II-7 



z = h cos px 



and inclined to this surface at an angle 8 whose cosine is equal to a. It can be 

 proven that the scattered wave will consist of the so-called specular reflection 

 term whose angle of inclination has a cos 9 = - a, plus successively higher 

 orders of scattering. The successively higher orders of scattering are inclined 



to the surface at an angle cos 8 = - a ± — ^, where k is the wave number of 



k 



the incoming wave and m runs through the positive integers (1,2, . . .). If the sur- 

 face were completely flat (p = 0), the entire scattered wave would consist of the 

 specular reflection alone. Several approximation methods have been devised to 

 obtain the amplitude of the higher order components of scattering, but all appear 

 to be limited to ranges of surface height and surface wavelength much smaller 

 than the incident wavelength. Most cases of interest in the ocean are not in this 

 category, and the theory therefore gives, at best, a qualitative explanation. It 

 turns out that the higher order scattered terms are important for incident waves 

 near normal incidence. If the incident wave makes a small angle with the horizon- 

 tal, i.e. , for grazing angles 8 < < 1, the specular term dominates. This general 

 conclusion appears to apply also under actual ocean conditions. 



If the movement of the surface wave is taken into account, the signal 

 received will no longer be a reflected version of the incident wave, but will be- 

 come phase -modulated since the path length to the receiver is changing in time. 



Some recent work by Marsh examines scattering from the surface based 

 on a more realistic spatial spectrum of the surface. His work, and some exten- 

 sions of it are reported here. This treatment, too, is limited by the condition 

 that the height of the surface wave must not be too large compared to the wavelength 

 of the incident sound. Nonetheless, for fairly low sea states and low frequency 

 sound, the theory permits the calculation of the attenuation due to surface reflec- 

 tion. The scanty data available from ocean experiments seems to confirm the 

 theoretical predictions. It should be pointed out that this is an important area in 

 which good experimental results under ocean conditions are very sorely lacking. 

 Scattering from the bottom is not treated in this report. 



C. SCATTERING BY WEAK INHOMOGENEITTES 



Chapter IV treats scattering by the weak inhomogeneities which result 

 principally through the turbulent breaking up of the layered structure of the ocean. 

 As a consequence of the turbulence, the sound velocity, density, etc. , of the ocean 

 medium fluctuates in space and in time. Of these, the fluctuations in sound velocity 

 are the most important, so that the main aspects of the propagation of sound are 

 still governed by the wave equation 



rS 



cp = 



z^ d t^ 



artbur H.IlittlcJjur. 



S-7001-0307 



