  High-Mass X-ray Binaries (HMXBs) offer a unique opportunity for the
investigation of accretion onto compact objects and of wind structure in
massive stars. A key source for such studies is the bright neutron star HMXB
Vela X-1 whose convenient physical and orbital parameters facilitate the
analysis and in particular enable studies of the wind structure in HMXBs. Here,
we analyse simultaneous XMM-Newton and NuSTAR observations at
$\phi_{\mathrm{orb}} \approx$ 0.36-0.52 and perform time-resolved spectral
analysis down to the pulse period of the neutron star, based on our previous
NuSTAR-only results. For the first time, we are able to trace the onset of the
wakes in a broad 0.5-78 keV range with a high-time resolution of $\sim$283 s
and compare to theoretical predictions. We observe a clear rise of the
absorption column density of the stellar wind $N_{\mathrm{H,1}}$ starting at
orbital phase $\sim$0.44, corresponding to the wake structure entering our line
of sight towards the neutron star, together with local extrema throughout the
observation possibly associated with clumps or other structures in the wind.
Periods of high absorption reveal the presence of multiple fluorescent emission
lines of highly ionised species, mainly in the soft X-ray band between 0.5 and
4 keV, indicating photoionisation of the wind.
