2011/09/13 by Jason Jackiewicz, J. Jackiewicz, A. C. Birch +9
Biochemistry, Genetics and Molecular Biology · Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Algorithm #Computer science #Fourier transform #Geomagnetism and Paleomagnetism Studies #Geometry #Geophysics and Gravity Measurements #Helioseismology #Inverse #Inverse problem #Inversion (geology) #Magnetic field #Mathematical analysis #Mathematics #Physics #Quantum mechanics #Solar and Space Plasma Dynamics #astro-ph.SR
paper · pdf · doi:10.1007/s11207-011-9873-8
published as Solar Phys, 2012, 276, 19-33 · 18 pages, 6 figures, accepted in Solar Physics
arxiv created 2011/09/13 · openalex publication_date 2011/11/14 · arxiv updated 2015/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 multichannel 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 multichannel SOLA algorithm is much faster and can easily be parallelized.