  Understanding convection is important in stellar physics, for example as an
input in stellar evolution models. Helioseismic estimates of convective flow
amplitudes in deeper regions of the solar interior disagree by orders of
magnitude among themselves and with simulations. We aim to assess the validity
of an existing upper limit of solar convective flow amplitudes at a depth of
0.96 solar radii obtained using time-distance helioseismology and several
simplifying assumptions. We generated synthetic observations for convective
flow fields from a magnetohydrodynamic simulation (MURaM) using travel-time
sensitivity functions and a noise model. We compared the estimates of the flow
with the actual values. For the scales of interest ($\ell<100$), we find that
the current procedure for obtaining an upper limit gives the correct order of
magnitude of the flow for the given flow fields. We also show that this
estimate is not an upper limit in a strict sense because it underestimates the
flow amplitude at the largest scales by a factor of about two because the scale
dependence of the signal-to-noise ratio has to be taken into account. After
correcting for this and after taking the dependence of the measurements on
direction in Fourier space into account, we show that the obtained estimate is
indeed an upper limit. We conclude that time-distance helioseismology is able
to correctly estimate the order of magnitude (or an upper limit) of solar
convective flows in the deeper interior when the vertical correlation function
of the different flow components is known and the scale dependence of the
signal-to-noise ratio is taken into account. We suggest that future work should
include information from different target depths to better separate the effect
of near-surface flows from those at greater depths. The measurements are
sensitive to all three flow directions, which should be taken into account.
