Computational helioseismology in the frequency domain

Acoustic waves in axisymmetric solar models with flows

Laurent Gizon, Hélène Barucq, Marc Duruflé, Chris S. Hanson, Michael Leguèbe, Aaron C. Birch, Juliette Chabassier, Damien Fournier, Thorsten Hohage, Emanuele Papini

    Research output: Contribution to journalArticle

    Abstract

    Context. Local helioseismology has so far relied on semi-analytical methods to compute the spatial sensitivity of wave travel times to perturbations in the solar interior. These methods are cumbersome and lack flexibility. Aims. Here we propose a convenient framework for numerically solving the forward problem of time-distance helioseismology in the frequency domain. The fundamental quantity to be computed is the cross-covariance of the seismic wavefield. Methods. We choose sources of wave excitation that enable us to relate the cross-covariance of the oscillations to the Green's function in a straightforward manner. We illustrate the method by considering the 3D acoustic wave equation in an axisymmetric reference solar model, ignoring the effects of gravity on the waves. The symmetry of the background model around the rotation axis implies that the Green's function can be written as a sum of longitudinal Fourier modes, leading to a set of independent 2D problems. We use a high-order finite-element method to solve the 2D wave equation in frequency space. The computation is embarrassingly parallel, with each frequency and each azimuthal order solved independently on a computer cluster. Results. We compute travel-time sensitivity kernels in spherical geometry for flows, sound speed, and density perturbations under the first Born approximation. Convergence tests show that travel times can be computed with a numerical precision better than one millisecond, as required by the most precise travel-time measurements. Conclusions. The method presented here is computationally efficient and will be used to interpret travel-time measurements in order to infer, e.g., the large-scale meridional flow in the solar convection zone. It allows the implementation of (full-waveform) iterative inversions, whereby the axisymmetric background model is updated at each iteration.

    Original languageEnglish (US)
    Article numberA35
    JournalAstronomy and Astrophysics
    Volume600
    DOIs
    StatePublished - Apr 1 2017

    Fingerprint

    helioseismology
    acoustic wave
    travel time
    travel
    acoustics
    Green function
    wave equation
    wave equations
    Green's functions
    time measurement
    perturbation
    meridional flow
    solar interior
    Born approximation
    sensitivity
    wave excitation
    finite element method
    iteration
    symmetry
    analytical method

    Keywords

    • Sun: Helioseismology
    • Sun: Interior
    • Sun: Oscillations

    ASJC Scopus subject areas

    • Astronomy and Astrophysics
    • Space and Planetary Science

    Cite this

    Gizon, L., Barucq, H., Duruflé, M., Hanson, C. S., Leguèbe, M., Birch, A. C., ... Papini, E. (2017). Computational helioseismology in the frequency domain: Acoustic waves in axisymmetric solar models with flows. Astronomy and Astrophysics, 600, [A35]. https://doi.org/10.1051/0004-6361/201629470

    Computational helioseismology in the frequency domain : Acoustic waves in axisymmetric solar models with flows. / Gizon, Laurent; Barucq, Hélène; Duruflé, Marc; Hanson, Chris S.; Leguèbe, Michael; Birch, Aaron C.; Chabassier, Juliette; Fournier, Damien; Hohage, Thorsten; Papini, Emanuele.

    In: Astronomy and Astrophysics, Vol. 600, A35, 01.04.2017.

