### 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 language | English (US) |
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Article number | A41 |

Journal | Astronomy and Astrophysics |

Volume | 593 |

DOIs | |

State | Published - Sep 1 2016 |

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### Keywords

- Methods: data analysis
- Sun: helioseismology
- Sun: oscillations

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astronomy and Astrophysics*,

*593*, [A41]. https://doi.org/10.1051/0004-6361/201628129