472 LIEBERMANN [CHAP. 11 



from an antenna submerged in the sea. Note that the large attenuation resulting 

 from propagation through the conducting sea-water occurs only during the 

 vertical portions of the path. 



The theory of this curious surface -wave propagation was first treated by 

 Sommerfeld (1909). Banos and Wesley (1960) have recently given an 

 accurate and exhaustive treatment of this subject with extensive references to 

 the literature. The various formulae for the three electric and three magnetic- 

 field components are rather lengthy and will not be given here. However, as an 

 example, the electric field in the vertical direction, Ez, is given below 



j^ ^ cos ^ I I . ,^. 



The quantity h represents the combined depths of the receiver and radiator ; 

 p is the dipole strength and p the horizontal range. Note the exponential 

 attenuation with increasing depth ; this justifies the assertion that the radiation 

 initially travels vertically up to the surface. In addition the field component 

 attenuates as the inverse square. Hence attenuation, even after the wave has 

 reached the sea-surface, is still considerably more rapid than long-distance 

 radio transmission in air, where attenuation is inverse first power. In all 

 experiments with the surface wave the radiating electric dipole must be 

 horizontal, for only the horizontal component of the electric field leads to the 

 surface wave, the vertical components exerting a negligible field at large 

 distances. 



A . Reflectivity of Electromagnetic Waves from the Sea-Surface 



Nearly all of electromagnetic radiation originating in the air above the sea is 

 reflected from the sea-surface. For example, at frequencies below the micro- 

 wave range (i.e. less than lO^^ c/s), the reflection coefficient magnitude, F, is 

 approximately unity, or perfectly reflecting at normal incidence. Reflectivity 

 can be somewhat less at other angles of incidence. The dependence of reflecti- 

 vity on the angle of incidence is given by the equation 



r =-{s-i)i{s + \), (5) 



where 



(1 + 



2a j cos Q 



Q being the incident angle, measured from the vertical. 



It is seen from the above equation that the reflectivity of sea-water depends 

 on its conductivity. Conductivity in turn depends on the temperature (salinity 

 variations will be neglected in this discussion). This suggests the possibility 

 that the reflectivity of electromagnetic waves might be used to measure surface 

 temperatures from an aircraft. It can readily be shown from the above equation 



