RODERICK: FORWARD SCATTERED LOW-FREQUENCY SOUND FROM THE SEA SURFACE 



some low- frequency, long-range propagation data, published by Ken 

 Mackenzie (1962) , that the envelope of the signals had periods on the 

 order of ocean swell waves and the spectrum looked narrowband. Based 

 on a resonance scattering theory he developed in the early 60s, he 

 derived the Dopier spectrum which was good to first order effects and 

 included multiple-bounce surface interactions. Remarkable intuitive 

 reasoning at that time put the theoretical prediction of the Doppler 

 spectrum ahead of the experimental evidence. 



What criterion do we use to distinguish between a rough and smooth 

 surface? Lord Rayleigh took a simple approach (Beckmann and Spizzi- 

 chino, 1963), pictured in Figure 1. He simply considered the phase 

 difference between rays reflected from an uneven surface. For the 

 wave shown, the crest to trough height is h, the grazing of the 

 acoustic rays is ((> , and the acoustic wave length is A — Walter Munk 

 might say here that this does not look like a sea surface wave, but 

 he must consider that the wave was measured on the east coast of the 

 United States. 



Very simply, Rayleigh reasoned that if the phase difference is 

 near zero, then the surface isn't very rough, that is, the path- 

 length difference is small. As the phase difference approaches it 

 there will be cancellation of energy in that direction and hence the 

 energy must have been scattered elsewhere — this would constitute a 

 rough surface. A criterion to separate smooth and rough surfaces is 

 to choose a point midway between zero and tt , say T7/2. As you can see, 

 the wave length, grazing angle, and wave height must be specified to 

 define the roughness. These three parameters crop up again with the 

 same relationship in more elaborate scattering models. As an example 

 of the above, consider long-range propagation with a 5-degree grazing 

 angle at the surface and an rms wave height of 2 feet — this 



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