490 EXPLORATION GEOPHYSICS 



forming the difference of the two resulting equations. That is, 



O2* 



_i_+±_2 f Qi +2y ^ I 



or 



.00 00 



5 = Za/JL + 4 y Q^ 2 y ^ I (17) 



k=i k=i 



Equation 17 is the generahzed formula which applies when the geological 

 structure consists of a semi-infinite medium of resistivity po overlain by a 

 homogeneous overburden of resistivity pi. 



In particular, if p\ = p2 — Pa, Q2 = 0, and 



2ira 



°'" E 



Pa= 2-Ka-r (18) 



Equation 18 is known as Wenner's formula.* Evidently this formula gives 

 an average resistivity pa for the area under investigation in terms of meas- 

 urable quantities {E/I and a). The average or apparent resistivity pa is 

 a mean or weighted value of the resistivity which is equal to the actual 

 resistivity only if the ground is isotropic and homogeneous. 



In interpreting experimental data obtained with a Wenner configura- 

 tion of electrodes, the conventional procedure is to plot the average re- 

 sistivity calculated from Equation 18 as a function of the electrode separa- 

 tion.** For an ideal two-layer case, the curve has the equation 



00 



Pa = 27ra -J- = Qpi ^^- + 4 > r_2 , a\'>.j->.^u. " 2 ^ 







* Equation 18 may also be obtained by computing the potential difference between 

 the two potential electrodes from Equation 8. 



** In investigations not employing the Wenner configuration, Equation 18 does not 

 obtain. However, it is always possible to plot the average resistivity as a function 

 of the electrode separation by deriving an equation which expresses the apparent 

 resistivity pa as a function of measurable quantities {E/I and electrode separations). 

 (Compare p. 518.) 



