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

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N2 - 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.

AB - 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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