PEDERSEN, GORDON, AND WHITE: SURFACE DECOUPLING EFFECTS 



Figure 4 illustrates the important mode theory quantities, which 

 were introduced in Figure 3. The computations are for the conditions 

 of Figures 1 and 2. 



The dashed curve is H which indicates how the smoothed propaga- 



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tion loss varies with depth. Ideally, one would like a simple theory 



which describes H in terms of dependence on various parameters, 

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Unfortunately, H is a very complicated function which depends on 

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source depth as well as profile parameters. The problem of approxi- 

 mating H is under consideration, but for now we must be content to 

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treat the surface decoupling effect as characterized by H (Z) . 



The solid curve H (Z) represents the standing wave pattern of 

 mode 14, which is the last trapped mode. The first node occurs at 

 the surface. The first antinode occurs at a depth of 206 yards. 

 According to our previous definition, this is the surface decoupling 

 depth, z • Also shown are a second node at 410 yards and a second 

 antinode at 590 yards. 



The relative maximum in the loss for H^ at 480 yards is associated 



with the second node in Hj^(Z). It is not as pronounced as a node because of 



the contribution of lower order modes which have nodes at different 



depths. However, at the surface, all modes have nodes. Thus, the 



major depth dependence of H will occur near the surface with 



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relatively minor changes below the surface decoupling region. 



Note that in the near surface region the shape of H is very 



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similar to the shape of H (Z) . This similarity results because N 



is not only the dominant mode, but also because other modes which 



contribute to H have similar shapes in the surface decoupling region, 

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Observe that the minimum loss in H occurs at a depth of 259 



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yards. One can demonstrate from mode theory that for any source 



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