  To understand the origin of Solar Energetic Particles (SEPs), we must study
their injection time relative to other solar eruption manifestations.
Traditionally the injection time is determined using the Velocity Dispersion
Analysis (VDA) where a linear fit of the observed event onset times at 1 AU to
the inverse velocities of SEPs is used to derive the injection time and path
length of the first-arriving particles. VDA does not, however, take into
account that the particles that produce a statistically observable onset at 1
AU have scattered in the interplanetary space. We use Monte Carlo test particle
simulations of energetic protons to study the effect of particle scattering on
the observable SEP event onset above pre-event background, and consequently on
VDA results. We find that the VDA results are sensitive to the properties of
the pre-event and event particle spectra as well as SEP injection and
scattering parameters. In particular, a VDA-obtained path length that is close
to the nominal Parker spiral length does not imply that the VDA injection time
is correct. We study the delay to the observed onset caused by scattering of
the particles and derive a simple estimate for the delay time by using the rate
of intensity increase at the SEP onset as a parameter. We apply the correction
to a magnetically well-connected SEP event of June 10 2000, and show it to
improve both the path length and injection time estimates, while also
increasing the error limits to better reflect the inherent uncertainties of
VDA.
