CAVANAGH: AMBIENT-NOISE MODELS 



The corresponding intensity per unit solid angle 



(df2 = cosep,deRd(t)) 

 at the receiver is then 



J T 



n(ej^,(|);dA,dfi) = ^(ej^,cJ);dA(R,(})) ) 



P(R,({);eg)RdRd(j) cose^3(R,cf);eg) /c » 2 



(^k)"" 



(5) 



in0 cosB d6 dd) 

 S R R 



^(^'*''^S^ B(R,cD;ej/ S 



smOg 



2 (6) 



= nO ,(J),R). 



IS. 



Note that n is independent of spreading losses. The total contribu- 

 tion to the noise field at angles 9 , c|) is then found as the incoherent 



JA, 



sum of n(6 ,4),R) over all ranges R. 

 R 



Until this point there have been no restrictions on the form of 



the sound speed field C(Z,R,(j)). However, to facilitate calculations, 



the ocean is assumed to be stratified and azimuthally symmetric within 



an appropriate bearing aperture: C(Z,R,4)) = C(Z) for (J) < <t><^2 ^^^ 



< z< D. This allows the use of recursive ray- tracing schemes. It 



further guarantees that although n(9 ,{{),R) becomes infinite for the 



K. 



ray (9 =6 ) which grazes the surface, the energy in any interval 

 R G 



0^,0 +£) is finite, provided that 0^ 7^ (i.e., C 7^ C^) . 

 G G G o K 



812 



