Geoscience Reference
In-Depth Information
5.6.3 Induced polarisation
Table 5.2 Geometric factors for the common surface arrays and
several downhole arrays.
Resistivity is measured during the application of a constant
d.c. current. Induced polarisation is measured with a varying
current, either d.c. or a.c. As described in Section 5.2.1.5 ,
capacitance can be measured in three ways: by measuring
the decay of the potential after switching off a d.c. current,
by comparing apparent resistivity obtained with a.c. cur-
rents of two different frequencies, and finally by comparing
the phase between an applied a.c. current and a measured
a.c. potential difference. The
Surface arrays
Geometric factor (k geom )
Pole
-
pole
2
π
X BM
Pole - dipole
2 π n ð n + 1 Þ X MN
Dipole
-
dipole
π
n
ð
n
+
1
Þð
n
+
2
Þ
X MN
Wenner
2 π X MN
2
π ð
X AB =
2
Þ
, X MN
X AB =
Schlumberger
20
first is a form of time domain
measurement; the other two are forms of frequency domain
measurement. Although the frequency domain and time
domain polarisation parameters are different, they both
produce the same anomaly shapes which are comparable.
Induced-polarisation surveys measure a range of parameters
to quantify the electrical polarisability of the subsurface.
X MN
L 2
X MN G
Gradient
2
π
ð
1
U
Þ
G
¼
ð
1
+
U
Þ
3
= 2
2
V 2
½
+ ð
1
U
Þ
+
2
3
=
2
½ V 2
+ ð 1 + U Þ
U
¼
x/L, V
¼
y/L, L
¼
X AB /2
Downhole arrays
5.6.3.1 Time domain measurements
In the time domain, the transmitter alternately turns on,
producing a steady current, and then off. A graph of the
signal from the transmitter is a square wave ( Fig. 5.37a ; see
Appendix 2 ) . Note that the polarity of the current is
reversed between successive
π
Normal log
4
X BM
X BM X BN
X MN
Lateral log
4
π
Applied potential
4
π
X BM
cycles to cancel the effects
of residual polarisation and to reduce the effects of ground
and telluric currents (see Atmospheric noise in Section
5.4.2.1 ) . The duration of the on and off periods is selected
after field tests prior to commencing the survey. As
described in Section 5.2.1.5 , it takes time for the electrical
polarisation to occur, so the on-time must be long enough
to achieve suf cient polarisation but no longer, since this
will increase the time required to complete the survey. The
on-time and off-time is typically in the range 1 s to 4 s,
usually 2 s.
Figure 5.37a shows the variation in potential measured
when the subsurface is electrically polarisable. When the
current is turned on, the potential immediately increases
sharply, then more slowly before reaching a steady value.
This is known as the primary voltage (V p ), and is that used
for the calculation of apparent resistivity. The gradual
increase is associated with
'
on
'
1
1
X AM
1
X BM
1
X AN +
1
X BN
k geom
¼
2
π
ð
5
:
18
Þ
Table 5.2 gives k geom for a number of commonly used
electrode arrays, i.e. reduced forms of Eq. (5.18) .
5.6.2.1 Apparent resistivity
Equation (5.17) gives the true resistivity (
) of an electric-
ally homogenous subsurface. As described in Section 5.6.1 ,
any resistivity inhomogeneity in the subsurface will distort
the electric
ρ
field and cause the measured potential differ-
ence to differ from that due to a homogeneous subsurface.
In this case the resistivity is known as the apparent resist-
ivity (
ρ a ) of the subsurface, because it assumes that the
measurements are made on an electrically homogeneous
subsurface, even though this is very unlikely to be the case.
The apparent resistivity depends on the true resistivity
distribution of the subsurface and the electrode con gur-
ation used for the measurement. Transforming a set of
apparent resistivity data into the true resistivity distribu-
tion of the subsurface is the fundamental challenge for
interpretation techniques, which we discuss in detail in
Section 5.6.6 .
of the subsurface
capacitor. When the transmitted current is turned off the
reverse occurs, i.e. there is an initial sharp drop in potential
and then a gradual decay. This secondary voltage (V s )is
dependent on the polarisation properties of the ground
and is associated with the
'
charging
'
of the capacitor.
It is the measurement of this decay that is the basis of the
time domain IP method.
'
discharging
'
 
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