A comparison of methods for inverting helioseismic data

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Abstract
The utilization of observed frequencies of solar oscillation to study the properties of the solar interior requires the application of accurate and efficient inversion techniques. Extensive development of such techniques has taken place for geophysical problems, and limited attempts have been made to apply them to helioseismic data. The properties of the inversion depend on the details of the modes being analysed, however, and hence the experience gained in geophysical inversions is not necessarily valid for the solar case. As a contribution to the systematic evaluation of inversion techniques, applied to helioseismic problems, we present the means for a unified comparison of linear inversion schemes in terms of their resolution and error properties; this approach is then applied to four commonly used techniques, for three different mode sets that may be representative for helioseismic data. In all cases it is possible to define measures of the amplification of errors resulting from the inversion, and of the resolution achieved. These measures are quite similar for the different methods. However, more subtle differences may make particular methods preferable for specific applications. Although we only consider inversions for a spherically symmetric angular velocity distribution, kernels for other properties of the solar interior are probably sufficiently similar to make our conclusions of more general validity.

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