44 SYLVAIN J. PIRSON 
ditions. Consequently the formulae of the apparent resistivity which 
have been established by Hummel (10) for homogeneous and isotropic 
layers can be easily extended to the anisotropic media considered 
here. We notice first that the reflection coefficient or resistivity factor 
K es ida = eh 
P20 — Pils 
which governs the intensities of the electrical images has not changed. 
We will then calculate the potential at a point of codrdinates £, 7, o 
on the surface of the ground (Fig. 2) when a current J is introduced 
into the ground at the origin of the system of coédrdinates. In order 
to facilitate the calculations, the dimensions in medium 2 are ex- 
pressed as functions of the coérdinate system £’, n’, ¢’. 
Thus the electrical potential due to J at the point (£, 7, 0) is given 
by: 
, nm=00 
a (Rasy eee a 
Ba WEN Ete) best Grete te tease) 

K" 
i Se NER MN 
aan eta {alr + On = =|} 
Expressing now é and 7 as functions of the original codrdinates x 
and y, we obtain: 
Ip'w I n= K- 
Ae PvAGe ae ayn | ra VCS shen ae (e200) 

K* 
iy ee nnn cs Sa 
te eva [et on 94/2 Ty 
If we consider now the Wenner-Gish-Rooney set-up of electrodes 
as given in Figure 1 and choose the x axis as the electrode line, the 
difference of potential at the inside electrodes due to the current J 
flowing through the outside electrodes is given by: 
I' piv I des I 
Vp, — Ve, = =+20 54 
VJ 
am | av/ay nay aa, + (2nh)? 


704 
