  We use molecular dynamics simulations to study the formation of surface waves
in vertically vibrated granular material. We find that horizontal movements of
particles, which are essential for the formation of the waves, consist of two
distinct processes. First, the movements sharply increase while the particles
are colliding with a bottom plate, where the duration of the collisions is very
short compared to the period of the vibration. Next, the movements gradually
decrease between the collisions, during which the particles move through the
material. We also find that the horizontal velocity field after the collisions
is strongly correlated to the surface profile before the collisions.
