SOI proposal 46 :

Title:         2D inversion of internal solar rotation


1) Lead investigator: Corbard Thierry

2) Members of the collaboration: Appourchaux T., Berthomieu G., Corbard T.,
               Gonczi G., Morel P., Provost J., Toutain T.

3) Abstract:

This project concerns the determination of internal solar rotation using
a 2D least square inversion code with emphasis on the convective/radiative
transition zone and on the structure of the core using the VIRGO  data.

4) Description of the project

A 2D regularized least square inversion code of the rotational splittings
to obtain the internal rotation of the Sun has been developed in Nice (OCA).
It has been applied to the rotational splitting data of
 Libbrecht et al. (poster at Pacific Grove Conference in April 1995)

We are looking to the influence of the form of the regularizing terms on the
inversed rotation and to the constraints that can be imposed at the surface
and at the center.

In our inversion code the rotation profile is approximated by a 2D
tensorial product of piecewise polynomials of arbitrary order; in each
direction they are expressed by the development on their B-splines basis.
We are studying how to take advantage of the properties of B-splines mainly
for improvement of  the regularization procedure, restoration of eventual
discontinuities and description of the boundaries.


We propose to combine the  SOI data with the VIRGO one, with hopefully g modes
and low frequency p modes splittings, to derive the internal rotation from
the surface to the core. We intend to study more specifically the behavior
of the rotation at the basis of the convection zone and to determine the size
of the transition zone between the quasi-rigid rotation of the radiative
interior and the differential rotation in the convection zone.
We are looking at the possibility of introducing in the code non linear
inversion schemes like the edge-preserving regularization algorithms
developed for image processing.