  Aims. Recent studies showed that time--distance inversions for flows start to
be dominated by a random noise at a depth of only a few Mm. It was proposed
that the ensemble averaging might be a solution to learn about the structure of
the convective flows, e.g., about the depth structure of supergranulation.
Methods. Time--distance inversion is applied to the statistical sample of
~$10^4$ supergranules, which allows to regularise weakly about the random-noise
term of the inversion cost function and hence to have a much better
localisation in space. We compare these inversions at four depths (1.9, 2.9,
4.3, and 6.2 Mm) when using different spatio-temporal filtering schemes in
order to gain confidence about these inferences. Results. The flows inferred by
using different spatio-temporal filtering schemes are different (even by the
sign) even-though the formal averaging kernels and the random-noise levels are
very similar. The inverted flows alterates its sign several times with depth.
It is suggested that this is due to the inaccuracies in the forward problem
that are possibly amplified by the inversion. It is possible that also other
time--distance inversions are affected by this issue.
