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

TL;DR

This paper introduces a non-linear, edge-preserving regularization method for helioseismic inversions, revealing a very thin solar tachocline with a width likely below 0.05 solar radii, improving the resolution over traditional methods.

Contribution

It applies edge-preserving regularization techniques from computed imaging to helioseismic rotation inversions, enabling more accurate detection of sharp gradients like the solar tachocline.

Findings

The tachocline is very thin, likely below 0.05 solar radii.

The new method produces results similar to traditional inversions but with better gradient preservation.

The tachocline width estimate is refined to a lower value than previous estimates.

Abstract

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 0.05R_sun which lowers our previous estimate of 0.05+/- 0.03R_sun obtained from the same dataset (Corbard et al. 1998).