PEDERSEN, GORDON, AND WHITE: SURFACE DECOUPLING EFFECTS 



Equation 3 represents the power addition of the mode amplitude 



functions. Here n is the mode number and N is the number of trapped 



modes. Z is the receiver depth and Z is the source depth. The U 



functions are the solutions to the Helmholtz equation. We need not 



discuss the detailed form of these functions. The boundary conditions 



require that the U functions go to zero at the ocean surface. Thus, 



H goes to plus infinity as the source or receiver depth approaches 

 o 



the ocean surface. The source and receiver depth enter the U 

 functions in exactly the same manner. This is consistent with the 

 acoustic property of reciprocity. 



In regions where the surface decoupling effect is the controlling 

 feature, the dominant contribution to the mode sum is often that of 

 the last trapped mode. Equation 4 defines H (Z) . This is the counter- 

 part of H for the last trapped mode. Here the mode sum of Equation 3 

 is replaced by the contribution of the dominant mode. We shall 

 presently see an example of H and H (Z) . This example will demon- 

 strate the relationship more clearly. 



Now H (Z) will have N maxima and N minima as Z varies from the 



N 



ocean surface to the ocean bottom. Equation 5 defines the surface 



decoupling depth, Z , as the depth of the first minimum in H (Z) . 



The surface decoupling depth is the depth of the shallowest antinode 



in the standing wave pattern of the last trapped mode. 



Equation 6 defines the surface decoupling loss, H . It is the 



difference between H (Z) and H evaluated at the decoupling depth, 



N N 



Z H is infinite at the surface and decreases monotonically to 

 SD. s 



zero value at the decoupling depth. 



Equation 7 follows immediately from Equations 4 and 6. We 

 5nt Equatior 

 source depth, Z 



present Equation 7 to demonstrate that H is independent of the 



s 



567 



