Download RMT Signature of the Rhineland Brown Coal I. Introduction

20. Kolloquium Elektromagnetische Tiefenforschung, Königstein, 29.09.-3.10.2003, Hrsg.: A. Hördt und J. B. Stoll
RMT Signature of the Rhineland Brown Coal
Karam S. I. Farag* and Bülent Tezkan*
E-mail: [email protected]
* Institut für Geophysik und Meteorologie (IGM), Universität zu Köln, Albertus-Magnus-Platz, D-50923 Köln
I. Introduction
Cologne-based RWE Rheinbraun AG is responsible for mining of lignite, or brown coal,
in Rhineland with an annual production of around 100 million metric tons. Rhineland brown coal
accounts for around 16% of German’s electricity supply. Growing competition from other
sources of energy, such as imported hard coal, made it essential to minimize costs, especially in
field-work functions like expensive drilling and direct-sampling. Here the geophysics enters the
picture. Since electromagnetic (EM) methods have become more population in surface-mining
applications, EM survey in advance of the drilling could help design the future drilling (or directsampling) pattern. A total number of 86 radiomagnetotelluric (RMT) and 33 transient
electromagnetic (TEM) soundings (five separate profiles) were carried out over the shallow coal
seams at the "Garzweiler I" mining district, west of Cologne (Fig. 1), to image the vertical
electrical resistivity structure of those seams. To determine what can be interpreted reliably from
EM measurements, 16 rock samples for different lithologies were collected from the surface
outcrops in the area and their direct current (DC) and alternating current (AC) resistivities were
measured in the laboratory. We present here the one- and two-dimensional RMT inversion
results for three profiles conducted over a coal-covered area (Fig. 2).
Figure 1: Field-panorama of the "Garzweiler I" mining district, west of Cologne.
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20. Kolloquium Elektromagnetische Tiefenforschung, Königstein, 29.09.-3.10.2003, Hrsg.: A. Hördt und J. B. Stoll
Well ID: WS1380
TEM 17
TEM
RMT
32
RMT
RMT 21
RMT 42
RMT 50
Profile III
RMT 43
RMT 1
RMT 49
RMT 22
Profile I
Profile II
Figure 2: The topography and locations of RMT soundings over the coal-covered area.
II. Radiomagnetotellurics (RMT)
Methods utilize EM radiation generated in the low frequency band by remote powerful
military (10-30 kHz) and civilian broad-casting (30-300 kHz) radiostations which transmit
continuously either an unmodulated carrier wave or wave with superimposed "Morse Code."
When the receiver locations are located at least seven "skin-depths" away from these transmitters,
EM waves are essentially planar and horizontal. If the waves are polarized in the xy-plane and
travel downward in the z-direction. In this case, simultaneous measurements of two orthogonal
components of the time-varying electric (Ex) and magnetic (Hy) fields, for selected frequencies,
using two ground potential-electrodes and a vertical coil respectively can be easily done.
Analogous to magnetotellurics (MT), data analysis commences with calculation of the apparent
resistivity ρa(ω) and the impedance-phase φ(ω) using the well-known "Cagniard formulae" of
MT.
For our field measurements, the RMT instrument was developed from a prototype built
at the Hydrogeological Institute of the University of Neuchâtel, Switzerland. The data can only be
acquired in scalar mode. Since the strike direction was often unknown, the measurements were
made at 6 different orthogonal azimuths, namely at 0o, 30o, 60o, 80o, 120o and 150o N (Fig. 3).
Due to the large number of distant transmitters in the Garzweiler region, it was easily possible to
cover the entire RMT spectrum using only the best-observed frequencies (19.6, 21.7, 23.4, 24,
61.9, 65.8, 75, 118.7, 153, 162, 177, 183, 198, 207, 216, 225, 234, 243 and 252 kHz).
