPT - Centre de Physique Théorique - UMR 6207
3 CPT - Centre de Physique Théorique - UMR 7332
4 GR - Géosciences Rennes
5 CEREGE - Centre européen de recherche et d'enseignement des géosciences de l'environnement

It is shown how a continuous wavelet technique may be used to locate and characterize homogeneous point sources from the field they generate measured in a distant hyperplane. For this a class of wavelets is introduced on which the Poisson semi-group essentially acts as a dilation.

Mots clés: Poisson semi-group; Wavelet theory; harmonic extension; homogeneity degree; inverse problem in potential theory

Domaines: Géophysique [physics.geo-ph]; Géophysique [physics.geo-ph]; Equations aux dérivées partielles [math.AP]; Théorie des groupes [math.GR]; Hydrologie; Volcanologie

F. Moreau, D. Gibert, M. Holschneider, Ginette Saracco. Wavelet analysis of potential fields. Inverse Problems, 1997, 13 (1), pp.165-178. ⟨10.1088/0266-5611/13/1/013⟩. ⟨hal-00805821⟩