Chap. 10] 



ELECTRICAL METHODS 



653 



amplitudes of the horizontal and the vertical components, as well as their 

 relative phase shift, are functions of the effective conductivity and dielec- 

 tric constants of the near-surface formations. According to Zenneck, 



Z2 



1 + jmi 



or 



V 



nio 



Vl 4- 



mi 



(10-18a) 



where the factor mo = /kopo/18-10^^ (ko = dielectric constant, / = fre- 

 quency, and p = resistivity in ohm-cm) refers to air, and the factor 

 mi = /kipi/18-10" refers to the effective ground properties. The phase 



Fig. 10-18. Elliptical polarization resulting from composition of a horizontal and a 

 vertical component which are out-of-phase. 



shift between the two components is proportional to the reciprocal of the 

 factor mi , so that 



tan 2<p = 



18.1 0' 



Uipi 



(10-186) 



Curves giving the ratio X/Z and their phase shift as functions of dielec- 

 tric constant and conductivity of the ground have been calculated by 

 Zenneck" and Feldman.'^ 



Because of the out-of-phase condition of the horizontal with reference 

 to the vertical component, the resultant electrical field vector describes 

 an ellipse; this phenomenon is referred to as elliptical polarization and 

 plays an important part in all electrical prospecting methods using inter- 

 mediate and high frequencies. In Fig. 10-18 a large vertical component 

 is shown as one wave train, and a horizontal component as another, with 



" Wireless Telegraphy (1915), Fig. 300, curves for 670-meter wave length. 

 " I.R.E. Proc, 21, 790 (June, 1933), Fig. 22, for 16-meter wave length. 



