Chap. 10] ELECTRICAL METHODS 811 



whose root-mean-square value is 



This expression is virtually the same as the radiation component from 

 a distance of X/27r (or x = 0.159) and outward, but in the near-zone this 

 field is very much greater than the radiation component. Hence, the 

 static and inductive field components must be considered in problems 

 involving distances from the conductor of less than ^ to j wave length. 

 In all electrical methods previously discussed, only the induction com- 

 ponent of the magnetic field (eq. [10-65]) is measured, and the radiation 

 component is neglected. 



If the source of radiation is in or beside a conductive medium, the elec- 

 trical and magnetic field components decrease more rapidly than stated 

 in eq. (10-65). This attenuation is largely due to the skin effect (see 

 page 652 and 685). In the formulas previously given, the displacement 

 current was neglected. If this is now considered, the "transmission 

 factor" may be written 



T.F. = e"~^ ^2^'' + jr-', (10-68a) 



where d is depth, c light velocity, k the dielectric constant, / frequency, 

 V permeability, <r conductivity, and lengths are in cm and physical con- 

 stants in e.s.u.'s. Usually, the ground permeJ^bility is unity, and the 

 transmission factor becomes 



e-^'^^Gy-(7)"-5, (10-686) 



which for K = is identical with formula (10-236). For a layer 124 feet 

 thick, Joyce^"^ has calculated the attenuation for various resistivities and 

 dielectric constants (Fig. 10-126). The dielectric constant is effective 

 only when it is accompanied by high resistivities; it causes the curves to 

 branch at the higher frequencies only (10* to 10^). For most geophysical 

 applications, the simpler formulas are therefore sufficient. The depths at 

 which a wave with horizontal front decreases to one-half of its initial 

 amplitude may be obtained from Fig. 10-127. It is evident that applica- 

 tion of radio methods is limited to dry climates, dry overburden forma- 

 tions, interiors of salt mines, and geologic problems where subsurface 

 structures are reflected in conductivity changes very near the surface. 

 Eve and Keys"" made extensive measurements in the Mammoth cave in 



"» J. W. Joyce, Bur. Mines Tech. PubL No. 497. See also A. S. Eve, and D. A. 

 Keys, A.LM.E. Tech. Publ. No. 316. 

 "" Loc. cit. 



