Statistics of the two-point cross-covariance function of solar oscillations
1 Max-Planck-Institut für
Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany
2 National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan
3 Department of Astronomical Science, SOKENDAI (the Graduate University for Advanced Studies), Mitaka, Tokyo 181-8588, Japan
4 Institut für Astrophysik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
Accepted: 17 June 2016
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.
Key words: Sun: helioseismology / Sun: oscillations / methods: data analysis
© ESO, 2016