Axial Focusing of Sound in the SOFAR Channel

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Abstract
Approximating by a polynomial a standard “velocity profile” of sound speed near the axis of the SOFAR channel, we have used normal-mode methods to explore recurrent focusing when a receiver and a CW point source are exactly on the axis, for acoustic frequencies of the order of 100 cps. A certain range R exists—about 26 km in the North Atlantic—at which the few lowest and strongest modes of the sound field add nearly coherently. Focusing is to be expected near R and, decreasingly, near integral multiples of R. A velocity profile nearly symmetric about the axis would also produce focusing near R/2, 3R/2, etc. Numerical calculations 100 cps show no such effect at R/2, but a modest focusing enhancement of about 3 dB near R and 2 dB near 2R. Our results disagree markedly with recent analysis by Hirsch, partly because he dealt with a pulsed source but more because he assumed a symmetric profile of sound speed. Axial focusing is evidently very sensitive to the profile. Experimental detection appears almost hopeless because the depths of axis, source, and receiver must be known with great precision.

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