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
The target of IP for waste detection is here the metallic content of common refuse, often
widely disseminated as small, discontinuous particles. The survey procedure is similar to that
for conventional galvanic resistivity surveying using grounded electrodes. In IP, it is particu-
larly important to utilize non-polarizing receiver electrodes in order to reduce electrode polariza-
tion effects. We used porous pots approximately 4.5 cm in diameter with copper rods immersed
in a saturated solution of copper sulfate. Electri- cal potential differences between pairs of these
electrodes in a water bath were typically less than 2 mV. The pots were wetted, when neces-
Ž .
sary, with a small amount about 50 ml of tap Ž
water to ensure low contact resistance typically .
less than 2000 V without altering the near
surface resistivity on this small scale. Transmit- Ž
ter electrodes were single nails typically 5 cm .
long wetted with 50–75 ml of salt water. Posi- tions of all electrodes were determined with a
measuring tape, and location accuracy is typi- cally 5 cm.
A dipole–dipole array was chosen for the work at the CTP because it provides both profil-
ing and sounding information simultaneously. While other arrays may offer improved resolu-
tion under some circumstances, the dipole–di- pole array is both economical and effective in a
wide variety of conditions, and the electromag- netic coupling effects are smaller than in sym-
metrical configurations. Fig. 1 shows the loca- tions of the eleven lines surveyed. Two elec-
trode spacings were employed; all lines were measured with a 5-m spacing, while the north-
ern four lines were also surveyed with a 2-m spacing. The 5-m lines provide more economi-
cal coverage of the area and a better resolution of the bottom of the waste seam, while the 2-m
data yield better resolution of the depth to waste.
Please note that the INEL CTP survey grid is in feet, with its origin at the southwest corner of
the stacked drums, while the IP survey is mea- sured in meters, with distances measured east
and west of the centre line through the CTP. All line numbers follow the official grid, e.g., Line
20 S is 20 ft south of the drum stack. Station numbers are in dipole units from the transmitter
position, e.g., station 3E is three dipoles east of the centre of the line, which is 15 m for 5-m
spaced lines.
All data were acquired with two or three dual-channel Aquila model A-1 phase measur-
Ž .
ing IP receivers a multi-channel system simi- Ž
. lar to that described by Frangos 1990 and a
battery-powered, current-regulated transmitter. Voltage and phase spectra were observed on
Line 7.5 N using 5-m dipoles between frequen-
Fig. 2. Spectra of complex resistivity measurements at Line 7.5 N, 5-m dipoles, transmitter at 0–1E, receivers to
Ž . Ž .
west. a Voltage. b Phase lag.
cies of 0.01 and 10 Hz. Transmitter dipole 0–1E was the source, and receivers were placed
on six dipoles to the west. The amplitude spec- Ž
. tra Fig. 2a show a considerable decrease with
rising frequency which would result in strong frequency effects for all dipole separations. The
slope can be well approximated by a straight line in double-logarithmic scale. The phase
Ž .
spectra Fig. 2b show large phase shifts which are virtually independent of frequency over the
observed range and consistent with the mono- tonic decrease of amplitude with increasing fre-
quency. This behaviour corresponds to the con- Ž
stant phase angle model van Voorhis et al., .
1973; Borner et al., 1991 .
¨
A single frequency was chosen for conve- nience in rapid data acquisition with the particu-
lar instrumentation employed. The spectral tests showed that 1 Hz is representative of the IP
response in this area.
The data are plotted in the standard pseudo- Ž
. section format e.g., Sumner, 1976, pp. 43–46 ,
with resistivity reported in V m and IP as phase Ž
. lag in milliradians mrad . Accuracy of the re-
Fig. 3. Typical resistivity and IP results across simulated waste, Line A, 5-m dipoles, 1 Hz.
sistivity data is principally limited by uncer- tainty of electrode locations and the transmitter
current and appears to be generally within 5. IP repeatability is approximately 2 mrad, based
on numerous reciprocal repeat points in the survey.
4. Survey results
