On the use of nonlinear regularization in inverse method for the tachocline profile determination

Inversions of rotational splittings have shown that the surface layers and the so-called solar tachocline at the base of the convection zone are regions in which high radial gradients of the rotation rate occur. The usual regularization methods tend to smooth out every high gradients in the solution and may not be appropriate for the study of a zone like the tachocline. In this paper we use nonlinear regularization methods that are developed for edge-preserving regularization in computed imaging (e.g. Blanc-F\'eraud et al. 1995) and we apply them in the helioseismic context of rotational inversions.