The solar atmosphere is extremely dynamic, and many important phenomena develop on small scales that are unresolved in observations with the Helioseismic and Magnetic Imager (HMI) instrument on the Solar Dynamics Observatory (SDO). For correct calibration and interpretation of the observations, it is very important to investigate the effects of small-scale structures and dynamics on the HMI observables, such as Doppler shift, continuum intensity, spectral line depth, and width. We use 3D radiative hydrodynamics simulations of the upper turbulent convective layer and the atmosphere of the Sun, and a spectro-polarimetric radiative transfer code to study observational characteristics of the Fe I 6173A line observed by HMI in quiet-Sun regions. We use the modeling results to investigate the sensitivity of the line Doppler shift to plasma velocity, and also sensitivities of the line parameters to plasma temperature and density, and determine effective line formation heights for observations of solar regions located at different distances from the disc center. These estimates are important for the interpretation of helioseismology measurements. In addition, we consider various center-to-limb effects, such as convective blue-shift, variations of helioseismic travel-times, and the concave Sun effect, and show that the simulations can qualitatively reproduce the observed phenomena, indicating that these effects are related to a complex interaction of the solar dynamics and radiative transfer.
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