ELECTRICAL METHODS 



491 



-/ 



//iX^/i^i^^ •i'^.ik^PK^i ^^A^/^J^V . 



-V- 





The quantities pa and pi can be obtained from measurements taken at the 

 surface, since pa is equal to pi for a << d (electrode separation small 

 relative to the thickness of the 

 overburden). 



Tagg's Graphical Method. 

 — Figure 293 represents a 

 two-layer structure comprising 

 a bed of resistivity pi and 

 thickness d overlying a me- 

 dium of resistivity p2 and in- 

 finite extent, t A Wenner 

 electrode configuration for 

 measuring the apparent resis- 

 tivity is shown schematically in 

 the upper portion of the figure. 



The depth d to the lower formation is obtained by making use of Equa- 

 _ P2 ~ pi _ 1 ~ pi/p2 



earth 



/? 



_^<::^ ^ r ^ ^ ^^ -^ '-/'^ ^^Bounc^ry Plane 



Fig. 293. — Wenner configuration applied to a two-layer 

 structure. 



tion 19 and the relation Q2 



It is clear that the two 



P2 + pi 1 + Pl/p2 

 "unknowns" in Equation 19 are Q2 and d/a. Also, it follows from the rela- 

 tion Q2 = 9\/9'2. ^^^ Q^ depends only on the ratio pi/p2. Also, Q2 can 



1 + pi/p2 

 only take on values between + 1 and — 1, corresponding to the values 

 between the extreme conditions pi < < p2 and pi > > p2 respectively. 

 The computed values of pi/p2 corresponding to various assumed values 



of Q2 are given in Table 16, where ^ = T~r7T~* 



P2 1 + U2 



It is possible to calculate the ratio of the average resistivity to the re- 

 sistivity in the upper stratum, pa/pi, by assuming various values for Q2 and 

 the ratio d/a. (Compare Equation 19.) This is done most conveniently 

 by a graphical method. When Q2 is positive, i.e., when p2 is greater than 

 pi, it is convenient to use the ratio of the conductivities oJ(j\, instead of 

 Po/pi. (ca is the apparent conductivity and is equal to 1/pa, while o-i is the 

 conductivity of the upper stratum and is equal to 1/pi.) 



This follows from Equation 19 

 ^ = 1 + 45* 



where 



-l|[-%n""[-""a)"i 



t G. F. Tagg, "Interpretation of Resistivity Measurements," A.I.M.E. Geophysical Prospecting, 

 1934, pp. 135-145. 



