Perturbation Calculations of Propagation Loss in the Deep Ocean

Abstract

Propagation loss expressions were derived by means of perturbation theory corrections to the normal-mode series solution to the acoustical wave equation with parabolic velocity profile and sinusoidal point source. A fourth-order power series was used to approximate nonparabolic velocity profiles with coefficients determined by a least squares fit. Perturbation corrections were made to second order for the wave functions and to third order for the eigenvalues. Calculations were made for two realistic velocity profiles and an idealized nonparabolic velocity profile. Local focusing of sound in a parabolic velocity profile had been reported in previous papers [H. Überall and N. C. Nicholas, “Range Focusing in a Deep Ocean Sound Channel with Parabolic Profile,” J. Acoust. Soc. Amer. 44, 1259–1261 (1968) and N. C. Nicholas and H. Überall, “Propagation Calculations for a Parabolic Velocity Profile,” J. Acoust. Soc. Amer. 47, 101 (A) (1969)] but no local focusing was found for the nonparabolic cases computed. Numerical results showed good agreement with the few available measurements and ray-acoustic estimates of propagation loss.