Signal and noise in helioseismic holography

Laurent Gizon, Damien Fournier, Dan Yang, Aaron C. Birch, Hélène Barucq

    Research output: Contribution to journalArticle

    Abstract

    Context. Helioseismic holography is an imaging technique used to study heterogeneities and flows in the solar interior from observations of solar oscillations at the surface. Holographic images contain noise due to the stochastic nature of solar oscillations. Aims. We aim to provide a theoretical framework for modeling signal and noise in Porter-Bojarski helioseismic holography. Methods. The wave equation may be recast into a Helmholtz-like equation, so as to connect with the acoustics literature and define the holography Green's function in a meaningful way. Sources of wave excitation are assumed to be stationary, horizontally homogeneous, and spatially uncorrelated. Using the first Born approximation we calculated holographic images in the presence of perturbations in sound-speed, density, flows, and source covariance, as well as the noise level as a function of position. This work is a direct extension of the methods used in time-distance helioseismology to model signal and noise. Results. To illustrate the theory, we compute the holographic image intensity numerically for a buried sound-speed perturbation at different depths in the solar interior. The reference Green's function is obtained for a spherically-symmetric solar model using a finite-element solver in the frequency domain. Below the pupil area on the surface, we find that the spatial resolution of the holographic image intensity is very close to half the local wavelength. For a sound-speed perturbation of size comparable to the local spatial resolution, the signal-To-noise ratio is approximately constant with depth. Averaging the image intensity over a number N of frequencies above 3 mHz increases the signal-To-noise ratio by a factor nearly equal to the square root of N. This may not be the case at lower frequencies, where large variations in the holographic signal are due to the contributions from the long-lived modes of oscillation.

    Original languageEnglish (US)
    Article numberA136
    JournalAstronomy and Astrophysics
    Volume620
    DOIs
    StatePublished - Dec 1 2018

    Fingerprint

    holography
    solar interior
    solar oscillations
    acoustics
    oscillation
    perturbation
    Green function
    signal-to-noise ratio
    spatial resolution
    signal to noise ratios
    Green's functions
    Born approximation
    helioseismology
    Helmholtz equations
    wave excitation
    pupils
    wave equation
    density current
    imaging techniques
    wave equations

    Keywords

    • Sun: helioseismology
    • Sun: interior
    • Sun: oscillations

    ASJC Scopus subject areas

    • Astronomy and Astrophysics
    • Space and Planetary Science

    Cite this

    Gizon, L., Fournier, D., Yang, D., Birch, A. C., & Barucq, H. (2018). Signal and noise in helioseismic holography. Astronomy and Astrophysics, 620, [A136]. https://doi.org/10.1051/0004-6361/201833825

    Signal and noise in helioseismic holography. / Gizon, Laurent; Fournier, Damien; Yang, Dan; Birch, Aaron C.; Barucq, Hélène.

    In: Astronomy and Astrophysics, Vol. 620, A136, 01.12.2018.

    Research output: Contribution to journalArticle

    Gizon, L, Fournier, D, Yang, D, Birch, AC & Barucq, H 2018, 'Signal and noise in helioseismic holography', Astronomy and Astrophysics, vol. 620, A136. https://doi.org/10.1051/0004-6361/201833825
    Gizon L, Fournier D, Yang D, Birch AC, Barucq H. Signal and noise in helioseismic holography. Astronomy and Astrophysics. 2018 Dec 1;620. A136. https://doi.org/10.1051/0004-6361/201833825
    Gizon, Laurent ; Fournier, Damien ; Yang, Dan ; Birch, Aaron C. ; Barucq, Hélène. / Signal and noise in helioseismic holography. In: Astronomy and Astrophysics. 2018 ; Vol. 620.
    @article{86700ccf40c54af380abf933669ed380,
    title = "Signal and noise in helioseismic holography",
    abstract = "Context. Helioseismic holography is an imaging technique used to study heterogeneities and flows in the solar interior from observations of solar oscillations at the surface. Holographic images contain noise due to the stochastic nature of solar oscillations. Aims. We aim to provide a theoretical framework for modeling signal and noise in Porter-Bojarski helioseismic holography. Methods. The wave equation may be recast into a Helmholtz-like equation, so as to connect with the acoustics literature and define the holography Green's function in a meaningful way. Sources of wave excitation are assumed to be stationary, horizontally homogeneous, and spatially uncorrelated. Using the first Born approximation we calculated holographic images in the presence of perturbations in sound-speed, density, flows, and source covariance, as well as the noise level as a function of position. This work is a direct extension of the methods used in time-distance helioseismology to model signal and noise. Results. To illustrate the theory, we compute the holographic image intensity numerically for a buried sound-speed perturbation at different depths in the solar interior. The reference Green's function is obtained for a spherically-symmetric solar model using a finite-element solver in the frequency domain. Below the pupil area on the surface, we find that the spatial resolution of the holographic image intensity is very close to half the local wavelength. For a sound-speed perturbation of size comparable to the local spatial resolution, the signal-To-noise ratio is approximately constant with depth. Averaging the image intensity over a number N of frequencies above 3 mHz increases the signal-To-noise ratio by a factor nearly equal to the square root of N. This may not be the case at lower frequencies, where large variations in the holographic signal are due to the contributions from the long-lived modes of oscillation.",
    keywords = "Sun: helioseismology, Sun: interior, Sun: oscillations",
    author = "Laurent Gizon and Damien Fournier and Dan Yang and Birch, {Aaron C.} and H{\'e}l{\`e}ne Barucq",
    year = "2018",
    month = "12",
    day = "1",
    doi = "10.1051/0004-6361/201833825",
    language = "English (US)",
    volume = "620",
    journal = "Astronomy and Astrophysics",
    issn = "0004-6361",
    publisher = "EDP Sciences",