    Research output: Contribution to journalArticle

    Gizon, L, Barucq, H, Duruflé, M, Hanson, CS, Leguèbe, M, Birch, AC, Chabassier, J, Fournier, D, Hohage, T & Papini, E 2017, 'Computational helioseismology in the frequency domain: Acoustic waves in axisymmetric solar models with flows', Astronomy and Astrophysics, vol. 600, A35. https://doi.org/10.1051/0004-6361/201629470
    Gizon, Laurent ; Barucq, Hélène ; Duruflé, Marc ; Hanson, Chris S. ; Leguèbe, Michael ; Birch, Aaron C. ; Chabassier, Juliette ; Fournier, Damien ; Hohage, Thorsten ; Papini, Emanuele. / Computational helioseismology in the frequency domain : Acoustic waves in axisymmetric solar models with flows. In: Astronomy and Astrophysics. 2017 ; Vol. 600.
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    abstract = "Context. Local helioseismology has so far relied on semi-analytical methods to compute the spatial sensitivity of wave travel times to perturbations in the solar interior. These methods are cumbersome and lack flexibility. Aims. Here we propose a convenient framework for numerically solving the forward problem of time-distance helioseismology in the frequency domain. The fundamental quantity to be computed is the cross-covariance of the seismic wavefield. Methods. We choose sources of wave excitation that enable us to relate the cross-covariance of the oscillations to the Green's function in a straightforward manner. We illustrate the method by considering the 3D acoustic wave equation in an axisymmetric reference solar model, ignoring the effects of gravity on the waves. The symmetry of the background model around the rotation axis implies that the Green's function can be written as a sum of longitudinal Fourier modes, leading to a set of independent 2D problems. We use a high-order finite-element method to solve the 2D wave equation in frequency space. The computation is embarrassingly parallel, with each frequency and each azimuthal order solved independently on a computer cluster. Results. We compute travel-time sensitivity kernels in spherical geometry for flows, sound speed, and density perturbations under the first Born approximation. Convergence tests show that travel times can be computed with a numerical precision better than one millisecond, as required by the most precise travel-time measurements. Conclusions. The method presented here is computationally efficient and will be used to interpret travel-time measurements in order to infer, e.g., the large-scale meridional flow in the solar convection zone. It allows the implementation of (full-waveform) iterative inversions, whereby the axisymmetric background model is updated at each iteration.",
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    AU - Gizon, Laurent

    AU - Barucq, Hélène

    AU - Duruflé, Marc

    AU - Hanson, Chris S.

    AU - Leguèbe, Michael

    AU - Birch, Aaron C.

    AU - Chabassier, Juliette

    AU - Fournier, Damien

    AU - Hohage, Thorsten

    AU - Papini, Emanuele

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    N2 - Context. Local helioseismology has so far relied on semi-analytical methods to compute the spatial sensitivity of wave travel times to perturbations in the solar interior. These methods are cumbersome and lack flexibility. Aims. Here we propose a convenient framework for numerically solving the forward problem of time-distance helioseismology in the frequency domain. The fundamental quantity to be computed is the cross-covariance of the seismic wavefield. Methods. We choose sources of wave excitation that enable us to relate the cross-covariance of the oscillations to the Green's function in a straightforward manner. We illustrate the method by considering the 3D acoustic wave equation in an axisymmetric reference solar model, ignoring the effects of gravity on the waves. The symmetry of the background model around the rotation axis implies that the Green's function can be written as a sum of longitudinal Fourier modes, leading to a set of independent 2D problems. We use a high-order finite-element method to solve the 2D wave equation in frequency space. The computation is embarrassingly parallel, with each frequency and each azimuthal order solved independently on a computer cluster. Results. We compute travel-time sensitivity kernels in spherical geometry for flows, sound speed, and density perturbations under the first Born approximation. Convergence tests show that travel times can be computed with a numerical precision better than one millisecond, as required by the most precise travel-time measurements. Conclusions. The method presented here is computationally efficient and will be used to interpret travel-time measurements in order to infer, e.g., the large-scale meridional flow in the solar convection zone. It allows the implementation of (full-waveform) iterative inversions, whereby the axisymmetric background model is updated at each iteration.

    AB - Context. Local helioseismology has so far relied on semi-analytical methods to compute the spatial sensitivity of wave travel times to perturbations in the solar interior. These methods are cumbersome and lack flexibility. Aims. Here we propose a convenient framework for numerically solving the forward problem of time-distance helioseismology in the frequency domain. The fundamental quantity to be computed is the cross-covariance of the seismic wavefield. Methods. We choose sources of wave excitation that enable us to relate the cross-covariance of the oscillations to the Green's function in a straightforward manner. We illustrate the method by considering the 3D acoustic wave equation in an axisymmetric reference solar model, ignoring the effects of gravity on the waves. The symmetry of the background model around the rotation axis implies that the Green's function can be written as a sum of longitudinal Fourier modes, leading to a set of independent 2D problems. We use a high-order finite-element method to solve the 2D wave equation in frequency space. The computation is embarrassingly parallel, with each frequency and each azimuthal order solved independently on a computer cluster. Results. We compute travel-time sensitivity kernels in spherical geometry for flows, sound speed, and density perturbations under the first Born approximation. Convergence tests show that travel times can be computed with a numerical precision better than one millisecond, as required by the most precise travel-time measurements. Conclusions. The method presented here is computationally efficient and will be used to interpret travel-time measurements in order to infer, e.g., the large-scale meridional flow in the solar convection zone. It allows the implementation of (full-waveform) iterative inversions, whereby the axisymmetric background model is updated at each iteration.

    KW - Sun: Helioseismology

    KW - Sun: Interior

    KW - Sun: Oscillations

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