MODE 1 

 MODE 2 

 MODE 3 



1520 

 SOUND SPEED, m/s 



Figure 1 . A two-layer sound speed profile for a 

 surface duct. The phase velocities of the first 

 three modes at 3 kHz are marked. The broken 

 line shows a modification of the upper layer to 

 prevent numerical breakdown in mode 1 . 



20loglU,(20) U 



50 

 E 75 



S 100 



125 



_ I 



10-'° 10"'^ 10"° 10^ 10" 



|U,(20Ut(z)| 



Figure 2. Depth function of mode 1 at 3 kHz, showing error in the computed 

 function. The true function cannot be computed without increasing computer 

 word length, but the corrected value can and it will not cause a large error in 

 the mode sum. 



17 



