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 sound-speed profile and sinusoidal point source. A fourth-order power series was used to approximate nonparabolic speed 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 speed profiles and an idealized nonparabolic speed profile. Local focusing of sound in a parabolic speed profile had been reported in previous papers [H. Überall and N. C. Nicholas, J. Acoust. Soc. Amer. 44, 1259–1261 (1968); and N. C. Nicholas and H. Überall, J. Acoust. Soc. Amer. 48, 745–753 (1970)], but no local focusing was found for the nonparabolic cases computed. Numerical results showed good agreement with the few available measurements and ray-acoustics estimates of propagation loss.
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