ADVANCES IN OIL PROSPECTING 127 
separations, say for 50, 100, and 150 feet (at the points 2, 3, and 4) the 
ratio of the apparent resistivity to the resistivity of the upper medium 
is computed (Fig. 18D). 
Diagrams have been prepared previously for this ratio = as a func- 
p 
tion of hk, a being constant for each diagram (Fig. 18 A-C). (The ap- 
pearance of the curves in these diagrams is much the same as those 
shown in the diagram of Figure 16, except that not a/h, but its 
reciprocal, #/a is used, and that a is a constant for each diagram.) 
In the example shown in Figure 18D, the ratio of apparent to surface 
resistivity is 0.9 for the separation 50 feet; hence, the lower diagram 
of Figure 18A is used, and the corresponding values of # and k which 
are intersected by the line 0.9 are noted and plotted (curve 2 in 
Figure 18D). Then the next point, a= 100, is taken, at which the ratio 
is 0.7; one proceeds as before, this time using the diagram in Figure 
18B, and plotting & as a function of / for the ratio 0.7. This gives 
curve 2 in the interpretation diagram. Curve 3 is obtained in the same 
manner. All three curves intersect at a depth of nearly 58 feet, whick 
is the desired depth of the formation boundary. 
Under favorable conditions, this method works very well for the 
2-layer case, and is often applicable in practice when the depth of 
overburden is to be determined. Its application, however, depends 
altogether on an accurate determination of the surface resistivity, 
which is not always easy to accomplish—or else, the resistivities de- 
termined at the surface do not represent at all the resistivity of the 
upper layer, the thickness of which is to be determined. In other 
words, the problem then is no longer a 2-layer problem.!:? 
Schlumberger uses the following method of interpretation which 
deviates in a number of respects from that of Tagg’s: 
1) As in Tagg’s method, the resistivity of the upper stratum is 
first determined from measurements with small electrode separations. 
2) The resistivity of the lower layers is then obtained from ex- 
posures or measurements in wells (Schlumberger’s “electrical cor- 
ing’’), or from assumptions based on past experience. 
3) With these resistivities, a diagram is constructed showing the 
apparent resistivity as function of electrode separation in several 
curves for a number of values of thickness of the upper stratum. 
1 Compare also the discussion of Tagg’s paper at the meeting of the American 
Institute of Mining and Metallurgical Engineers, February, 1932. 
2 The extension of Tagg’s method to the three-layer case has recently been worked 
out by Manhart (ref. list No. 11,7). 
457 
