First arriving signals in layered waveguides. An approach based on   dispersion diagrams
  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. 
Andrey V. Shanin
math.AP