approximately 13 m. The comparison with the real depth of 4.5 m reveals that the vertical
resolution of the IP survey is not satisfactory. A 2-D inversion of the data acquired along
Line A was performed by Yaoguo Li and Doug Oldenbourg
of the
University of
British Ž
. Columbia Oldenburg and Li, 1994 . The result-
ing amplitude and phase images are similar to those in Fig. 7, also showing different depths to
the bottom of the waste by resistivity amplitude
Ž .
and phase lag Frangos, 1997 . The finer grid used in 2-D inversion results in a high variabil-
ity of near surface resistivities. The use of a coarse grid and SIRT in the 3-D algorithm
yields smooth images emphasizing the real dominant structures and ignoring noise in the
data. The resolution of the bottom of the waste could not be improved by a 3-D processing.
There are at least three possible reasons for the modest depth resolution.
Ž . a The dipole–dipole configuration is more
suitable for finding vertical discontinuities, as demonstrated by this survey.
Ž . b The SIRT used generates smooth models
fitting the data with the lowest possible contrast in the resistivity amplitude and phase values.
No additional information or constraint is used. Ž .
c The inversion algorithm cannot overcome the ambiguity of both resistivity and IP data. A
high contrast in the intrinsic resistivity and po- larizability is necessary to explain the data.
According to the principle of equivalence, a further increase of the contrast between waste
and soil material would result in a lesser depth to the bottom of the trench.
7. Modelling experiment
To investigate the ambiguity of the data, forward modelling was performed. The model
shown in Fig. 8 consists of three layers: the top layer with a resistivity of 25 V m, a second
layer with 60 V m and the underlying halfspace with 200 V m. The phase angles are chosen to
be 5 mrad. The waste filled cell is designed as a
Ž . Fig. 8. Three layer model with embedded waste body. a
Ž . Vertical section at Line A. b Horizontal plane at a depth
of 4 m.
rectangular body situated in the second layer with a resistivity of 5 V m and phase angles of
50, 130, 200, 300 and 400 mrad. In the first step, 2-D models were run assum-
ing an infinitely long trench. In Fig. 9a, the calculated and measured apparent resistivities
are compared at the position of line A for a dipole separation of 20 m. The corresponding
results for the different phase angles are shown in Fig. 9b. Both the measured and the calculated
phase curves show two positive anomalies at the edges of the trench and a minimum in the centre
of the structure. The best fit is achieved with an intrinsic phase angle of 200 mrad.
In the second step, 3-D models were run assuming a finite extent of the waste body in
y-direction as indicated in Fig. 8b. Though the general shape of the resulting anomalies is com-
parable to those from 2-D modelling, the central minimum becomes deeper reaching even nega-
tive apparent phases, and the fit with the mea-
Ž .
sured values is better Fig. 10b . Using the
different curves as master curves, the intrinsic phase value of the waste structure is determined
to be approximately 250 mrad. Since the resis-
tivities of the layers have been chosen from the inversion result the measured resistivity ampli-
tudes are also well fitted by the 2-D and 3-D Ž
. models see Fig. 9a, Fig. 10a .
This modelling experiment has shown that the measured IP data can be confirmed if the
waste body is located at the known depth, and if an extremely high intrinsic phase value is as-
sumed. The inversion starting with a back pro- jection and searching for a smooth model yields
Fig. 9. Result of 2-D modelling and measured values for a Ž .
dipole separation of 20 m. a
Amplitude of apparent Ž .
resistivity. b Phase lag. Fig. 10. Result of 3-D modelling and measured values for
Ž . a dipole separation of 20 m. a Amplitude of apparent
Ž . resistivity. b Phase lag.
an equivalent model fitting the data, but the conductive, polarizable structure is located at a
greater depth.
8. Comparison with other methods
