ADVANCES IN OIL PROSPECTING 123 
give depth directly, but the electrode separation or depth of penetra- 
tion divided by the thickness of the upper layer. As both the re- 
sistivity and the thickness of the upper layer are constants, this 
method of graphical representation does not change the shape of the 
curves. 
It is seen from the figures that in this case the boundaries of the 
formations underneath are reflected as points of maximum curvature, 
or as third derivatives of the apparent resistivity with respect to the 
electrode separation. 
The curve denoted by ‘‘k equal to one”’ is of very great importance 
in practical work; it is frequently encountered in applying resistivity 


SACoRCEL 
Fic. 16.—Curves of apparent resistivity over surface layer of thickness / for differ- 
ent ratios of resistivities of surface layer and infinite lower layer (after Hummei). 
methods in civil engineering work and related geological problems 
where the thickness of the overburden above bedrock is to be de- 
termined. In such cases the resistivity of the bedrock is ordinarily so 
much greater than the resistivity of the overburden that the curves 
approach the theoretical case where the lower resistivity may be 
considered as infinite. For a comparison with the results obtained in 
practice, see the curves shown in Figure 27. 
The diagrams shown in Figure 17 a and 6 represent the results of 
the theoretical analysis for the 3-layer case. In Figure 17 a, the second 
medium has the lowest resistivity; in Figure 17 5, the second medium 
has the highest resistivity. It is seen that in this case (3-layer prob- 
lem) the peaks in the curves represent approximately the depth to 
453 
