748 



ELECTRICAL METHODS 



[Chap. 10 



Fig. 10-77c. Potential-drop ratios for two 

 layers as functions of distance, for constant 

 electrode separation (adapted from Baird). 



expanding electrode system. 

 If the electrode interval is one- 

 half the distance to the first 

 (A) stake (which is the same 

 as one-third of the center 

 stake distance), the curves 

 peak at a depth closely equal 

 to the A stake distance (for 

 positive k values). 



When a good conductor 

 occurs below a poor conduc- 

 tor, A; is negative and the 

 series terms in eq. (10-42/) 

 become alternatingly positive 

 and negative. The series con- 

 verge less rapidly and the 

 peaks are located at center 

 stake distances nearly twice 

 the depth (for constant elec- 

 trode spacing equal to one-half 

 the depth) . For extreme con- 

 ductivity contrasts, the con- 

 vergence of the series is very 

 slow and the ratio drops 



rapidly. Preliminary calculations" indicate a ratio peak at about 3| times 

 the depth. 



2. Dipping layers. The effect of dip on P.D.R. may be calculated from 

 the correspondmg apparent resistivity relations. Only one set of images 

 is required for one source, since the other electrode may be assumed to be 

 at infinity. The potentials must be figured for three instead of two points 

 and their difference and the difference ratio must be formed.^ P.D.R.'s 

 so calculated are shown in Fig. 10-78 for various angles of dip of a smgle 

 layer. It was assumed in all cases that the near-power electrode was so 

 located as to make the depth, normal to the dipping bed, 18.5, regardless 

 of dip. Calculations were carried out for one resistivity ratio only (k = 1). 

 The results are valid for an electrode system moved downward in the 

 direction of maximum dip. Results in Fig. 10-78a are for a constant elec- 

 trode separation and in Fig. 10-78f) for an expanding system. 



3. Vertical contacts. A determination of the effects of vertical bound- 

 aries is of practical importance for the location of contact zones, faults, 



" John Baird, Doctor's Thesis, Colorado School of Mines, May, 1940. 

 »* M. Jameson, Master's Thesis, Colorado School of Mines, 1937. 



