### Abstract

Context. The interpretation of helioseismic measurements, such as wave travel-time, is based on the computation of kernels that give the sensitivity of the measurements to localized changes in the solar interior. These kernels are computed using the ray or the Born approximation. The Born approximation is preferable as it takes finite-wavelength effects into account, although it can be computationally expensive. Aims. We propose a fast algorithm to compute travel-time sensitivity kernels under the assumption that the background solar medium is spherically symmetric. Methods. Kernels are typically expressed as products of Green's functions that depend upon depth, latitude, and longitude. Here, we compute the spherical harmonic decomposition of the kernels and show that the integrals in latitude and longitude can be performed analytically. In particular, the integrals of the product of three associated Legendre polynomials can be computed. Results. The computations are fast and accurate and only require the knowledge of the Green's function where the source is at the pole. The computation time is reduced by two orders of magnitude compared to other recent computational frameworks. Conclusions. This new method allows flexible and computationally efficient calculations of a large number of kernels, required in addressing key helioseismic problems. For example, the computation of all the kernels required for meridional flow inversion takes less than two hours on 100 cores.

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

Article number | A156 |

Journal | Astronomy and Astrophysics |

Volume | 616 |

DOIs | |

State | Published - Aug 1 2018 |

### Fingerprint

### Keywords

- Methods: numerical
- Sun: helioseismology
- Sun: interior
- Sun: oscillations

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astronomy and Astrophysics*,

*616*, [A156]. https://doi.org/10.1051/0004-6361/201833206

**Sensitivity kernels for time-distance helioseismology : Efficient computation for spherically symmetric solar models.** / Fournier, Damien; Hanson, Chris S.; Gizon, Laurent; Barucq, Hélène.

Research output: Contribution to journal › Article

*Astronomy and Astrophysics*, vol. 616, A156. https://doi.org/10.1051/0004-6361/201833206

}

TY - JOUR

T1 - Sensitivity kernels for time-distance helioseismology

T2 - Efficient computation for spherically symmetric solar models

AU - Fournier, Damien

AU - Hanson, Chris S.

AU - Gizon, Laurent

AU - Barucq, Hélène

PY - 2018/8/1

Y1 - 2018/8/1

N2 - Context. The interpretation of helioseismic measurements, such as wave travel-time, is based on the computation of kernels that give the sensitivity of the measurements to localized changes in the solar interior. These kernels are computed using the ray or the Born approximation. The Born approximation is preferable as it takes finite-wavelength effects into account, although it can be computationally expensive. Aims. We propose a fast algorithm to compute travel-time sensitivity kernels under the assumption that the background solar medium is spherically symmetric. Methods. Kernels are typically expressed as products of Green's functions that depend upon depth, latitude, and longitude. Here, we compute the spherical harmonic decomposition of the kernels and show that the integrals in latitude and longitude can be performed analytically. In particular, the integrals of the product of three associated Legendre polynomials can be computed. Results. The computations are fast and accurate and only require the knowledge of the Green's function where the source is at the pole. The computation time is reduced by two orders of magnitude compared to other recent computational frameworks. Conclusions. This new method allows flexible and computationally efficient calculations of a large number of kernels, required in addressing key helioseismic problems. For example, the computation of all the kernels required for meridional flow inversion takes less than two hours on 100 cores.

AB - Context. The interpretation of helioseismic measurements, such as wave travel-time, is based on the computation of kernels that give the sensitivity of the measurements to localized changes in the solar interior. These kernels are computed using the ray or the Born approximation. The Born approximation is preferable as it takes finite-wavelength effects into account, although it can be computationally expensive. Aims. We propose a fast algorithm to compute travel-time sensitivity kernels under the assumption that the background solar medium is spherically symmetric. Methods. Kernels are typically expressed as products of Green's functions that depend upon depth, latitude, and longitude. Here, we compute the spherical harmonic decomposition of the kernels and show that the integrals in latitude and longitude can be performed analytically. In particular, the integrals of the product of three associated Legendre polynomials can be computed. Results. The computations are fast and accurate and only require the knowledge of the Green's function where the source is at the pole. The computation time is reduced by two orders of magnitude compared to other recent computational frameworks. Conclusions. This new method allows flexible and computationally efficient calculations of a large number of kernels, required in addressing key helioseismic problems. For example, the computation of all the kernels required for meridional flow inversion takes less than two hours on 100 cores.

KW - Methods: numerical

KW - Sun: helioseismology

KW - Sun: interior

KW - Sun: oscillations

UR - http://www.scopus.com/inward/record.url?scp=85053504568&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85053504568&partnerID=8YFLogxK

U2 - 10.1051/0004-6361/201833206

DO - 10.1051/0004-6361/201833206

M3 - Article

AN - SCOPUS:85053504568

VL - 616

JO - Astronomy and Astrophysics

JF - Astronomy and Astrophysics

SN - 0004-6361

M1 - A156

ER -