  The first arriving signal (FAS) in a layered waveguide is investigated. It is
well known that the velocity of such a signal is close to the velocity of the
fastest medium in the waveguide, and it may be bigger than the fastest group
velocity given by the dispersion diagram of the waveguide. Usually the FAS
pulse decays with the propagation distance. A model layered waveguide is
studied in the paper. It is shown that the FAS is associated with the
pseudo-branch structure of the dispersion diagram. The velocity is determined
by the slope of the pseudo-branch. The decay is exponential and it depends on
the structure of the pseudo-branch. A new type of phase integral is introduced
for FAS.