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20. Kolloquium Elektromagnetische Tiefenforschung, Königstein, 29.09.-3.10.2003, Hrsg.: A. Hördt und J. B. Stoll
0o
ρa,xy(ω) =
2
1
ω µo
φxy(ω) = tan-1
30 o
Ex(ω)
H y(ω)
60 o
80 o
Im [Ex(ω)/Hy(ω)]
Re [Ex(ω)/Hy(ω)]
120 o
150
Transmitter
Vertical
Coil
o
Electric Field
Component (Ey)
Potential
Electrode
RMT Instrument
y
x
Magnetic Field
Component (Hy)
252 kHz
z
198 kHz
75 kHz
19.6 kHz
Figure 3: Multi-frequency RMT field-setup over a horizontally-layered earth.
III. Interpretation of RMT Data
The interpretation of RMT data at the IGM is currently carried out using a standard
scheme of successive techniques as follows;
a. Viewing Resistivity and Impedance-phase
Plotting of apparent resistivity and phase values versus measuring distance (Fig. 4-a)
showed a slight increase for apparent resistivity and decrease for phase values throughout the
profiles from SW to NE. All apparent resistivity curves showed a descending behavior with
increasing the frequency. While phase curves showed a change from about 25o to 50o with
increasing the frequency (Fig. 4-b). This can roughly be explained by an upper conductor
overlying a resistive medium. Plotting of apparent resistivity and phase values versus measuring
azimuth, for every RMT-frequency band, (Fig. 4-c) showed that the change of either resistivity or
phase is quite small (i.e. they are independent of the transmitter’s azimuth). This may assume that
the data are almost consistent with the one-dimensional (1-D) resistivity model.
b. ρ*-z* Transformation
Theoretically, observed RMT data can be interpreted according to the ρ*(z*)
transformation (Schmucker, 1987) which allows estimates of the conductivity depth distribution
using modified (or substitute) resistivity values for phases ranging from 0o to 45o or from 45o to
90o. The ρ*(z*) depth sections below the three profiles (see as example, Fig. 5) showed a
monotonic increase of ρ* values downwards with decreasing frequencies indicating an upper
conductor overlying a resistive medium, the z* values are scattered at the lowest frequencies. This
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20. Kolloquium Elektromagnetische Tiefenforschung, Königstein, 29.09.-3.10.2003, Hrsg.: A. Hördt und J. B. Stoll
is interpreted as thin coal seam overlying a sand layer. The coal seam has a gradual thickness
decrease from SW to NE. In the sense of ρ*(z*) transformation, the maximum investigation
depth was about 12 m. As Ziebell (1997) pointed out, in the case of an upper conductor
overlying a resistive medium (e.g. a waste mass overlaying an undisturbed resistive-geology), 2z*
can be used as a maximum investigation depth for 2-D RMT interpretation. We found that 2.5z*
is quite satisfactory in our case, either for one- or two-dimensional (2-D) interpretation (see Sections
III-c and III-d).
[a]
100
60
Transmitters at 120o N
Transmitters at 120o N
RMT 1
24 kHz
61.9 kHz
118.7 kHz
153 kHz
207 kHz
252 kHz
RMT 21
Impedance Phi [Deg.]
App. Rho [Ohm*m]
50
40
30
20
10
RMT 1
24 kHz
61.9 kHz
118.7 kHz
153 kHz
207 kHz
252 kHz
RMT 21
0
10
0
100
200
[b]
100
300
400
Distance [m]
0
500
100
60
200
300
Distance [m]
400
500
All transmitters
All transmitters
RMT 1
RMT 5
RMT 9
RMT 13
RMT 17
RMT 21
10
RMT 2
RMT 6
RMT 10
RMT 14
RMT 18
RMT 4
RMT 8
RMT 12
RMT 16
RMT 20
40
30
20
100
Frequency [kHz]
[c]
10
10
1000
60
RMT 1
RMT 5
RMT 9
RMT 13
RMT 17
RMT 21
0
RMT 2
RMT 6
RMT 10
RMT 14
RMT 18
RMT 3
RMT 7
RMT 11
RMT 15
RMT 19
RMT 4
RMT 8
RMT 12
RMT 16
RMT 20
RMT 2
RMT 6
RMT 10
RMT 14
RMT 18
RMT 3
RMT 7
RMT 11
RMT 15
RMT 19
100
Frequency [kHz]
RMT 4
RMT 8
RMT 12
RMT 16
RMT 20
1000
High RMT-frequency band
[234.0, 243.0 and 252.0 kHz]
50
Impedance Phi [Deg.]
