PEDERSEN, GORDON, AND WHITE: SURFACE DECOUPLING EFFECTS 



The receiver depth of 320 feet, as illustrated by the dashed curve, 

 is below the surface decoupling region and has an entirely different 

 character. 



The repetitive shape of the propagation loss curves in the 

 surface decoupling region points up a newly found deficiency in ray 

 theory. We have observed pronounced disagreements between ray and 

 mode theory in cases where the caustic structure of the convergence 

 zones varies markedly with depth in the surface decoupling region. 

 These disagreements occur under conditions of severe near-surface 

 gradients. In this case ray theory predicts a marked difference in 

 convergence zone structure with near-surface depth, whereas the more 

 accurate mode theory predicts no change in shape at all, but only in 

 amplitude. We have found cases for near-surface receivers where the 

 region of minimum propagation loss in mode theory convergence zones 

 lies in the shadow zones of ray theory. 



Figure 3 presents normal mode expressions pertaining to the 

 surface decoupling effect. Equation 1 is an expression for the propa- 

 gation loss associated with the random phase or power addition of 

 modes. This process smoothes out the detailed interference beats 

 between modes and enables one to distinguish between the basic range 



and depth effects. The H term in Equation 1 is independent of 



o 



range. The second term represents cylindrical spreading while the 

 third term represents an attenuation loss. 



Our interest is in the H term of Equation 2. This term contains 



o 



the dependence of the smoothed propagation loss on frequency, sound 

 speed profile, and source and receiver depths. In Equation 2, C is 

 the mean phase velocity of the trapped modes and f is the acoustic 

 frequency in Hz. 



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