Chap. 10] 



ELECTRICAL METHODS 



731 



obtained for the depth (hi + hz). Determine the resistivity of the bottom 



P3 



P2 



layer ps from ki = '^1——^''. (7) Repeat the above with better values of 



P2 + P3 



Pi to obtain a more accurate figure for (hi + hz), and so on. As an ej^mple 

 of the application of the above procedure, the curve of Fig. 10-54 (a typi- 

 cal water indication) may be selected, with resistivity values of pi = 100, 

 P2 = 300, and ps = ohm-foot. The first point of the resistivity curve 

 at depth is 100. Multiplying the vertical scale by 10 (if hi = 10) gives 

 the apparent resistivity values in Table 73. 



Since a theoretical curve is analyzed here, steps (1) and (2) may be 

 disregarded. Proceeding directly to the analysis of the first part of the 

 curve (from 5 to 25 feet), we obtain the data in Table 74. 



Table 74 



The best agreement of depth values prevails in the row ki = 0.5. The 

 average there is 10 feet. This gives 300 ohm-feet for pz . The inflection 

 point in the curve indicative of the second interface is at 60 feet. Hence, 

 ^1 + /i2 = f -60 = 40 feet, and 40/p( = twu + ^^A- Thus p[ = 200 ohm- 

 feet. The approximation curve is then traced, starting with pi = 200, 

 tangent to the resistivity curve at the lower inflection point. The points 

 chosen for applying Tagg's method to the bottom part appear in Table 75, 

 which gives the best agreement of depth values in the lowest row for A; = 1. 

 The average of the depth values in this row is 40.1, which is in close 

 enough agreement with the depth assumed in the construction of the 

 theoretical curve. 



3. Quantitative interpretation (type curves), based on an interpolation of 

 theoretical curves, is used almost exclusively by Schlumberger and his 

 associates. Curves are calculated for given k values with layer thickness 