App. Rho [Ohm*m]
High RMT-frequency band
[234.0, 243.0 and 252.0 kHz]
10
RMT 1
RMT 5
RMT 9
RMT 13
RMT 17
RMT 21
0
10
100
RMT 3
RMT 7
RMT 11
RMT 15
RMT 19
Impedance Phi [Deg.]
App. Rho [Ohm*m]
50
40
30
RMT 1
RMT 5
RMT 9
RMT 13
RMT 17
RMT 21
20
10
RMT 2
RMT 6
RMT 10
RMT 14
RMT 18
RMT 3
RMT 7
RMT 11
RMT 15
RMT 19
RMT 4
RMT 8
RMT 12
RMT 16
RMT 20
0
50
100
Tx-azimuth [Deg.]
0
150
50
100
Tx-azimuth [Deg.]
150
Figure 4: Apparent resistivity and phase versus measuring distance (a), frequency (b), and azimuthdirection (c), profile I.
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20. Kolloquium Elektromagnetische Tiefenforschung, Königstein, 29.09.-3.10.2003, Hrsg.: A. Hördt und J. B. Stoll
Figure 5: ρ*(z*) depth section below profile I.
c. One-dimensional (1-D) Inversion
Models for different RMS obtained from Occam’s inversion (Constable, 1987) of the
sounding RMT 32, close to the stratigraphic-control borehole "WS 1380", (Fig. 6-a) showed
smoothing curves exhibiting an upper conductor (Garzweiler coal seam) overlying a resistive
medium (sand). The coal-sand boundary is not quite clear as the RMS threshold increases.
Because the RMT data are skin-depth limited, only the first two layers (i.e. Garzweiler coal and
the underlying sand) are needed to explain the data. Throughout each profile, Occam’s results
were quite consistence (Fig. 7-a). Only for profile III, we had to skip up to 50 % from its data
before inversion. The blocked-layer thicknesses, after adjusting from the borehole-geology, and
their average resistivity obtained from smoothed-earth model were used to formulate a good
starting model for the full non-linear inversion to drive the layered-earth model (Inman, 1975) at
the sounding RMT 32. Beginning from this reference sounding and using a kind of recursive
starting modeling (which means the inversion results for the previous sounding is used as starting
model for the present one), the inverted sections could be driven reasonably (Fig. 7-b) with a
resolution depth up to 30 m.
[a]
[b]
1000
100
10
0.1
Start model [based on Occam's model]
End model
Equivalent model
Start model
RMT=2.059
RMS=1.601
RMS=1.552
RMS=1.538
RMS=1.528
RMS=1.497
1
Rho [Ohm*m]
Rho [Ohm*m]
1000
100
Depth [m]
10
10
0.1
100
1
Depth [m] 10
Figure 6: 1-D smoothed-earth (a) and layered-earth (b) models, sounding RMT 32, profile II.
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20. Kolloquium Elektromagnetische Tiefenforschung, Königstein, 29.09.-3.10.2003, Hrsg.: A. Hördt und J. B. Stoll
[a] RMS%=0.85-1.699
[b] RMS%=1.002-1.865
Figure 7: 1-D smoothed-earth (a) and layered-earth (b) inverted section below profile I.
d. Two-dimensional (2-D) Inversion
Using "Tikhonov regularization", non-linear conjugate gradients (NLCG) algorithm (Rodi
and Mackie, 2001) finds a regularized solution of the 2-D inverse problem for RMT data. The
inversion procedure uses the predicted impedances from the forward calculation, using a finitedifference algorithm, to modify the model parameters that minimize the objective function. To
begin, one must develop an initial guess (start model) of the electric structure of the subsurface.
