  We present here a detailed study of the influence of the transverse motion of
the atoms in a free-fall gravimeter. By implementing Raman selection in the
horizontal directions at the beginning of the atoms free fall, we characterize
the effective velocity distribution, ie the velocity distribution of the
detected atom, as a function of the laser cooling and trapping parameters. In
particular, we show that the response of the detection induces a pronounced
asymetry of this effective velocity distribution that depends not only on the
imbalance between molasses beams but also on the initial position of the
displaced atomic sample. This convolution with the detection has a strong
influence on the averaging of the bias due to Coriolis acceleration. The
present study allows a fairly good understanding of results previously
published in {\it Louchet-Chauvet et al., NJP 13, 065025 (2011)}, where the
mean phase shift due to Coriolis acceleration was found to have a sign
different from expected.
