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

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