The SOLA method for helioseismic inversion
Abstract
The Subtractive Optimally Localized Averages (SOLA) method is a versatile and efficient technique for inverting helioseismic data. The SOLA method is based on explicit construction of Backus-Gilbert averaging kernels, but whereas the more usual formulations of the optimally localized averages (OLA) method use a multiplicative penalty function to localize the kernels, the distinctive idea of SOLA is that one specifies a desired target form for the kernels and then minimizes the integrated squared difference between the kernels and the target form. This allows great versatility in the choice of target form, and furthermore SOLA has the significant advantage of being computationally more efficient than the usual OLA formulations. A Gaussian target function is a useful choice, and we use the example of determining the Sun's internal rotation to explore how the parameter values (such as the Gaussian's width) should best be chosen. Some alternatives to using a Gaussian function as target function are discussed and applied to artificial data in a blind experiment. In particular we show that it is possible to invert directly for the gradient of the rotation. This may be of interest if there are localized large gradients in the rotation rate.
- Publication:
-
Astronomy and Astrophysics
- Pub Date:
- January 1994
- Bibcode:
- 1994A&A...281..231P
- Keywords:
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- Helioseismology;
- Solar Interior;
- Solar Oscillations;
- Solar Rotation;
- Gauss Equation;
- Numerical Analysis;
- Solar Physics