Van Mater and Neat 



'0 

 The patch length becomes. 



^^ = ^-1' mih^ ^'' <^) 



^^ = -'^4o ^(^)^- 



(10) 



If E(w) is the energy per unit frequency of the source dis- 

 turbance then the energy between orthogonals in a frequency band, 

 do), near the source will be 



E(a)) do 



2660 



Since the energy of the patch has been assumed constant this will also 

 be the value at the field point, i, and this in turn may be equated 

 to the local wave energy: 



E(co) dco^=-|pgTif 6C 64, (11) 



where T|j is the local wave amplitude. Substituting the expressions 

 for 6; and 6^ from Eqs. (8) and (10) gives: 



The final result is , 



m-^'li ^^^^O-[vj'4(iir)^0- '^^) 



-^ ' ^ y ' 



CXs 



The first bracketed factor, a,, represents the effect of geometric 

 spreading between rays while the second bracketed factor, Pj , 

 represents the effect of the spatial stretching of energy between 

 adjacent frequencies, or frequency separation. 



Computationally, E(w) will be evaluated using the results of 

 the previous section, Eq. (4), at a point sufficiently removed from 

 the source and over bottom depths nearly enough uniform to satisfy 

 the conditions on application of that equation. From that point on 

 inshore new a's and P's will be computed numerically for each 



248 



