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

    Fournier, Damien ; Hanson, Chris S. ; Gizon, Laurent ; Barucq, Hélène. / Sensitivity kernels for time-distance helioseismology : Efficient computation for spherically symmetric solar models. In: Astronomy and Astrophysics. 2018 ; Vol. 616.
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