摘要：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.
关键词：Sun: helioseismology;Sun: oscillations;methods: data analysis
