  As large--distance rays (say, 10\,-\,$24 ^\circ$) approach the solar surface
approximately vertically, travel times measured from surface pairs for these
large separations are mostly sensitive to vertical flows, at least for shallow
flows within a few Mm of the solar surface. All previous analyses of
supergranulation have used smaller separations and have been hampered by the
difficulty of separating the horizontal and vertical flow components. We find
that the large separation travel times associated with supergranulation cannot
be studied using the standard phase-speed filters of time-distance
helioseismology. These filters, whose use is based upon a refractive model of
the perturbations, reduce the resultant travel time signal by at least an order
of magnitude at some distances. More effective filters are derived. Modeling
suggests that the center--annulus travel time difference $[\delta t_{\rm{oi}}]$
in the separation range $\Delta=10$\,-\,$24 ^\circ$ is insensitive to the
horizontally diverging flow from the centers of the supergranules and should
lead to a constant signal from the vertical flow. Our measurement of this
quantity, $5.1 \pm 0.1\secs$, is constant over the distance range. This
magnitude of signal cannot be caused by the level of upflow at cell centers
seen at the photosphere of $10\ms$ extended in depth. It requires the vertical
flow to increase with depth. A simple Gaussian model of the increase with depth
implies a peak upward flow of $240\ms$ at a depth of $2.3\Mm$ and a peak
horizontal flow of $700\ms$ at a depth of $1.6\Mm$.
