“…Some of these methods include matched field processing which attempts to maximize an objective function which correlates the modeled and measured acoustic fields (Bucker, 1976;Baggeroer et al, 1988;Fawcett et al, 1996); modal decomposition methods which seek to match the modeled and measured modal amplitudes as a function of depth (Shang, 1985;Yang, 1987;Glattetre et al, 1989); matched mode methods which endeavor to match modeled and observed mode amplitudes as measured on a horizontal line array by use of the frequency-wavenumber (f-k) transform (Nicolas et al, 2006); and waveguide invariant approaches which are based on Chuprov's (1982) parameterization relating range and frequency to the slope of the striations in acoustic pressure in a frequency-range plot (Brekhovskikh and Lysanov, 1991;D'Spain and Kuperman, 1999). The waveguide invariant is commonly interpreted in terms of constructive and destructive interference of propagating normal modes (Turgut and Orr, 2010), but it has also been described in terms of ray theory (Gerstoft et al, 2001) and variations in eigenray arrival times (Harrison, 2011), and related to the wavenumber integration technique (Cockrell and Schmidt, 2010).…”