Non linear regularization for helioseismic inversions - Application for the study of the solar tachocline

Inversions of rotational splittings have shown that there exists at the bas e of the solar convection zone a region called the tachocline in which high radial gradients of the rotation rate occur. The usual linear regularizati on methods tend to smooth out any high gradients in the solution, and may n ot be appropriate fur the study of this zone. In this paper we use, in the helioseismic context of rotation inversions, regularization methods that ha ve been developed for edge-preserving regularization in computed imaging. I t is shown from Monte-Carlo simulations that this approach can lead directl y to results similar to those reached by linear inversions which however re quired some assumptions on the shape of the transition in order to be decon volved. The application of this method to LOWL data leads to a very thin ta chocline. From the discussions on the parameters entering the inversion and the Monte-Carlo simulations, our conclusion is that the tachocline width i s very likely below 0.05R.. which lowers our previous estimate of 0.05 +/- 0.03R. obtained from the same dataset (Corbard et al. 1998).