DEEP-WATER TRANSMISSION 



239 



layer; h\ is the height of the sound projector above 

 the top of the thermochne, that is, above the top of 

 the 30-ft interval in which Ac is measured; r is the 

 range from projector to hydrophone. The last term 

 on the right is taken over from equation (8); the 

 values of the attenuation coefficient used are given 

 in Table 2. Equation (9) has been checked in detail 

 at 24 kc only, but presumably gives an approximate 

 indication of the anomalies expected below the 

 thermocline at all frequencies above a few hundred 

 cycles. At increasing depths below the thermocline, 

 the anomaly decreases somewhat, the decrease being 

 most marked for the shallower thermoclines. 



10.2.3 Temperature Gradients near 

 Surface 



When temperature gradients are present in the 

 top 50 ft of the ocean, the transmission loss from a 

 projector at 16 ft to a distant hydrophone is corre- 

 lated with the following variables : the sharpness and 

 depth of the gradients (for practical purposes, the 

 decrease of temperature from the surface down to 

 30 ft) ; and A, the depth at which the temperature is 

 0.3 F less than the surface temperature. For a deep 

 hydrophone, the temperature gradients at intermedi- 

 ate depths are also of importance. 



Sharp Sukface Gkadients 



When the temperature change in the top 30 ft is 

 more than 1/100 times the surface temperature, the 

 sound beam is bent downward by the decrease of 

 sound velocity with increasing depth. The plot of 

 transmission anomaly against range usually shows 

 three different regions as follows: 



1. The direct sound field from the projector out to 

 the shadow boundary. The anomaly within the direct 

 soimd field is primarily the result of absorption, and 

 equation (8) is applicable. 



2. The near shadow zone. Beyond the shadow 

 boundary, the soimd intensity decreases very rapidly 

 for some distance. Representative values for this de- 

 crease are 50 db per kyd at 25 kc and about one- 

 third this at 5 kc. These coefficients of attenuation in 

 the shadow zone are apparently about half the values 

 estimated from the theory of diffraction by a smooth 

 velocity gradient. The range to the shadow boundary 

 increases with depth in accordance with ray theory, 

 but seems to be systematically somewhat less than 

 predicted. 



3. The far shadow zone. With standard echo-rang- 

 ing gear and pulses 100 msec long, the transmission 



anomaly of scattered sound at ranges of several 

 thousand yards is about 50 db. Thus when the trans- 

 mission anomaly of the direct or diffracted sound in 

 the shadow zone exceeds about 50 db, the observed 

 sound is scattered sound, with an anomaly which 

 does not depend strongly on further increases in 

 range. This scattered sound is incoherent. For short 

 pulses the intensity of this scattered sound is propor- 

 tional to the pulse length; it becomes negligibly small 

 for explosive sound. 



To predict the anomalies expected under given 

 temperature conditions, it is simplest to use curves 

 of average anomalies for such conditions. Since un- 

 explained deviations are frequently found between 

 individual anomalies and the predictions of ray 

 theory, use of average curves gives results about as 

 accurate as the more elaborate methods. An example 

 of this approach is Figure 40 of Chapter 5, where 

 average curves are given for different values of D2, 

 the depth at which the temperature is 0.3 F less than 

 the surface temperature. 



Weak SxmFACE Gradients 



When the temperature change in the top 30 ft is 

 less than 1/100 of the surface temperature, but gradi- 

 ents are present in the top 50 ft, the division of the 

 sound field into the three regions described previously 

 is usually not observed. Since a small change in such 

 temperature conditions may lead to a large change of 

 transmission anomaly, the observed anomalies are 

 highly variable and can neither be compared with 

 theory nor predicted practically with much accuracy. 

 Average anomalies for different values of D2 are given 

 in Figure 49 in Chapter 5 for a shallow hydrophone. 

 For a deep hydrophone, below the thermocline, equa- 

 tion (9) may be used for approximate results. 



10.2.4 



Sound Channels 



When the velocity of sound above and below the 

 sound source is appreciably greater than the velocity 

 at the source, the sound rays which leave the source 

 with small inclinations will propagate out indefinitely 

 without surface or bottom reflections, bending back 

 and forth but always remaining within some fixed in- 

 terval of depths. 



Surface Sound Channels 



When the sound projector lies below a sharp nega- 

 tive gradient and above a sharp positive gradient, 

 sound channel effects should be marked, with regions 

 of alternately high and low anomaly found out to 



