III-117 



It may be well at this point to restate the assumptions used in this 

 development . 



(i) The development giving the general expression for the scattered 

 intensity depended upon: 



(a) The representation of the scattered wave as an 

 integral sum of plane waves . 



(b) The existence of a convergent expansion in powers 

 of (kh) for $ , the weighting function in the foregoing 

 integral sum. 



(c) The applicability of certain Fourier inversion theorems . 



(d) A description of the sea surface as a single -valued 

 function of position in a plane parallel to and below 

 the surface. This precludes certain curling condi- 

 tions in ocean waves . 



The operator representation and theorems from generalized harmonic analysis 

 used by Marsh are not needed for the further developments . The entire develop- 

 ment is formalistic in nature, consisting of the manipulation of formulas on 

 functions to which they may or may not be applicable. No attempt is made to 

 ascertain the applicability of these operations, either by physical arguments or 

 analytical considerations . 



(2) In applications, the sea surface is assumed to be isotropic --i.e. , 

 no particular direction to the waves - -and the sea surface spectrum is given by 

 the Neumann -Pierson model 



A-(«.)=4 e -'g"/^'^' (III-161) 



where c is a constant (not the velocity of sound) . This expression is needed to 

 obtain the autocorrelation function of the sea surface. 



(3) In applications, it is assumed that in the power series expression 



for # (,V , v.). 



m=0 



^ *'m(^'^^ (III-162) 



artbur B.llittle.Hnir. 



S-7001-0307 



