## SVD preprocessing of helioseismic data for solar structure inversion
^{1} Teoretisk Astrofysik Center, Danmarks
Grundforskningsfond, Institute for Fysik og Astronomi, Aarhus
Universitet, DK-8000 Aarhus C, Denmark^{2} Institute for Fysik og Astronomi, Aarhus Universitet,
DK-8000 Aarhus C, Denmark^{3} Astronomy Unit, Queen Mary and Westfield College, Mile
End Road, London E1 4NS, UK
Helioseismic inversion to determine solar structure is based on the analysis of very substantial numbers of modes and hence may involve considerable computational expense. This is particularly true for inversions using methods of optimally localised averages, which require inversion of matrices whose order is the number of modes in the set; yet such methods are desirable to make the full use of the data. On the other hand, there is considerable redundancy in the data, different modes carrying almost the same information about solar structure. Thus, in the unavoidable presence of data errors, the number of independent pieces of information is generally much less than the number of modes. This suggests that the modeset can be reduced by forming suitable combinations of the data before the more computationally intensive inversion is performed. We show that such combinations may be based on singular value decomposition (SVD) of the problem, leading to a drastically reduced inverse problem whose solution is essentially indistinguishable from the solution of the original problem. In addition, the results of the SVD provide insight into the information content of the helioseismic data.
## Contents- 1. Introduction
- 2. Discretization and SVD of the matrix of kernels
- 3. OLA inversion of the transformed problem
- 4. The effect of the surface term
- 5. The effect of realistic errors
- 6. Conclusions
- Acknowledgements
- References
© European Southern Observatory (ESO) 1997 Online publication: June 30, 1998 |