716 ELECTRICAL METHODS 



ratio of apparent resistivity, pa , and true resistivity, pi , is 



Pi 



1+4E 



k" 



-4Z 



k" 



y.+ffy »-v 



1+4E 



-4E 



*-efL 



A;* 



v^+("y "-v^H" 



2nY 



[Chap. 10 



> (10-38) 



where u = a/h, the ratio of electrode separation and depth. 



Fig. 10-52. Apparent resistivity ratio as a function of electrode separation in terms 

 of depth, for various true resistivity ratios (after Hummel). 



Fig. 10-52 shows the ratio of apparent and top-layer resistivity as a 

 function of the ratio of electrode separation and depth, for various re- 

 sistivity contrasts. If the resistivities are equal, the apparent resistivity 

 is equal to the true resistivity. If A; = 1 (lower layer of infinite resistivity), 

 the apparent resistivity increases in direct proportion to the electrode 

 separation, the proportionality factor being about 1.386. (with a/h). The 

 apparent resistivity ratios for the A;-values between and 1 approach 

 asymptotically the true resistivity ratios for large electrode separa- 

 tions. 



