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I
V
+ I
- I
C 1
P 1
P 2
C 2
na
a
na
(a)-Schlumberger
I
V
+ I
- I
C 1
P 1
P 2
C 2
a
a
a
(b)-Wenner
I
V
+ I
- I
C 1
C 2
P 1
P 2
a
na
a
(c)-Dipole-Dipole
fIGURe 5.4 Arrangement and spacing of current electrodes ( C 1 and C 2 ) and potential electrodes ( P 1 and P 2 )
for the three resistivity electrode arrays most commonly employed.
“noise” caused by naturally occurring electric currents (Dobrin, 1976; Milsom, 2003; Parasnis,
1986). When using any of the three electrode arrays shown in Figure 5.4 for the purpose of areal
resistivity mapping, the measured apparent resistivity value, ρ a , is referenced to the midpoint loca-
tion between the two outer electrodes, although it is clearly understood that ρ a in fact represents a
continuous volume of the subsurface beneath the entire electrode array.
The traditional Schlumberger array is symmetric, and as shown in Figure 5.4a, typically has the
current electrodes on the outside of the array and the potential electrodes placed within the array's
interior. The spacing between the current electrodes is by a large factor greater than the spacing
between the potential electrodes. Being able in practice to move the outer current electrodes further
apart, while potential electrode positions are kept constant, makes the Schlumberger array one of
the best available for determining variations of resistivity with depth. Referring to the Figure 5.4a
setup for the Schlumberger array, the apparent resistivity is calculated as follows:
V
I
= () ( )
ρ
π
nn
1
a
(5.13)
a
where a is a distance value, and n is a factor by which that distance is multiplied.
The Wenner array (Figure 5.4b) is also symmetric, again typically with the current electrodes
on the outside and the potential electrodes on the inside of the array. The spacing between all adja-
cent electrode pairs is the same within the Wenner array (
=== This electrode
array is often used for mapping lateral changes in ρ a , partly because when the array is moved from
one location to the next, there is less chance of setup error if the spacing between all adjacent elec-
trode pairs is the same for the entire geophysical survey. Based on the Wenner array setup shown in
Figure 5.4b, the equation for apparent resistivity is
CP
PP
PC
a
).
11
12
22
= 2
V
I
ρ
π
a
(5.14)
a
 
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