Inferring solar internal structure and rotation from p-mode frequencies and frequency splittings I & II - ABSTRACT

Interesting inverse problems arise in helioseismology, the seismic study of the interior of the Sun using the frequencies of its global resonant modes of oscillation. Moreover, such techniques as inverse analyses have been key to making detailed quantitative inferences about the solar interior from the observed oscillation frequencies. In particular, one can use the frequencies to investigate how the rotation and the radial stratification of the Sun vary beneath the visible surface. In these lectures I shall discuss the methods and tools that have been used in the helioseismic inversion problem, how the spatial resolution of inversions is assessed and the trade-offs between resolution and controlling uncertainties due to noise in the data. I shall also present results of inversions for different physical quantities inside the Sun and discuss how they were obtained. In the companion hands-on tutorial, there will be opportunity to experiment with some inversion techniques to see how the inversion results change with different choices of trade-off and inversion method.

Some preliminary reading

Thompson, M.J., 1995, Linear inversions for the Sun's internal rotation, Inverse Problems 11, 709-730.
http://www.iop.org/EJ/abstract/0266-5611/11/4/007

Chapter 9 of Lecture notes on stellar oscillations, J. Christensen-Dalsgaard
http://astro.phys.au.dk/~jcd/oscilnotes/

For a gentle introduction, including a very little bit about inversion, see http://astro.phys.au.dk/helio_outreach/english/engHA0.html

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Prof. Michael J. Thompson            Tel +44 (0)114 222 3733
Head of Department                   FAX +44 (0)114 222 3739
Dept. of Applied Mathematics 
University of Sheffield
Sheffield S3 7RH, U.K.
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