The Solar Dynamics Observatory/Helioseismic and Magnetic Imager (SDO/HMI) filtergrams, taken at six wavelengths around the Fe I 6173.3 {AA} line, contain information about the line-of-sight velocity over a range of heights in the solar atmosphere. Multi-height velocity inferences from these observations can be exploited to study wave motions and energy transport in the atmosphere. Using realistic convection simulation datasets provided by the STAGGER and MURaM codes, we generate synthetic filtergrams and explore several methods for estimating Dopplergrams. We investigate at which height each synthetic Dopplergram correlates most strongly with the vertical velocity in the model atmospheres. On the basis of the investigation, we propose two Dopplergrams other than the standard HMI-algorithm Dopplergram produced from HMI filtergrams: a line-center Dopplergram and an average-wing Dopplergram. These two Dopplergrams correlate most strongly with vertical velocities at the heights of 30 - 40 km above (line-center) and 30 - 40 km below (average-wing) the effective height of the HMI-algorithm Dopplergram. Therefore, we can obtain velocity information from two layers separated by about a half of a scale height in the atmosphere, at best. The phase shifts between these multi-height Dopplergrams from observational data as well as those from the simulated data are also consistent with the height-difference estimates in the frequency range above the photospheric acoustic cutoff frequency.
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