Statistics of the two-point cross-covariance function of solar oscillations

Kaori Nagashima, Takashi Sekii, Laurent Gizon, Aaron C. Birch

    Research output: Contribution to journalArticle

    Abstract

    Context. The cross-covariance of solar oscillations observed at pairs of points on the solar surface is a fundamental ingredient in time-distance helioseismology. Wave travel times are extracted from the cross-covariance function and are used to infer the physical conditions in the solar interior. Aims. Understanding the statistics of the two-point cross-covariance function is a necessary step towards optimizing the measurement of travel times. Methods. By modeling stochastic solar oscillations, we evaluate the variance of the cross-covariance function as function of time-lag and distance between the two points. Results. We show that the variance of the cross-covariance is independent of both time-lag and distance in the far field, that is, when they are large compared to the coherence scales of the solar oscillations. Conclusions. The constant noise level for the cross-covariance means that the signal-to-noise ratio for the cross-covariance is proportional to the amplitude of the expectation value of the cross-covariance. This observation is important for planning data analysis efforts.

    Original languageEnglish (US)
    Article numberA41
    JournalAstronomy and Astrophysics
    Volume593
    DOIs
    StatePublished - Sep 1 2016

    Fingerprint

    solar oscillations
    oscillation
    statistics
    travel time
    signal-to-noise ratio
    travel
    time lag
    solar interior
    helioseismology
    modeling
    ingredients
    planning
    far fields
    signal to noise ratios

    Keywords

    • Methods: data analysis
    • Sun: helioseismology
    • Sun: oscillations

    ASJC Scopus subject areas

    • Astronomy and Astrophysics
    • Space and Planetary Science

    Cite this

    Statistics of the two-point cross-covariance function of solar oscillations. / Nagashima, Kaori; Sekii, Takashi; Gizon, Laurent; Birch, Aaron C.

    In: Astronomy and Astrophysics, Vol. 593, A41, 01.09.2016.

    Research output: Contribution to journalArticle

    Nagashima, Kaori ; Sekii, Takashi ; Gizon, Laurent ; Birch, Aaron C. / Statistics of the two-point cross-covariance function of solar oscillations. In: Astronomy and Astrophysics. 2016 ; Vol. 593.
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    abstract = "Context. The cross-covariance of solar oscillations observed at pairs of points on the solar surface is a fundamental ingredient in time-distance helioseismology. Wave travel times are extracted from the cross-covariance function and are used to infer the physical conditions in the solar interior. Aims. Understanding the statistics of the two-point cross-covariance function is a necessary step towards optimizing the measurement of travel times. Methods. By modeling stochastic solar oscillations, we evaluate the variance of the cross-covariance function as function of time-lag and distance between the two points. Results. We show that the variance of the cross-covariance is independent of both time-lag and distance in the far field, that is, when they are large compared to the coherence scales of the solar oscillations. Conclusions. The constant noise level for the cross-covariance means that the signal-to-noise ratio for the cross-covariance is proportional to the amplitude of the expectation value of the cross-covariance. This observation is important for planning data analysis efforts.",
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