### 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 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.

Original language | English (US) |
---|---|

Pages (from-to) | 19-33 |

Number of pages | 15 |

Journal | Solar Physics |

Volume | 276 |

Issue number | 1-2 |

DOIs | |

State | Published - Feb 1 2012 |

### Fingerprint

### Keywords

- Helioseismology
- Inverse modeling

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Solar Physics*,

*276*(1-2), 19-33. https://doi.org/10.1007/s11207-011-9873-8

**Multichannel Three-Dimensional SOLA Inversion for Local Helioseismology.** / Jackiewicz, J.; Birch, A. C.; Gizon, Laurent; Hanasoge, Shravan; Hohage, T.; Ruffio, J. B.; Švanda, M.

Research output: Contribution to journal › Article

*Solar Physics*, vol. 276, no. 1-2, pp. 19-33. https://doi.org/10.1007/s11207-011-9873-8

}

TY - JOUR

T1 - Multichannel Three-Dimensional SOLA Inversion for Local Helioseismology

AU - Jackiewicz, J.

AU - Birch, A. C.

AU - Gizon, Laurent

AU - Hanasoge, Shravan

AU - Hohage, T.

AU - Ruffio, J. B.

AU - Švanda, M.

PY - 2012/2/1

Y1 - 2012/2/1

N2 - 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.

AB - 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.

KW - Helioseismology

KW - Inverse modeling

UR - http://www.scopus.com/inward/record.url?scp=84856120924&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84856120924&partnerID=8YFLogxK

U2 - 10.1007/s11207-011-9873-8

DO - 10.1007/s11207-011-9873-8

M3 - Article

VL - 276

SP - 19

EP - 33

JO - Solar Physics

JF - Solar Physics

SN - 0038-0938

IS - 1-2

ER -