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



As mentioned previously. Parkins predicted the Doppler spectrum 

 of an acoustic signal reradiated from the ocean surface using physical- 

 optics techniques. He uses basically the same formulation of the Helm- 

 holtz Integral as Eckart, but also includes a slope correction term 

 originally formulated by Brekhovskikh and Isakovich (1952) . The 

 Doppler spectrum is obtained through the Fourier transform of the 

 reradiated autocovariance function. For low frequencies, the Doppler 

 spectrum consists of a specularly reflected component at the fre- 

 quency of the incident radiation and two scattered components that 

 are Doppler shifted symmetrically about the incident frequency. The 

 magnitude of the deviation of the sideband frequencies is the same 

 and depends on the angles of incidence and observation relative to 

 the wind direction and also on the incident frequency. 



In 1970, Ben Cron and I did some experimental measurements 

 (Roderick and Cron, 1970) of the Doppler spectrum. An acoustic path 

 that included a surface reflection at a grazing angle of 7 degrees 

 was used between the DOSS array and the TVA. The DOSS array consists 

 of two magnetostrictive scrolls which generate 750 and 1,500 Hertz 

 in the water. The TVA consists of 40 hydrophones positioned in a 

 vertical array and was used to beamform to receive the surface 

 reflected signals and minimize undesirable multipaths. The spectrum 

 in the upper left of Figure 7 represents the spectrum of the signal 

 incident on the surface. Before we go any further, the analysis was 

 done on a real-time spectrum analyzer in a frequency range of zero to 

 five Hertz. The acoustic signals were bandshifted to a center fre- 

 quency of 2.5 Hertz. On the upper right of Figure 7 is a spectrum 

 of the wave height measured at Argus Island using a resistive wave 

 staff. The wave height was measured at the same time as the acoustic 

 reflections from the surface and at a location which was 30 miles west 

 of the isonified area. The spectrum in the lower left is from the 



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