Analytical Models for Cross‐Correlation Signal in Time‐Distance Helioseismology

In time-distance helioseismology, the time signals (Doppler shifts) at twopoints on the solar surface, separated by a fixed angular distance arecross-correlated, and this leads to a wave packet signal. Accurately measuringthe travel times of these wave packets is crucial for inferring the sub-surfaceproperties in the Sun. The observed signal is quite noisy, and to improve thesignal-to-noise ratio and make the cross-correlation more robust, the temporaloscillation signal is phase-speed filtered at the two points in order to selectwaves that travel a fixed horizontal distance. Hence a new formula to estimatethe travel times is derived, in the presence of a phase speed filter, and itincludes both the radial and horizontal component of the oscillationdisplacement signal. It generalizes the previously used Gabor wavelet that wasderived without a phase speed filter and included only the radial component ofthe displacement. This is important since it will be consistent with theobserved cross-correlation that is computed using a phase speed filter, andalso it accounts for both the components of the displacement. The new formuladepends on the location of the two points on the solar surface that are beingcross correlated and accounts for the travel time shifts at different locationson the solar surface.Comment: 27 pages, 8 figures, ApJ in pres