ELECTRICAL METHODS 603 



and (3) inductive type methods are relatively rapid for reconnaissance 

 work. 



Detailed descriptions of the many modifications of these methods will 

 not be given, but an attempt has been made to describe certain of the 

 methods to illustrate general principles of operation and theory. 



The theoretical considerations of electromagnetic exploration are usually 

 based upon Maxwell's equations for the electromagnetic field. f An alternate 

 solution is through the use of Hertzian vectors, which are particularly 

 applicable when a dipole is used for energizing the ground. For a full 

 discussion of this treatment, reference should be had to articles by Horton| 

 and Wolf .§ 



Slichter has solved the inverse boundary value problem to which the 

 reader is referred. ff The problem consisted in determining the variation 

 with depth of the conductivity and dielectric constant from a knowledge of 

 the (measured) electromagnetic field due to a prescribed oscillatory source, 

 at the surface of a semi-infinite medium (earth). The method of attack 

 started with the use of Maxwell's field equations, in cylindrical coordinates 

 for convenience. 



The following discussion will be limited to the application of the 

 various techniques to exploration problems. 



PHYSICAL PRINCIPLES 



The present electromagnetic methods employing inductive energizing 

 means are limited essentially to investigations at fairly shallow depths 

 (of the order of a few hundred feet under favorable conditions). From 

 a practical viewpoint, therefore, the inductive methods are chiefly useful 

 for the location of ore bodies lying near the surface when covered with 

 a thin overburden. 



In general, the effect that an ore body will have on the measurements 

 will depend on the size of the body, its relative electrical resistivity, the 

 frequency of the energizing current, and the type and relative resistivity 

 of the overburden. 



The larger the effective length of the ore body the greater will be its 

 effect on the magnetic field and consequently the easier will be its detec- 

 tion. The resistivity of the ore body relative to the surrounding earth is 

 also important ; the larger the ratio of resistivities the greater will be the 

 effect of the ore body. Furthermore, it is important to realize that the 

 relative resistivities may vary with the frequency used. (In particular. 



t J. A. Stratton, "Electromagnetic Theory," McGraw-Hill, 1941. 



W. R. Smythe, "Static and Dynamic Electricity," McGraw-Hill, 1939. 

 t C. W. Horton, "On the Use of Electromagnetic Waves in Geophysical Prospecting," Geo- 

 physics, XI, 4, p. 505. 



§ A. Wolf, "Electric Field of an Oscillating Dipole on the Surface of a Two Layer Earth," 

 Geophysics, XI, 4, p. 518. 



ft L. B. Slichter, "An Inverse Boundary Value Problem in Electrodynamics," Physics, Vol. 4, 

 No. 12, December, 1933. 



