Effect of Foreshortening on Center-to-Limb Variations of Measured Acoustic Travel Times

We use data observed near the solar disk center by the Solar Dynamics Observatory/Helioseismic and Magnetic Imager (SDO/HMI) to mimic observations at high-latitude areas after applying geometric transform and projection. These data are then used to study how foreshortening affects the time-distance measurements of acoustic travel times. We find that foreshortening reduces the measured mean travel-times through altering the acoustic-power weighting in different harmonic degrees, but the level of reduction and the latitude dependence are not as strong as those measured from the observation data at the same latitude. Foreshortening is not found to be accountable for the systematic center-to-limb effect in the measured acoustic travel-time differences, which is an essential factor for a reliable inference of the Sun's meridional-circulation profile. The differences in the acoustic power spectrum between the mimicked data and the observation data in high-latitude areas suggest that the optical spectrum-line formation height or convection cells in these areas may be the primary cause of the center-to-limb effect in helioseismic analyses.