PEDERSEN, GORDON, AND WHITE: SURFACE DECOUPLING EFFECTS 



profile of this paper with a 460- foot surface layer. The region to 

 the right, labeled BB, represents the bottom bounce region. For 

 these two profiles, the corresponding surface decoupling depths lie 

 between 1.5 and 0.25 wave lengths. 



The region in the middle of the figure labeled CZL and CZH 

 represents the convergence zone region. The rays in a convergence 

 zone are folded at the caustic into two branches. Here CZL represents 

 the lower-angle branch and CZH represents the higher-angle branch. 

 For most cases the higher-angle branch will be more important than 

 the lower-angle branch. For the two profiles, the higher-angle 

 branch spans values of decoupling depth from 3.7 to 1.3 wavelengths. 

 This span may be regarded as typical for convergence zone propagation. 



The region to the left of the figure, labeled SC , is the surface 

 channel region. Here the decoupling depth exceeds 4 wavelengths. 

 Although the decoupling depths expressed as number of wavelengths can 

 be huge for surface channel propagation, the physical decoupling 

 depths are limited because only high frequencies propagate in surface 

 channels. For example, on the basis of normal mode theory, one can 

 demonstrate that the surface decoupling depth can never exceed 

 55.4 percent of the layer depth. This limit corresponds to the onset 

 of trapping for the first mode. If two modes are trapped, then the 

 surface decoupling depth cannot exceed 20.5 percent of the layer depth. 



Figure 9 presents the surface decoupling loss for the linear 

 approximation expressed in terms of the dimensionless ratio Z/Z . 

 For small values of x> sii^ X is proportional to x- Thus, for small 

 ratios halving the depth increases the loss by 6 dB. This rule does 

 not hold for large values. For example, a 50 percent ratio corres- 

 ponds to 3 dB loss — not 5 dB loss. 



578 



