Solar Physics

, Volume 276, Issue 1–2, pp 19–33 | Cite as

Multichannel Three-Dimensional SOLA Inversion for Local Helioseismology

  • J. Jackiewicz
  • A. C. Birch
  • L. Gizon
  • S. M. Hanasoge
  • T. Hohage
  • J.-B. Ruffio
  • M. Švanda
Open Access


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.


Helioseismology Inverse modeling 


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Copyright information

© The Author(s) 2011

Authors and Affiliations

  • J. Jackiewicz
    • 1
    • 2
  • A. C. Birch
    • 3
  • L. Gizon
    • 1
    • 4
  • S. M. Hanasoge
    • 1
    • 5
  • T. Hohage
    • 6
  • J.-B. Ruffio
    • 1
    • 7
  • M. Švanda
    • 1
  1. 1.Max-Planck-Institut für SonnensystemforschungKatlenburg-LindauGermany
  2. 2.Department of AstronomyNew Mexico State UniversityLas CrucesUSA
  3. 3.Colorado Research Associates DivisionNorthWest Research Associates Inc.BoulderUSA
  4. 4.Institut für AstrophysikGeorg-August-Universität GöttingenGöttingenGermany
  5. 5.Department of GeosciencesPrinceton UniversityPrincetonUSA
  6. 6.Institut für Numerische und Angewandte MathematikUniversität GöttingenGöttingenGermany
  7. 7.Université de ToulouseISAE-SUPAEROToulouse Cedex 4France

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