312 



SHALLOW-WATER REVERBERATION 



directivity is known in sufficient detail, although in 

 practice it may prove difficult to obtain even this 

 information. The scattering strength of the bottom 

 is in general a function of the angle of incidence of the 

 rays striking the bottom. Temperature gradients in 

 the ocean are frequently sufficiently large that the 

 sound rays in the main transducer beam have suf- 

 fered appreciable bending by the time they reach the 

 bottom. For this reason bottom reverberation is 

 likely to depend much more strongly on transmission 

 conditions than surface reverberation. To accurately 

 predict bottom reverberation levels, therefore, it is 

 necessary to have detailed knowledge of the ray paths 

 and transmission loss to the bottom. 



Unfortunately, there are practically no reported 

 bottom reverberation measurements for which the 

 transmission to the bottom can be regarded as known 

 in detail (including knowledge of the ray paths and 

 the transmission loss along these paths). Conse- 

 quently, any comparison of predicted reverberation 

 levels with experimental observations must be based 

 on assumptions about the transmission ; and detailed 

 agreement in any single experiment between pre- 

 dicted bottom-reverberation levels and observed 

 levels should not be expected. Rather, because of this 

 uncertainty concerning the transmission from the 

 transducer to the bottom, the comparison of theory 

 and experiment becomes even more a purely statis- 

 tical process than was the case for surface and volume 

 reverberation. 



This statistical approach, which is described later, 

 is in some respects justifiable. Transmission studies 

 made to date reveal little likelihood that detailed 

 knowledge of the transmission can be obtained 

 aboard an ordinary echo-ranging warship in any 

 practicable way. What is required is a statement of 

 the average reverberation levels to be expected for 

 various broad classifications of echo-ranging gear, 

 transmission conditions, and bottom types. 



15.2 



EFFECTS OF REFRACTION 



Some of the results of a statistical analysis of bot- 

 tom reverberation are described in an internal report 

 by UCDWR.i In this report, many bottom rever- 

 beration curves were plotted against range. The data 

 comprising these curves were all taken at 24 kc with 

 standard Navy gear directed horizontally, but were 

 obtained in a variety of regions, over many different 

 types of bottoms, at differing depths, and with vary- 

 ing refraction conditions. Examination of these data 



showed a number of similar features on almost all the 

 curves. In general, the curves showed the following 

 characteristics. 



1. A peak which comes in shortly after the out- 

 going signal and results from surface reverberation. 



2. A rapid decay of reverberation with the level 

 reaching a minimum at a range of two times the 

 depth of water. 



3. A broad rise in level as the range increases, de- 

 veloping a second peak at a range of about six times 

 the depth of water. This rise is due to bottom rever- 

 beration. 



4. Beyond the second peak a rapid decrease of in- 

 tensity, approximately proportional to the inverse 

 fourth power of the range. However, very large varia- 

 tions from this type of decay were observed. 



The range of the bottom reverberation peak de- 

 pends of course on refraction; for this reason, the 

 dependence of the range of this peak on depth be- 

 comes a statistical problem. If there were no refrac- 

 tion, in other words, if the sound rays always traveled 

 in straight lines, then the ratio of the range of the 

 peak to the depth (over plane and smooth bottoms) 

 would obviously always be a fixed quantity depend- 

 ing only on the directivity pattern of the transducer. 

 In fact, for standard 24-kc echo-ranging gear, with 

 a beam width of 5 to 6 degrees, the range of the peak 

 would be 10 to 12 times the water depth, if refraction 

 were absent. 



In order to judge the usefulness of the statistical 

 study in reference 1, it is necessary to know what 

 kinds of temperature gradients were included, and 

 the extent to which these refraction patterns obtained 

 near San Diego are typical of refraction conditions 

 in other localities. There are reasons for believing that 

 the results of reference 1 may be valid for a wide 

 variety of temperature gradients. Bathythermograph 

 patterns are not completely arbitrary in shape; posi- 

 tive gradients are relatively rare, with the result that 

 most patterns other than isothermal ones show a 

 continuous decrease of temperature between surface 

 and bottom. Furthermore, the effect of refraction is 

 greatest for horizontal or nearly horizontal rays. 

 Once the rays have been bent through an appreciable 

 angle, the amount of additional bending, even by 

 quite sharp negative gradients, is relatively small. 

 For these reasons, the ratio of the range of the peak 

 to the depth may be expected to be relatively con- 

 stant for a wide variety of gradients excluding isother- 

 mal or "nearly isothermal" types, where, for the 

 purpose of this discussion, "nearly isothermal" water 



