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

TL;DR

This paper investigates the first arriving signal in layered waveguides, linking it to dispersion diagram pseudo-branches, and introduces a new phase integral to better understand its velocity and decay characteristics.

Contribution

It presents a novel approach connecting FAS to pseudo-branch structures in dispersion diagrams and introduces a new phase integral for analysis.

Findings

FAS velocity relates to pseudo-branch slope

FAS decay is exponential and structure-dependent

New phase integral for FAS analysis

Abstract

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.