  This paper investigates the onset time of Solar Energetic Particle (SEP)
events with numerical simulations, and analyses the accuracy of the Velocity
Dispersion Analysis (VDA) method. Using a 3-dimensional focused transport
model, we calculate the fluxes of protons observed in the ecliptic at 1 AU in
the energy range between 10 MeV and 80 MeV. In particular, three models are
used to describe different SEP sources produced by flare or coronal shock, and
the effects of particle perpendicular diffusion in the interplanetary space are
also studied. We have the following findings: When the observer is disconnected
from the source, the effects of perpendicular diffusion in the interplanetary
space and particles propagating in the solar atmosphere have significant
influence on the VDA results. As a result, although the VDA method is valid
with impulsive source duration, low background, and weak scattering in the
interplanetary space or fast diffusion in the solar atmosphere, the method is
not valid with gradual source duration, high background, or strong scattering.
