114 



DEEP-WATER TRANSMISSION 



cline. The first term on the right in formula (13) 

 represents the attenuation caused by absorption, and 

 the second term represents the attenuation due to 

 refraction. 



For the data plotted in Figures 24 and 25, the 

 average depth to the top of the thermocHne is about 

 150 ft, which gives a value of 135 ft for hi. The aver- 

 age value of Ac is about 1 5 ft per sec, which for a sur- 

 face temperature of 70 F corresponds to a tempera- 

 ture decrease of 3 F in the top 30 ft of the thermo- 

 cHne. If these numerical values are substituted into 

 equation (13), and this term plotted against the 

 range R, the dashed curve of Figure 25 results. The 

 agreement between theory and observation is fairly 

 close at ranges between 1,000 and 4,000 yd. 



This agreement is rather surprising since equation 

 (13) is theoretically not valid at ranges so large that 

 the upward bending in the isothermal layer becomes 

 important and d^ in equation (11) is no longer equal 

 to hi/R. A more detailed theory, which takes into ac- 

 count this upward refraction and assumes reflection 

 of sound from a flat surface, would predict a shadow 

 boundary at about 3,000 yd, with a very large anom- 

 aly at greater ranges. Possibly, sound reflected from 

 the irregular ocean surface, temperature microstruc- 

 ture, or small systematic negative gradients near the 

 surface, discussed in Section 5.4.2, might explain why 

 equation (13) agrees so well with the facts beyond its 

 expected range of validity. Regardless of the explana- 

 tion, however, equation (13) may be regarded tenta- 

 tively as a semi-empirical formula which may be 

 used to predict the sound intensity below a ther- 

 mocHne of given depth and sharpness. A detailed 

 comparison between this equation and the observa- 

 tional data is given in Section 5.3.4. 



Early Studies 



One would expect from equation (13) that the dif- 

 ference in intensity above and below the thermocHne 

 would depend both on the depth of the layer and on 

 the magnitude of the temperature change in the 

 thermocHne. Two early studies along this line were 

 made at UCDWR. Although these studies have not 

 been conclusive and are largely superseded by the 

 more recent results in the following section, they are 

 given here for completeness. 



A preliminary plot of the intensity difference 

 above and below the thermocHne was made in a 

 UCDWR internal report,'^ using data obtained in 

 10 vertical runs, during which the hydrophone depth 

 was slowly changed. A least squares solution, with A 



as the dependent variable and log (1 -|- 2AcR^/coh'^) 

 as the independent variable, gave the relation 



2AcR'\ 



A = -0.3 + 2.85 log 11 + 



CqW / 



(14) 



with h set equal to the thermocHne depth, and c to the 

 total velocity change from the isothermal layer to the 

 measuring hydrophone. The measurements extended 

 over a spread of 10 to 5,000 for 2AcR'^/cJi^. Use of the 

 velocity change in the top 30 ft of the thermocHne 

 would probably not have changed the results ap- 

 preciably because of this large spread in 2AcR^/coh^. 

 Thus these data indicated a difference of transmission 

 anomaly only about half of that predicted by equa- 

 tion (13); also, the scatter from the mean curve was 

 very great. However, the temperature gradients near 

 the surface were not specified, and an analysis of runs 

 with isothermal water at the surface might be ex- 

 pected to give better agreement. Of possible im- 

 portance also is the fact that during the appreciable 

 time required for vertical runs the temperature pat- 

 tern could change appreciably. 



More recent analyses have dealt not with trans- 

 mission anomalies but with values of Rw, the range 

 at which the sound intensity is 40 db below the in- 

 tensity measured with the hydrophone at 16-ft depth 

 at a range of 100 yd. Further, a single parameter is 

 frequently useful to characterize each transmission 

 run, especially when a preliminary analysis of many 

 runs is being attempted. For these reasons Rm has 

 been widely used in analyses of transmission data. 



Studies have been made of ARm, the difference in 

 the Rio values determined above and below the layer. 

 Since the values of AE40 are based on differences be- 

 tween intensities measured simultaneously in the 

 isothermal layer and below the thermocHne, it was 

 hoped that these values would be less influenced by 

 variability than individual values of Rm- However, 

 the study of Aft^, given in a UCDWR internal re- 

 port,^^ has yielded relatively few results, apart from 

 providing general confirmation of the presence of 

 layer effect. For isothermal layei's deeper than 40 ft, 

 the average value of AR^o was 800 yd at 24 kc. How- 

 ever, no correlation of AR40 at 24 kc could be found 

 with the depth or sharpness of the thermocHne under- 

 lying the isothermal layer, or with any other feature 

 of the temperature distribution. 



This result may be attributed in part to the fact 

 that ^40 above the thermocHne apparently shows 

 some correlation with both the depth and the sharp- 

 ness of the thermocHne. The data in reference 32 sug- 



