DAUBIN: STATISTICAL ANALYSIS OF SHIP GENERATED NOISE 



the source level is assumed to be zero. This may not be the case in 

 all observations. Equation (2) then becomes: 



E(I) = N E(T) E(S) . 



(3) 



Now the average value in any situation of the transmission from 

 source to receiver is given by 



= ^ ZT. = ^ I f 



T(R) 6(R. - R) dR 



Z 6 (R, - R) dR. 

 3 



(4) 



Allowing the number of ships to get very large, we obtain the expec- 

 tation value of the transmission curve, that is, the integral over 

 all ranges of the product of the transmission and the probability 

 density in range, p{r) of the ships: 



Lim T 

 n->°o 



= E (T) , 



((5) 



with 



E{T) 



= / 



T{R) p(R) dR. 



(6) 



Therefore, the expectation value of the local received intensity is 

 given by 



/ 



E(I) = N E(S) E(T) = N E(S) / T (R) p (R) dR. (7) 

 Similarly, the variance of the intensity can be calculated as: 



Var (I) 



N 



2 2 



a + u 

 s ^s 



Var (T) 



(8) 



854 



