238 



SUMMARY 



water is effectively shallow for most situations. Away 

 from the continental shelf, the ocean is always deep 

 when sharply directional sound is used (as in echo- 

 ranging at supersonic frequencies), but may be 

 shallow when listening at audible frequencies to a 

 target at long range. 



10.2 



DEEP-WATER TRANSMISSION 



The transmission loss in the open ocean depends 

 on the way the velocity of sound changes with posi- 

 tion in the sea, since velocity gradients distort the 

 sound beam. These velocity gradients change with 

 time and location, but in any localized region at any 

 given time depend primarily on depth and relatively 

 little on horizontal position within that region. 

 Changes in sound velocity in deep water closely 

 follow changes in water temperature; the effect of 

 pressure changes is relatively slight and usually need 

 not be considered except for transmission to great 

 depths. 



The following subsections tell of the transmission 

 anomalies expected for various common temperature- 

 depth distributions in the ocean. 



10.2.1 



Isothermal Water 



When the top 50 ft of the ocean are isothermal, 

 transmission anomalies are determined by two major 

 effects, absorption and surface reflection. 



Sonic Fbeqctencies 



At low sonic frequencies, sound is reflected from 

 the sea surface in somewhat the same way as from 

 a flat, perfectly reflecting mirror. The partial can- 

 cellation of direct and surface-reflected sound reduces 

 the sound intensity at long range near the surface. 

 The transmission anomaly at any range may be com- 

 puted from the equation 



4 = - 10 log ( 1 



4:rhih2 , 



a It 



(7) 



where hi is the depth of the sound source, h is the 

 depth of the receiving hydrophone, R is the range 

 from source to hydrophone, and X the wavelength. 

 The quantity ja, called the effective reflection co- 

 efficient of the surface, is a semi-empirical param- 

 eter; its average value for different frequencies is 

 given in Table 1. 



Table 1. Effective reflection coefficient of the surface. 



Frequency in cycles 200 600 1,800 



Ta 0.8 0.7 0.5 



Absorption has little effect on sound transmission 

 at frequencies below 2,000 c. 



High Sonic and Supersonic Frequencies 



At frequencies above 2,000 c, the value of 7a to be 

 used in equation (7) is seldom greater than 0.5 in the 

 open sea and is frequently so small that image inter- 

 ference can scarcely be said to exist. Absorption plays 

 an increasingly important role as the frequency in- 

 creases. The transmission anomaly A may be com- 

 puted from the relation. 



A = 



ar 



1,000' 



(8) 



where r is the range in yards and where a is the at- 

 tenuation coefficient in decibels per kiloyard. Average 

 values of a at a number of frequencies are given in 

 Table 2. At frequencies above 1,000 kc, the attenua- 



Tablb 2. Attenuation coefficient in the sea. 



tion coefficient is about three times the value pre- 

 dicted from the viscosity of the water. At frequencies 

 of 24 kc and below, a is more nearly 100 times this 

 theoretical value. 



10.2.2 Thermocline below Isothermal 

 Layer 



When sound from an isothermal layer passes at 

 grazing angle into a thermocline or temperature 

 layer, where the temperature decreases sharply with 

 increasing depth, the sound rays are bent downward 

 and become more spread out. The increased distance 

 between sound rays in and below the thermocline 

 reduces the sound intensity; this phenomenon is 

 known as layer effect. The transmission anomaly 

 below the thermocline, at ranges out to 4,000 yd, 

 may be computed from the equation 



/ 2Ac — rA ar 



log(^l-f- „ )+r^^> (9) 



A = 5 



Cnhi 



1,000 



where Ac is the change in sound velocity in the top 

 30 ft of the thermocline. (If several thermoclines lie 

 above the hydrophone or if the gradient in the ther- 

 mocline increases with depth, Ac is the velocity 

 change in the 30-ft interval giving the maximum 

 value of i^c/h\.) ca is the sound velocity in the surface 



