

The subscript zero refers to a reference point (usually 1 yd away from a 

 point source), and 6a is the cross-sectional area of an infinitesimal ray tube. 

 The intensity satisfies the conservation of energy law along a ray tube. It can 

 be shown that pressure, on the other hand, satisfies the law of reciprocity. 



In the case of a horizontally stratified ocean, that is, the sound speed and 

 ocean boundaries are independent of both horizontal coordinates, the rays re- 

 main in a vertical plane and obey Snell's law, 



1 dr 



— — = constant , 

 c ds 



where 



r^ = x^ + y2 . 



SOUND SPEED REPRESENTATIONS 



When ray theory was first implemented on digital computers, the primary 

 concern was to integrate the ray tracing equations accurately and efficiently. 

 Pedersen2 motivated the design of many ray tracing programs by demonstrating 

 the fact that discontinuities in the sound speed gradient could introduce anomalies 

 in the computed value of geometrical spreading loss. 



This effect is illustrated by fitting the sound speed profiles of figure 1 with 

 piecewise linear, 1 piecewise quadratic, 2 and cubic spline*^ representations. 

 Differences are more readily seen in the sound speed gradients shown in this 

 figure. The corresponding ray diagrams, figure 2, show that caustics due to 

 discontinuities in the gradient of the piecewise linear fit disappear when smoother 

 sound speed representations are employed. Propagation losses computed ac- 

 cording to classical ray theory tend to accentuate this effect, but consider what 

 would happen if a ray theory generalized to treat caustics correctly were used 

 instead. Figure 3 indicates that the effect of different sound speed representa- 

 tions is insignificant providing that each representation accurately describes the 

 input data to be fitted. 



97 