    }

    TY - JOUR

    T1 - Signal and noise in helioseismic holography

    AU - Gizon, Laurent

    AU - Fournier, Damien

    AU - Yang, Dan

    AU - Birch, Aaron C.

    AU - Barucq, Hélène

    PY - 2018/12/1

    Y1 - 2018/12/1

    N2 - Context. Helioseismic holography is an imaging technique used to study heterogeneities and flows in the solar interior from observations of solar oscillations at the surface. Holographic images contain noise due to the stochastic nature of solar oscillations. Aims. We aim to provide a theoretical framework for modeling signal and noise in Porter-Bojarski helioseismic holography. Methods. The wave equation may be recast into a Helmholtz-like equation, so as to connect with the acoustics literature and define the holography Green's function in a meaningful way. Sources of wave excitation are assumed to be stationary, horizontally homogeneous, and spatially uncorrelated. Using the first Born approximation we calculated holographic images in the presence of perturbations in sound-speed, density, flows, and source covariance, as well as the noise level as a function of position. This work is a direct extension of the methods used in time-distance helioseismology to model signal and noise. Results. To illustrate the theory, we compute the holographic image intensity numerically for a buried sound-speed perturbation at different depths in the solar interior. The reference Green's function is obtained for a spherically-symmetric solar model using a finite-element solver in the frequency domain. Below the pupil area on the surface, we find that the spatial resolution of the holographic image intensity is very close to half the local wavelength. For a sound-speed perturbation of size comparable to the local spatial resolution, the signal-To-noise ratio is approximately constant with depth. Averaging the image intensity over a number N of frequencies above 3 mHz increases the signal-To-noise ratio by a factor nearly equal to the square root of N. This may not be the case at lower frequencies, where large variations in the holographic signal are due to the contributions from the long-lived modes of oscillation.

    AB - Context. Helioseismic holography is an imaging technique used to study heterogeneities and flows in the solar interior from observations of solar oscillations at the surface. Holographic images contain noise due to the stochastic nature of solar oscillations. Aims. We aim to provide a theoretical framework for modeling signal and noise in Porter-Bojarski helioseismic holography. Methods. The wave equation may be recast into a Helmholtz-like equation, so as to connect with the acoustics literature and define the holography Green's function in a meaningful way. Sources of wave excitation are assumed to be stationary, horizontally homogeneous, and spatially uncorrelated. Using the first Born approximation we calculated holographic images in the presence of perturbations in sound-speed, density, flows, and source covariance, as well as the noise level as a function of position. This work is a direct extension of the methods used in time-distance helioseismology to model signal and noise. Results. To illustrate the theory, we compute the holographic image intensity numerically for a buried sound-speed perturbation at different depths in the solar interior. The reference Green's function is obtained for a spherically-symmetric solar model using a finite-element solver in the frequency domain. Below the pupil area on the surface, we find that the spatial resolution of the holographic image intensity is very close to half the local wavelength. For a sound-speed perturbation of size comparable to the local spatial resolution, the signal-To-noise ratio is approximately constant with depth. Averaging the image intensity over a number N of frequencies above 3 mHz increases the signal-To-noise ratio by a factor nearly equal to the square root of N. This may not be the case at lower frequencies, where large variations in the holographic signal are due to the contributions from the long-lived modes of oscillation.

    KW - Sun: helioseismology

    KW - Sun: interior

    KW - Sun: oscillations

    UR - http://www.scopus.com/inward/record.url?scp=85058441475&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=85058441475&partnerID=8YFLogxK

    U2 - 10.1051/0004-6361/201833825

    DO - 10.1051/0004-6361/201833825

    M3 - Article

    VL - 620

    JO - Astronomy and Astrophysics

    JF - Astronomy and Astrophysics

    SN - 0004-6361

    M1 - A136

    ER -