508 



EXPLORATION GEOPHYSICS 



TV POWER SUPPLY AND 

 DISTANT ELECTROOe 



Fig. 305. 



-Assumed equipotential bowl surrounding 

 electrode Si. 



rules were developed may not obtain in the particular area under investi- 

 gation. Two of the many "short cuts" in interpretation will be discussed 

 here. 



Many literature references contain discussions of the "potential bowl" 

 theory, t The apparent validity of this method of interpretation derives 

 from the following considerations. In an isotropic, homogeneous medium, 

 all points equidistant from the current electrode lie on an equipotential 

 surface. Hence, the potential at a point P, at any fixed distance along 

 the surface of the ground from the current source S\, will define the sur- 

 face trace of the particular equi- 

 potential hemisphere having a 

 radius Vg equal to the distance 

 F^'i. (Figure 305.) It is assumed 

 that any subsurface condition 

 which may alter the potential 

 value at any point a distance Vg 

 from the point ^'i will cause a 

 like change in the surface poten- 

 tial measured between P and S-^. 

 In other words, the equipotential bowl is assumed to be a rigid, non-dis- 

 torted surface ; and if this were true, the depth of investigation d would 

 be equal to the distance rg. 



Obviously, this equipotential bowl theory must be modified to correct 

 for the distortion of the equipotential surface caused by the effect of the 

 distant power electrode, and also for the distortion of the equipotential 

 surface caused by the subsurface inhomogeneities, including the effect of 

 the distortion due to the layer whose depth is to be determined. In extreme 

 cases (where an excellent conductor exists at depth) the depth of investi- 

 gation may be greater than the surface radius of the equipotential bowl, 

 while in other cases where high resistivity materials exist at depth it may 

 even be less than ^ of the bowl radius. With these limitations it is obvious 

 that the theory must be applied with extreme caution. 



Empirical formulas relating the electrode spacing at the surface of 

 the ground with the depth to an underlying stratum have also been derived 

 for the Wenner electrode arrange- 

 ment. (Figure 306.) Again it is 

 assumed that the equipotential sur- 

 faces about the two power elec- 

 trodes are undistorted hemispheres 

 and that the depth of measurement 

 is equal to the distance a; i.e., the 

 effective depth of measurement is 

 assumed to be one-third the separation of the energizing electrodes. 



t See, for example, A. S. Eve and D. A. Keys, Applied Geophysics (Cambr. Univ. Press), 

 1938, pp. 95-97. 



Fig. 306. — Equipotential bowl theory applied to 

 the Wenner configuration. 



