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Astron. Astrophys. 344, 696-708 (1999)

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Non linear regularization for helioseismic inversions

Application for the study of the solar tachocline

T. Corbard 1, L. Blanc-Féraud 2, G. Berthomieu 1 and J. Provost 1

1 Laboratoire G.-D. Cassini, CNRS UMR 6529, Observatoire de la Côte d'Azur, B.P. 4229, F-06304 Nice Cedex 4, France
2 Projet Ariana, CNRS/INRIA/UNSA, 2004 route des Lucioles, B.P. 93, F-06902 Sophia Antipolis Cedex, France

Received 31 August 1998 / Accepted 8 January 1999


Inversions of rotational splittings have shown that there exists at the base of the solar convection zone a region called the tachocline in which high radial gradients of the rotation rate occur. The usual linear regularization methods tend to smooth out any high gradients in the solution, and may not be appropriate for the study of this zone. In this paper we use, in the helioseismic context of rotation inversions, regularization methods that have been developed for edge-preserving regularization in computed imaging. It is shown from Monte-Carlo simulations that this approach can lead directly to results similar to those reached by linear inversions which however required some assumptions on the shape of the transition in order to be deconvolved. The application of this method to LOWL data leads to a very thin tachocline. From the discussions on the parameters entering the inversion and the Monte-Carlo simulations, our conclusion is that the tachocline width is very likely below [FORMULA] which lowers our previous estimate of [FORMULA] obtained from the same dataset (Corbard et al. 1998).

Key words: methods: numerical – Sun: interior – Sun: oscillations – Sun: rotation

Present address: NCAR/High Altitude Observatory, P.O. Box 3000, Boulder, CO 80307, USA

Send offprint requests to: T. Corbard

Correspondence to: corbard@hao.ucar.edu

© European Southern Observatory (ESO) 1999

Online publication: March 18, 1999