Ž .
and therefore more expensive induced polar- Ž .
ization IP
method exploits electrochemical phenomena at interfaces between regions of
metallic and electrolytic conduction within a heterogeneous medium.
While the first reported recognition of what Ž
. we now call IP was by Schlumberger 1920 ,
much of its early development sprang from mine warfare research during World War II
Ž .
Grow, 1982; Collett, 1990 . The principal ap- plication of IP has been prospecting for dissemi-
nated base and precious metal ore deposits, a technology transfer of the wartime research
Ž .
Bleil, 1953; Collett, 1990 . In an early investi- gation of cultural contamination of domestic
Ž .
water supplies, Angoran et al. 1974 used IP to trace town dumps in the state of Massachusetts,
Ž .
USA. Frangos and Andrezal 1994 reported IP measurements over a landfill and toxic waste
pond in Slovakia. The increase in resolution of small polarization effects in sediments enabled
the successful application of IP measurements in environmental investigations such as the de-
tection of contaminants or the determination of
Ž hydraulic properties
Vanhala et al., 1992; .
Weller and Borner, 1996 .
¨
2. Induced polarization and complex conduc- tivity
The IP phenomena are of electrochemical origin and are caused either by metallic mineral
particles in a rather poorly conducting rock matrix or by differences in the ion concentra-
tions in the pore space or at the interface be-
Ž .
tween matrix and pore space Sumner, 1976 . Any current in a polarizable medium is hindered
from flowing by the chargeability m of the Ž
. medium Seigel, 1959 . Therefore, the conduc-
tivity of a polarizable medium s is reduced
with respect to the conductivity s of that
medium without polarizable constituents s s s 1 y m .
1
Ž .
Ž .
The current flowing in one direction ‘charges’ all the polarizable elements, and generates a
secondary voltage V . After a long duration of
s
current flow all the elements are saturated, and the primary voltage V is reached. The values of
p
primary and secondary voltages may be approx- imated in time domain IP surveys performing
Ž .
voltage measurements immediately before V
p
Ž . or after the feeding current is shut off V . The
s
chargeability is given by the ratio V
s
m s .
2
Ž .
V
p
A comparable quantity is determined in the frequency domain. In general, the amplitude of
Ž . resistivity r v
decreases with increasing fre- quency. If the resistivity is measured at two
frequencies, with v - v , the frequency effect
1 2
Ž .
FE is calculated, thus: r v
y r v
Ž .
Ž .
1 2
FE s ,
3
Ž .
r v
Ž .
2
describing the fractional decrease of the resistiv- ity amplitude with increasing frequency.
Regarding a theoretical limit of the frequency effect, the apparent resistivity of the lower fre-
quency v is estimated by the DC-value
1
V
p
r v s 0 s K ,
4
Ž .
Ž .
I with I being the current, and K the geometric
factor. The apparent resistivity at the higher frequency v may be approximated by the limit
2
V y V
p s
lim r v s K .
5
Ž . Ž .
v ™`
I Using these limits, the results from measure-
ments in time- and frequency-domain become transferable to each other:
m FE s
. 6
Ž .
1 y m Frequency effect and chargeability are not
the only quantities characterizing the polariza- tion effects of rocks. Generally, IP data contain
more information regarding the decay curve of
time-domain measurements over a wide time-in- terval or spectral IP measurements recording the
amplitude and phase angle in a frequency range. The resulting amplitude and phase spectra show
the frequency dispersion of the apparent con- ductivity.
The electrical conductivity s of rocks, which includes both conduction and polarization ef-
fects, generally may be presented as a complex Ž
X
. quantity. Both the real s
and the imaginary Ž
Y
. s
parts are frequency dependent: s v s s
X
v q is
Y
v , 7
Ž . Ž .
Ž . Ž .
with v being the angular frequency and i the imaginary unit. The in-phase component corre-
sponds to the intrinsic or Ohmic conductivity, and the quadrature component to polarization
effects which are caused by a kind of capacitive conductivity component in rocks. A complex
quantity can also be represented by the ampli- tude
2 2
X Y
s v s s v
q s v
, 8
Ž . Ž .
Ž . Ž .
Ž .
Ž .
and the phase angle s
Y
v
Ž .
w v s arctan .
9
Ž . Ž .
X
ž
s v
Ž .
The reported phase angle is the phase shift between the injected current and the measured
voltage caused by polarization effects. Note that if alternating current is used, the measured sig-
nal is also influenced by induction effects which results in an additional phase shift. Complicated
procedures to remove electromagnetic coupling
Ž .
from IP data Pelton et al., 1978 can be avoided if a frequency range and a geometry of voltage
and current electrodes are used such that these effects can be ignored. Since the complex resis-
tivity r is the inverse of the complex conductiv- ity s
1 r v s
, 10
Ž . Ž .
s v
Ž .
a measurement of conductivity or resistivity can be transformed into each other. The sign of all
phase angles given below is related to the defi- Ž .
nition in Eq. 9 . An IP measurement run at a single frequency
yields both resistivity amplitude and phase shift. The processing and interpretation of these mea-
surements requires accurate and fast modelling and inversion algorithms. While geologic struc-
tures like horizontally stratified media can be described by one-dimensional models, arbitrar-
ily shaped bodies require two-dimensional or
Ž .
three-dimensional 3-D modelling and inver-
Ž sion. In the IP frequency range i.e., below 10
. Hz and survey geometry used herein, electro-
magnetic effects are negligible. Ž .
According to Eq. 1 , the ultimate effect of chargeability alters the effective conductivity of
the media when current is applied. Thus, IP modelling can be performed by carrying out two
forward DC modelling steps using the original conductivity s and a perturbed distribution s .
The apparent chargeability is obtained from these two DC results. This procedure is used in
Ž many IP forward modelling programs
e.g., .
Weller, 1986; Oldenburg and Li, 1994 . In this paper, an alternative technique is used
which is based on the originally measured quan- tities in the frequency domain. The IP equip-
ment directly records the amplitude of the ap- parent resistivity and the phase shift between
the injected current signal and the measured voltage. These two quantities describe a com-
plex number, in this case a complex apparent resistivity, which is directly used in the inver-
sion algorithm.
3. Experimental procedure
