370 



DIRECT MEASUREMENT TECHNIQUES 



m 

 o 



10 



< 

 o 20 



z 

 o 



in 



30 



< 



40 



1000 2000 3000 4000 5000 6000 7000 



RANGE IN YARDS 

 Figure 5. Typical transmission anomaly at 24 kc for an isothermal layer 70 feet deep. 



8000 



The transmission loss H is defined as the loss in 

 intensity, in decibels, as the sound travels between 

 a point 1 yd on the axis of the sound beam from a 

 small projector, and the target. If the medium 

 through which the sound travels is ideal — if no 

 sound is absorbed, scattered, or refracted, or re- 

 flected from the ocean surface or bottom — then the 

 intensity of the sound varies inversely as the square 

 of the distance from the source, as pointed out in 

 Section 19.1.1, and the transmission loss, in decibels, 

 is simply 20 log r, where r is the range in yards. In 

 this case the total transmission loss 2H as the sound 

 travels to the target and back to the projector again 

 is simply 40 log r. 



This inverse square loss, however, is only a part of 

 the total transmission loss of sound in water. Sound 

 energy is absorbed by the water and dissipated as 

 heat energy. Small particles in the water scatter the 

 sound in all directions. Furthermore, as the beam is 

 refracted by a temperature gradient, it is bent and 

 the cross section of the beam changes in area, chang- 

 ing the intensity of the sound correspondingly. 



To account for transmission loss due to absorption, 

 scattering, and divergence arising from refraction, 

 the transmission anomaly is defined as the difference 

 between the total measured transmission loss, and 

 the transmission loss due to divergence according 

 to the inverse square law alone. In decibels, then, 



A = H -20logr, (1) 



where A is the transmission anomaly, H the total 



transmission loss, and r the range. A typical plot of 

 the transmission anomaly against the range is il- 

 lustrated in Figure 5. 



The transmission anomaly has been found to de- 

 pend rather strongly on the prevailing oceanographic 

 conditions and most particularly on the variation of 

 the temperature of the water with depth. The water 

 in the ocean is usually characterized by a mixed layer 

 of nearly constant temperature down to a certain 

 depth; below that depth, a decrease in temperature 

 with depth, or thermocline, will appear. The trans- 

 mission anomaly depends markedly on the depth to 

 this thermocline as well as on the depth of the hydro- 

 phone receiving the echoes. 



When the temperature difference in the top 30 ft 

 of water is 0.1 F or less, the transmission anomaly 

 may be considered a linear function of range (see 

 Chapter 5). Hence, it is convenient to define an 

 attenuation coefficient as the change in transmission 

 anomaly with range. As a derivative, 



a = — (2) 



dr 



where a is the attenuation coefficient, A the transmis- 

 sion anomaly, and r the range. Since in target- 

 strength runs the attenuation coefficient is measured 

 not as a derivative, but as an average over range in- 

 tervals of 500 or 1,000 yd, a is usually taken as 



a = -■ (3) 



