ELECTRICAL PROSPECTING 7 
fluenced more and more by the deeper layers. The surface layers become less 
important. In order to illustrate this effect values of u = 270:r V,/I were plotted 
against values of 7/a for various ratios of o2/o1 (Fig. 3). The potentials are 
multiplied by 7 in order to eliminate the normal drop of potential with dis- 
tance. If the ground is homogeneous the potential curve is a horizontal line, 
the ordinate of which depends on the conductivity. Thus for an earth of con- 
ductivity 01, “=1 for all values of 7. For any other conductivity o2, u=01/o2 
for all 7. In Fig. 3 the earth is of conductivity o; to a depth a, below which the 
conductivity is o2. The curves for ~ start at ~=1 for r=0 then approach the 
lines “ =01/o2 asymptotically. These curves illustrate the gradually increasing 
effect of the lower medium as r/a increases. 
Fig. 4 shows similar curves for a slightly mcre complicated case. There is 
a surface layer of conductivity 01, then a second layer of conductivity o2, and 
finally a medium whose conductivity is the same as that of the surface layer, 

Fig. 4. Theoretical potential curves for three conducting layers. 
o;. The thickness of the surface layer is a and that of the second layer 2a. Two 
curves are shown in Fig. 4: (a) for vz=30,, and (b) for o;=30:2. In curve (a) 
“u=1 at r=0, and then wu decreases for increasing r reaching a minimum at 
about r=2.5a where the second layer has most effect and finally approaching 
the line «= 1 asymptotically. Curve (b) rises from u=1 when r=0 to a max- 
imum and then decreases rapidly as it approaches its asymptote w=1. Thus 
the effect of the second layer on the potential is small near the electrode. It is 
a maximum at a distance equal to roughly the depth of the layer, and the 
effect diminishes as r increased beyond this point. These simple cases are 
sufficient to show how the potential due to a single electrode is affected by 
vertical changes in conductivity. 
In practice it has usually been found more convenient to measure po- 
tential differences rather than absolute potential. One method is to put the 
current electrodes a long distance apart and measure potential differences in 
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