Abstract
Ray and wave analyses predict repeated paraxial focal zones along the SOFAR axis from a point acoustic source on axis, given various roughly parabolic profiles of refractive index symmetric about this axis (quite unrealistic). Experimental corroboration is lacking. Wave analysis leads to focusing if propagation constants of successive normal modes display constant increments for a large subset of all modes. We examine this requirement with an index profile expressible near the axis in z2, z3, and z4, matching the standard Pekeris profile fairly well. Perturbation treatment of the quantum-mechanical anharmonic oscillator is applicable. The lowest 0.2 f modes (f, frequency in cps) approximate focusing requirements, but alternate ones, being nearly of odd parity, contribute little on axis. Interfocal separations are about 6 miles. Near calculated foci, these modes add almost coherently; all higher ones are assumed incoherent. “Enhancements” of energy in focal regions are then calculable. At 100 cps, enhancement is an undetectable few percent—in general agreement with Hirsch and Shear [J. Acoust. Soc. Am. 36, 1015 (A) (1964)]. [Work supported in part by the U. S. Office of Naval Research.]
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