Corrections to the Magnitude of Cross-Correlation Functions for Dispersion of Solar Acoustic Waves

The cross-correlation function is a useful tool in helioseismology. The magnitude of the cross-correlation function has been used to represent the power of wave packets. Dispersion causes a decrease in amplitude and an increase in width of wave packets. This leads to a decrease in magnitude and an increase in width of cross-correlation functions. The effect of dispersion on the magnitude of cross-correlation functions needs to be adequately corrected for in order to use the magnitude of cross-correlation functions to represent the power of wave packets. In this study, we investigate how the magnitude of cross-correlation functions changes with the number of skips owing to dispersion and the method to correct it. Our study, using simulated and observational data, indicates that the correction should be three dimensional instead of the one-dimensional correction adopted in previous studies. Using the three-dimensional correction, the measured dissipation rate in the quiet Sun is smaller than the value of previous studies.