Multi-Channel Three-Dimensional SOLA Inversion for Local Helioseismology

TL;DR

This paper introduces an efficient multi-channel SOLA inversion algorithm in Fourier space for local helioseismology, significantly reducing computational time while accurately mapping solar interior properties.

Contribution

It presents a novel Fourier domain SOLA inversion method that exploits horizontal translation invariance, enabling faster and parallelizable solutions for 3D helioseismic inverse problems.

Findings

The multi-channel SOLA method is much faster than traditional approaches.

Both real and Fourier space methods successfully solve the inverse problem.

The Fourier domain approach is easily parallelizable.

Abstract

Inversions for local helioseismology are an important and necessary step for obtaining three-dimensional maps of various physical quantities in the solar interior. Frequently, the full inverse problems that one would like to solve prove intractable because of computational constraints. Due to the enormous seismic data sets that already exist and those forthcoming, this is a problem that needs to be addressed. To this end, we present a very efficient linear inversion algorithm for local helioseismology. It is based on a subtractive optimally localized averaging (SOLA) scheme in the Fourier domain, utilizing the horizontal-translation invariance of the sensitivity kernels. In Fourier space the problem decouples into many small problems, one for each horizontal wave vector. This multi-channel SOLA method is demonstrated for an example problem in time-distance helioseismology that is small enough to be solved both in real and Fourier space. We find that both approaches are successful in solving the inverse problem. However, the multi-channel SOLA algorithm is much faster and can easily be parallelized.