Sensitivity kernels for time-distance helioseismology: Efficient computation for spherically symmetric solar models

Damien Fournier, Chris S. Hanson, Laurent Gizon, Hélène Barucq

Research output: Contribution to journalArticle

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 languageEnglish (US)
Article numberA156
JournalAstronomy and Astrophysics
Volume616
DOIs
StatePublished - Aug 1 2018

Fingerprint

Born approximation
helioseismology
Green function
travel time
sensitivity
spherical harmonics
longitude
travel
decomposition
wavelength
Green's functions
meridional flow
solar interior
Legendre functions
products
rays
poles
method
product
inversions

Keywords

  • Methods: numerical
  • Sun: helioseismology
  • Sun: interior
  • Sun: oscillations

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

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

In: Astronomy and Astrophysics, Vol. 616, A156, 01.08.2018.

Research output: Contribution to journalArticle

@article{1de501e451974bce9b185aab57e419bd,
title = "Sensitivity kernels for time-distance helioseismology: Efficient computation for spherically symmetric solar models",
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.",
keywords = "Methods: numerical, Sun: helioseismology, Sun: interior, Sun: oscillations",
author = "Damien Fournier and Hanson, {Chris S.} and Laurent Gizon and H{\'e}l{\`e}ne Barucq",
year = "2018",
month = "8",
day = "1",
doi = "10.1051/0004-6361/201833206",
language = "English (US)",
volume = "616",
journal = "Astronomy and Astrophysics",
issn = "0004-6361",
publisher = "EDP Sciences",

}

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 -