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ELECTRICAL METHODS 



[Chap. 10 



be calculated in the same manner as for horizontal beds and by using the 

 theory of images. In this case the number of images is no longer infinite.*" 

 The images lie on the circumference of circles with radii equal to the dis- 

 tances of source or sink from a hypothetical point of intersection of the 

 interface with the surface. The number of effective images is x/2^, 

 where 6 is the dip. Fig. 10-57 shows a number of curves calculated for 

 various dip angles for a constant resistivity ratio. The abscissa is the 

 ratio of apparent and true surface-layer resistivity, the ordinate the ratio 

 of electrode separation and depth (under the down-dip power electrode, 



Fig. 10-57. Effect of dip on apparent resistivity {k = 2/3) (after Aldredge). 



normal to the bed). For electrode separations less than one-half the depth 

 the influence of dip is very small and is approximately proportional to the 

 sine of the dip angle. For large ratios of a/h, the curves straighten out 

 appreciably. Since it is difficult to calculate dip analytically fromup-dip 

 and down-dip profiles, it is better to determine dip indirectly by profiles 

 parallel to the strike. 



6. Effects of three-dimensional geologic bodies. The effects of ore bodies, 

 lenticular conductors, and the like, can be calculated by considering them 

 as the equivalents of electrical doublets. The calculation is simplified by 

 assuming that the doublet is situated below the midpoint of the electrode 



^•R. F. Aldredge, Colo. Sch. Mines Quart., 32(1), 171-186 (Jan., 1937). 



