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



condition would require an acoustic frequency of less than 1,000 Hz to 

 constitute a low-roughness surface. 



About 1966, Allen Ellinthorpe published an article (Ellinthorpe, 

 1966) on sea-surface induced frequency smear. It should be noted that 

 Doppler spectrum, frequency smear, and frequency spread all have the 

 same meaning. Ellinthorpe was interested in determining the integra- 

 tion time for a communication system and performed a surface scattering 

 experiment in Bermuda. To compare the experimental results, he derived 

 the Doppler spectrum of the forward scattered sound based on a phase 

 modulation technique. Assumptions were made that the surface scattered 

 signal was only phase modulated, the surface wave height h was a 

 Gaussian random variable, and the power spectral density of the surface 

 waves was given by a Bretschneider spectrum. With these assumptions, 

 he uses an equation derived by Middleton to determine the power 

 spectral density of a signal that is phase modulated by a random vari- 

 able that has a known power spectral density. The phase modulation 

 index is given by a. 



Ellinthorpe compares the theoretical results that were derived, 

 based on the Middleton equation, to experimental data measured off 

 the coast of Bermuda. In Figure 2, I have selected a comparison 

 made at two frequencies. You can see that the agreement is close 

 in the spectral peaks, but the spectral width of the predicted is 

 narrower than the measured. In general, this is true of all his 

 predictions. The predictions do not give an absolute value of the 

 energy in the carrier and sidebands, and the predictions were obtained 

 by varying the parameters to obtain a best fit. No oceanographic data 

 were available. There is something of interest that will come up 

 later — the sidebands of the measured spectrum are asymmetrical as 

 shown for the carrier frequency of 856 Hz. 



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