Closed-form Asymptotic Solution Research Articles

Propagation Calculations for a Parabolic Velocity Profile

The normal-mode series solution for the parabolic velocity of sound profile Co2/C2 = 1 − a2Z2 is discussed. The full series representation was evaluated to exhibit focusing in both range and depth, show the effect of frequency on focusing, validate the series cutoff indicated by analysis, and test an asymptotic closed-form solution valid near the convergence zones [H. Überall and N. C. Nicholas, J. Acoust. Soc. Amer. 44, 1259–1261 (1968)].