o 



_l 



z 

 o 



< 



< 



o 



3.10 3.12 3.14 



RANGE (kyd) 



3.16 



Figure 7. Propagation Loss for a 0. 8-kyd Receiver Depth 



Computed More Accurately Than That for Classical or 



Modified Ray Theories 



Consider what would happen if a theory generalized to treat caustics correctly 

 were used instead. The result, figure 7, indicates that there is no discontinuity 

 in propagation loss at the ray that grazes the ocean surface and also that classical 

 ray theory appears to be more accurate to the right of the grazing ray than to 

 the left. Consequently, modified ray techniques should be exercised with caution. 



Spofford was one of the first to implement modified ray theory in a practical 

 computer program. The procedure, based on the work of Ludwig, 7 assumes that 

 the reduced wave equation has an asymptotic solution of the form 



P = exp (iwT)l gAi (w^/^ p) + Ai' (w p) 



ico 



1/3 



subject to the orthogonality condition 



VT • Vp = , 



104 



