  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.
