IV-21 



The micro- structure of the ocean changes with time. The rate of 

 change is very slow compared to the passage of an acoustic wave, but the change 

 can be expected to be substantial over a period of the order of minutes, and un- 

 recognizable over a period of hours. We desire, therefore, a statistical 

 description of this micro- structure. Clearly, the most we can hope for would 

 be the joint probability density of the values of the index of refraction at sets of 

 points in the ocean. Some measurements have been made of the probability 

 distribution of the temperature differential between pairs of points in the ocean. 

 Two such measurements are shown in Figure IV-7 and indicate that the tempera- 

 ture difference between two fixed points in the ocean tends to have a normal dis- 

 tribution. 



70 



PERCENT OF 



FLUCTUATION 



LARGER THAN 80 



ABSCISSA 90 



95 



64 in. 



THERMISTOR 



SPACING 



99.98 1 I 11 I I I II 



I I I 



TEMPERATURE DIFFERENTIAL ^ 



FIGURE IV-7 PROBABILITY DISTRIBUTION OF TWO- 



POINT TEMPERATURE DIFFERENCE 



It is very likely, therefore, that the joint probability density function of the index 

 of refraction is multivariate normal. In most applications, the principal char- 

 acteristic of the index of refraction u (x) required is the so-called structure 

 function: 



B (x, 



u -' 



r) = 



\ / e 



(IV-52) 



ensemble or time 



Arthur M.llittk.Tint. 



S-7001-0307 



