A few conments about the scope of the technique and the assumptions are 

 in order. First, the set of acoustic parameters can be enlarged. That is, 

 the technique is sufficiently basic to be used as a tool in the investiga- 

 tion of more extensive and more difficult problems. Secondly, the set of 

 assumptions can be reduced. In particular, source and receiver depth can be 

 varied. This has not been done in the present paper because it does not 

 contribute to an understanding of the basic techniques. Thirdly, bottom- 

 limited profiles (that is, profiles with a maximum velocity in the surface 

 layers) can also be included if a small portion of the sound field is elim- 

 inated from the prediction system. This is a special case which will not be 

 treated in this paper. 



PROBLEM DEFINITION 



The establishment of a prediction system that will perform the tasks 

 just described must deal with the following three general problem areas: 



(1) Characterization and description of the state of the environment- 

 both spatially and temporally 



(2) Performance of the computations to obtain the set of acoustic para- 

 meters which describe the sound fields 



(3) Display, presentation, and indexing of the output of the prediction 



system. 



The technique presented below addresses itself to each of these problem areas. 



The first task is to answer the following question: Given (l) The value 

 of sonar range, say %, and (2) A variation in the sound velocity profile, 

 say from ?i to P2 in Figure 1, which describes the total -variation in the 

 soTind velocity structure through which the rays must pass, then what are the 

 extreme values of the acoustic parameters that can occur at the range H^? 



DESCRIPTION OF TECm\IIQUE 



In Figure 1 the shaded region between the two profiles depicts the 

 region through which P]_ must pass to assume the position of P2. Correspond- 

 ing to this variation in the profile is the variation of the sound rays, 

 shown on the right in Figure 1 as a shaded region in a vertical cross-section 

 of the ocean. Assuming, for the moment, that we know these extreme values, 

 it is observed that if the difference between the extreme values of the 

 acoustic parameters is sufficiently small, then the average of these ex- 

 treme values is a prediction with which is associated a known possible error . 

 This error is the difference between the average value and either of the two 

 extreme values. This error is also dependent on the size of the ocean area 

 in which the prediction is to be valid. Therefore, the ability to specify 

 the region in which the prediction is valid will provide some control over 

 the magnitude of these errors. 



46 



