THE SMOOTH SOUNDING GRAPH. A Manual for Field Work ... - BGR

2.2.8. Insulation and leakage current
48
The insulation presents one of the most important problems in geoelec-
trics. In the following quite real case we may use 200V direct voltage for
the power supply of the electrodes A and B. Between the potential elec-
trodes M and N approximately 2mV are assumed to be measured. In this
example the voltage ratio would be 100 000:1.
One could have the opinion, that a sounding curve is susceptible against
leakage current, when the first layer has a perfect conductivity. That is
however a wrong thinking. The poorer the conductivity of the first layer is
the more susceptible is a curve against leakage current. Another paradox?
We have to study this fact in detail.
From chapter 1 we know that the information about the resistivity distri-
bution in the layered underground is reflected to the earth's surface by
the current density j "below our feet" between the potential electrodes M
and N. As we cannot measure j directly we do it by recording the voltage
U between M and N using the formula from chapter 1.3:
U = j ρ
(11)
a
From this voltage U the apparent resistivity is calculated after formula
(13) given in chapter 1.4:
We now compare two cases
U
a K
I
= ρ (13)
I. high resistivity of the surface layer: ρ1 (I) =10 000 Ωm
II. low resistivity of the surface layer : ρ1 (II) = 10 Ωm
We now assume that our measurements are carried out by using the
same current intensity I and that this current I creates by leakage any-
where outside or inside the instrument an additional current density j’
between M and N. This means that this j’ will keep its value if there is no
change in I.
Taking into account this "disturbing" j’ we have to write formula (11) in
the form
U =
( j + j')
ρ
a
1