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The first arriving signal (FAS) in a layered waveguide is investigated. It iswell known that the velocity of such a signal is close to the velocity of thefastest medium in the waveguide, and it may be bigger than the fastest groupvelocity given by the dispersion diagram of the waveguide. Usually the FASpulse decays with the propagation distance. A model layered waveguide isstudied in the paper. It is shown that the FAS is associated with thepseudo-branch structure of the dispersion diagram. The velocity is determinedby the slope of the pseudo-branch. The decay is exponential and it depends onthe structure of the pseudo-branch. A new type of phase integral is introducedfor FAS.

First arriving signals in layered waveguides. An approach based on dispersion diagrams