## Title:

Helioseismic Inversions: Massive Data Sets and the Determination of Solar
Structure

## Author:

- Sarbani Basu
- Theoretical Astrophysics Center
- Institute for Physics and Astronomy, Aarhus Univ.
- DK-8000 Aarhus C, Denmark

** Abstract: **
Solar oscillation frequencies are normally described by spherical harmonics
and have three `quantum' numbers associated with them -- the radial order
$n$, the degree $\ell$ and the azimuthal order $m$. In the absence of
asphericities, all modes with the same $n$ and $\ell$ have the same
frequency and the frequency is determined by the spherically symmetric
structure, particularly the sound-speed profile of the Sun. Asymmetry
is introduced mainly by rotation and cause the $(n,\ell)$ multiplet to
``split'' into $2\ell +1$ components. Since the mode-frequencies depend on
the spherically symmetric structure and the asphericities, they can be
inverted to determine these quantities. The total number of modes
observed is of the order of $10^6$ and thus inverting these is a
computationally challenging task.

In this talk I shall describe some of the common methods used in helioseismic
inversions and their limitations, and talk about some of the techniques used
to reduce the problem to a manageable form -- both in terms of memory
and time required. In particular, I shall show how the ill-conditioned
nature of the problem can be exploited to reduce the size of the
inversion. I shall also outline some steps where better algorithms
will be of help.