Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, EpiSciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).

# Wavelet frames: an alternative to spherical harmonic representation of potential fields

Abstract : 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.

Keywords :
Document type :
Journal articles

https://hal-insu.archives-ouvertes.fr/insu-03601100
Contributor : Nathalie POTHIER Connect in order to contact the contributor
Submitted on : Tuesday, March 8, 2022 - 3:28:48 PM
Last modification on : Thursday, March 10, 2022 - 3:31:40 AM
Long-term archiving on: : Thursday, June 9, 2022 - 7:31:12 PM

### File

163-3-875.pdf
Publisher files allowed on an open archive

### Citation

Aude Chambodut, I. Panet, M. Mandea, M. Diament, M. Holschneider, et al.. Wavelet frames: an alternative to spherical harmonic representation of potential fields. Geophysical Journal International, Oxford University Press (OUP), 2005, 163, pp.875-899. ⟨10.1111/j.1365-246X.2005.02754.x⟩. ⟨insu-03601100⟩

Record views