The earth is broken down into discrete blocks for solving the problem. Because the calculation is
extremely sensitive to the geometry of the mesh, during the course of discretizing the 2-D earthmesh, four meshing parameters should be well-adjusted to aid in the design: (1) the "skin-depth
limit", (2) the "size-delta limit", (3) the "mesh extension", and (4) the "topographic inputs". The
L-curve criterion (Hansen, 1999) provides a means of estimating an appropriate value of the
trade-off parameter (τ) between the size of the regularized solution and the quality of the fit that
it provides the given data. If the model norm is plotted against the misfit for a wide range of τ,
the resulting curve tends to have a characteristic "L-shape", especially when plotted on doublelogarithmic axes (Fig. 8). The corner (i.e. the point of maximum curvature) of this L-curve
corresponding to a roughly equal balance of the two terms.
The 2-D inverted section below profile I, as an example, is shown in Figure 9, with a
resolution depth up to 30 m. Figure 10 shows the inversion models in comparison with the
borehole-geology at the sounding RMT 32, one can see a smooth resistivity change in the case of
2-D model at the layer-boundary whereas the transition to the lower sand is more sharp in the
case of 1-D models.
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20. Kolloquium Elektromagnetische Tiefenforschung, Königstein, 29.09.-3.10.2003, Hrsg.: A. Hördt und J. B. Stoll
Solution Norm
1000
10
Iteration No. 5
0.1
0.3
1
3
10
15
25
30
50
70
100
Optimal
Tau=20
Iteration No. 10
Iteration No. 15
Iteration No. 20
Iteration No. 25
Iteration No. 30
300
1000
3000
0.1
1000
Residual Norm
100000
Figure 8: The L-curves at different iterations and the optimal regularization parameter, profile I.
Overall RMS%= 1.342
Figure 9: 2-D smoothed-earth inverted sections below profile I.
Figure 10: Comparison of the RMTE inverted models with the borehole-geology, sounding RMT 32, profile II.
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20. Kolloquium Elektromagnetische Tiefenforschung, Königstein, 29.09.-3.10.2003, Hrsg.: A. Hördt und J. B. Stoll
IV. Concluding Remarks
Over the coal-covered area, the specially designed field setup (i.e. the multi-directional,
multi-frequency RMT survey) enabled the data to be interpreted extensively by 1-D and 2-D
resistivity models. Comparison of the inversion techniques showed that 1-D smoothed- and
layered-models represent the coal-sand boundary very clearly and accurately where the geology
and the model are reasonably matched, while the 2-D smoothed-earth model shows a less distinct
boundary. One of the best uses of the 2-D inversion was to confirm that 1-D inversion is quite
valid for all soundings. The simplicity of 1-D inversion can provide sometimes an interpretation
with much resolution and more detail, with no aid of a complex 2-D inversion.
V. Acknowledgment
We would like to thank Mr. B. Becker and Mr. K. Schneider from RWE Rheinbraun AG
for providing the filed support during the measurements at the "Garzweiler I" mine and allowing
us to use the stratigraphical, topographical and well logging data.
VI. References
Constable, S. C., R. L. Parker and C. G. Constable, Occam's Inversion: a practical algorithm
for generating smooth models from EM sounding data, Geophysics, 52, 289-300, 1987.
Hansen, P. C., The L-curve and its use in the numerical treatment of inverse problems, Tech.
Report, IMM-REP 99-15, Dept. of Math. Model., Tech. Univ. of Denmark, 1999.
Inman, J. R., Resistivity inversion with ridge regression, Geophysics, 5, 798-817, 1975.
Rodi, W. and R. Mackie, Nonlinear conjugate gradients algorithm for 2-D magnetotelluric
inversion, Geophysics, 66, 174-187, 2001.
Schmucker, U., Substitute conductors for electromagnetic response estimates, PAGEOPH, 125,
341-367, 1987.
Ziebell, M., Untersuchung einer Altlast in Köln-Holweide mit Radiomagnetotellurik unter
Verwendung verschiedener Interpretationssoftware, Diplom-thesis, Institut für Geophysik und
Meteorologie, Universität zu Köln, 1998.
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