III-119 



If the soundwaves make several surface contacts, it is clear that the only signi- 

 ficant propagated mode is that involving the specularly reflected waves The 

 nonspecular components are incoherent, undergoing three-dimensional scattering. 



Let Ji be the intensity of the ray, Ti, at some point just prior to a 

 reflection, and J{ the intensity of the specularly reflected ray just after reflec- 

 tion. Then J i - J^ Qgpec • The total field is the sum of all terms Jj which cor- 

 respond to rays reaching a given point by specular reflection. Marsh asserts 

 that It has been well established that a reasonable account of scattering losses 

 can be obtained by considering only the limiting ray. In this, the losses attributed 

 to scattering are partitioned equally over the number of surface contacts made by 

 the limiting ray . 



In terms of the above diagram, we have for the limiting ray, 



cos 83 _ Cs _ c, + GL . GL 



cos9i " ^- -^, ^ ~i (111-166) 



where 



Cs - speed of sound at the depth L 



ci = speed of sound at the surface 



G = increase in the speed of sound due to the pressure increase, 

 per unit distance. 



Then 



and so 



, GL 



cos a sa 1 - 



c 



(III -167) 



/ 2GL 



~~^ ' (III-168) 



Using ci « 5000 ft sec"^ and G = 0.018 sec"^ , we have 



Y = sin 01 « e, « 2.7 • 10-^ L* (III-169) 



;artbur B.HittlcJnt. 



S-7001-0307 



