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



reflected specularly and for small acoustic-to-surface wavelength 

 ratios the energy is scattered in space symmetrically about the 

 specular direction. For the direction of surface wave propagation 

 shown, you would receive a down-Doppler in the backscatter direction. 

 On the other side of the specular direction you would receive an up- 

 Doppler. Reversing the direction of surface wave propagation, you 

 would also reverse the directions of the Doppler shifts, e.g., an up- 

 Doppler would be received in the backscatter direction. 



The scattering directions of the n order sidebands are given 

 by the angles 6 and 6 ; 



X 

 n _a 



1 cos e, A 

 1 s 



X 



a 

 n - — sm a 

 A 



s 



cos a (6) 



(7) 



where 6 is the angle measured from the normal to the surface and is 

 an angle of elevation, and 6 is an azimuthal angle measured from the 

 vertical plane containing the angle of incidence and reflection. The 

 directions in which the energy is scattered are functions of the ratio 

 of the acoustic-to-surface wavelength, the angle of incidence, and the 

 direction of surface wave propagation. 



The effect on the azimuthal scattering angle 6 by the direction 

 of surface wave propagation and the acoustic-to-surface wavelength 

 ratio is shown in Figure 4. For small ratios the scattering is close 

 to the specular direction, and it is not possible to resolve only the 

 specular component at the transmitted frequency. The Doppler fre- 

 quencies are scattered on each side of the specular direction. 



334 



