RANGE (kyd) 

 2 



Figure 5. Ray Diagram for a 1-kyd Source Depth 

 Computed by Using the Sound Speed of Figure 4 



Pedersen and Gordon^ compared the classical solution (solid line) with 

 Brekhovskikh's^ modified ray theory (broken line) in figure 6. Classical ray 

 theory predicts an infinite intensity at the caustic at 3159 yd and an infinite 

 propagation loss in the shadow zone to the right of the caustic. Pedersen and 

 Gordon explain that the abrupt change in loss at 3130 yd occurs at the ray that 

 grazes the ocean surface. The modified ray theory did not apply to the left of 

 this ray. 



The above remark points out the difficulty of applying modified ray theories 

 to the simplest of caustic geometries. Additional effects due to the ocean bound- 

 aries, cusped caustics, etc. , prevent the theory from being applicable every- 

 where. One can program as many special cases as practical considerations 

 suggest, but, more often, one uses classical and modified theories outside 

 their domain of validity. Since caustic corrections are usually obtained by 

 including additional terms of a high frequency ejspansion, errors increase as 

 the frequency decreases. 



102 



