discovery of a major coal deposit in china with the use of ... · discovery of a major coal deposit...
TRANSCRIPT
Discovery of a Major Coal Deposit in China with the Use of a Modified CSAMT Method
Guoqiang Xue1,*, Shu Yan2, L.-J. Gelius3, Weiying Chen1, Nannan Zhou1 and Hai Li1
1Key Laboratory of Mineral Resources, Institute of Geology and Geophysics, Chinese Academy of Sciences,
19 Beitucheng Western Road, Beijing 100029, China2School of Computer Science and Telecommunication Engineering, Jiangsu University, 301 Xuefu Road,
Zhenjiang 212013, China3Department of Geosciences, University of Oslo, 1072 Blindern, 0316 Oslo, Norway
*Email: [email protected]; Tel.: +86-10-82998193
ABSTRACT
Conventional use of the controlled-source audio-frequency magneto-telluric (CSAMT)
method is based on calculating the apparent or Cagniard resistivity from the amplitude ratio of
the horizontal electric and magnetic field components. However, direct comparison between
these two components shows that the electric field is more sensitive to the underground medium
resistivity than its magnetic counterpart. Thus, use of the electric component only should
provide adequate information about the electric properties of the subsurface. The measurementstypically belong to the far-field zone, but show a non-dipolar characteristic because of the
source. In this paper, we therefore propose a simplified CSAMT technique based on measuring
the electric field component only. As part of this new formulation, a related theoretical model
for the electric field component accounting for the non-dipolar nature of the transmitter
antenna is introduced. This is accompanied with a new apparent resistivity definition, including
a procedure to transform it into pseudo-phase data, thus removing the static shifts.
The potential of this modified CSAMT method is demonstrated using a field case from the
Shanxi province in China. Until recently, it has been thought that no coal deposits exist in thisregion. However, application of the single-component CSAMT technique as advocated for here,
revealed a major coal deposit, which was verified later by drilling.
Introduction
The development of the controlled-source audio
frequency magneto-telluric (CSAMT) method was
inspired by the magneto-telluric (MT) technique (Gold-
stein, 1971; Goldstein and Strangway, 1975). Because of
the many advantages of CSAMT regarding information
content, signal strength, work efficiency and detection
accuracy, the technique has received increasing atten-
tion. CSAMT has been successfully applied within
metaliferous mining (Boerner, 1993; Chen, 1993),
petroleum exploration (Ranganayaki, 1992), deep sea
environmental investigations (Di, 2002), groundwater
studies (Christensen, 2000) and geothermal exploration
(Sandberg and Hohmann, 1982; Batrel and Jacobson,
1987; Wannamaker, 1997). Bartel and Jacobson, 1987)
used CSAMT surveying to identify faults and fissure-
type water storage structures in mountainous karstic
terrain. The CSAMT method has also proven very
useful when searching for certain ore structures, because
of its ability to delineate the abnormal shape and
position of a body (Boschetto and Hohmann, 1991). In
the prediction of geology in advance of mining, it is
important to locate faults and karst caves. CSAMT has
been successful in preventing and controlling disasters
by detecting the distribution of water-bearing ore zones
in the roof and floor ahead of extraction (Chen and
Yan, 2005).
To reduce field data costs, in a practical CSAMT
survey six electrical field points will share one magnetic-
field recording station, as shown in Fig. 1. Apparent
resistivities are then estimated from the ratio between
the measured horizontal components of the electric and
magnetic fields, Ex and Hy, respectively (Goldstein and
Strangway, 1975; Zong et al., 1986, 1991). This type of
acquisition inherently acknowledges the fact that the
electric field component is the most important informa-
tion carrier of the subsurface. In this paper, we propose
to use the electric field component only, and present a
modified theoretical model to analyze the data and
provide apparent resistivity maps (referred to as the
single-component resistivity formula). This modified or
single-component CSAMT technique was applied in the
Shanxi region in China, an area that was earlier assumed
47
JEEG, March 2015, Volume 20, Issue 1, pp. 47–56 DOI: 10.2113/JEEG20.1.47
to be free of coal deposits. However, use of the method
revealed a major coal deposit at depth, between 600 m
and 800 m. This prospect was later verified by drilling.
Methodology
Single-component Resistivity Formula
A simple analysis supporting the idea of using the
electric component only is given in Appendix A. In thefollowing, we proceed to analyze this field component
only. In the case of far field, the apparent resistivity
effectively normalizes out the effects of current strength,
dipole length, frequency, source-receiver distance and
orientation relative to the source. Thus, it can be defined
through a single component of the electric or magnetic
field in the far-field zone (Kaufman and Keller, 1983).
When using the inline electric field component, theapparent resistivity is given by:
rEx(v)~
4p:r3
I :l
Ex(v)
3 cos 2a{1
��������2
, ð1Þ
where I is the current, l is the length of the source, a is
the angle between the observation point vector and the
source line direction, and r is the distance from the
observation point and the center of the transmittingantenna. The x-component of the electric field was
chosen because of its larger magnitude since it is
oriented parallel to the source orientation.
In this work, we propose to further refine the
expression in Eq. (1) by taking into account the non-
dipole nature of the transmitter antenna. A finite-length
antenna with length AB is then subdivided into many
small segments as shown in Fig. 2. The reader is referred
to Appendix B for the necessary details of the
derivation; we only state the main result here:
rEx
i (v)~p:r3
MN:l: 4r2zl2
r(8r2zl2):DVi(v)
I, ð2Þ
where DVi(v) is the observed voltage difference between
two neighboring receiver (MN) electrodes.
The single-component resistivity formula, as given
by Eq. (2), is derived for a uniform half-space. Thus, by
using this formula to estimate the apparent resistivity in
the case of a layered Earth model, a volume-averaged
resistivity estimate should be obtained. We consider a
simple synthetic case to verify this assumption. To
further test the validity of Eq. (2), we also compare it
with the resistivity estimate obtained employing the
standard two-component formula according to Cag-
niard (1950, 1953):
rEx=Hyv (v)~
1
vm0
Ex(v)
Hy(v)
��������2
: ð3Þ
Note that Eq. (3) is derived assuming a homogenous
Earth.
Figure 1. Typical acquisition layout of standard
CSAMT survey.
Figure 2. Sketch indicating a small element along the
current line AB for which the electric field contribution is
computed at receiver position r. The total contribution is
obtained by summing over all such incremental responses.
48
Journal of Environmental and Engineering Geophysics
A three-layer electrical model with the following
properties was used as an example: r1 5 100 V?m, r2 5
10 V?m, r3 5 100 V?m, d1 5 500 m, and d2 5 100 m (rrepresenting layer resistivity and d layer thickness with
subscripts denoting the various layers). The length of the
transmitting source was 1,000 m and its 1-Amp
transmitting current spans a frequency range from
0.125 Hz to 8,192 Hz. Figures 3(a)–(b) show plots of
apparent-resistivity versus frequency for three different
source–receiver offsets (r 5 2,000 m, 6,000 m and
10,000 m). According to Spies (1989), the skin depth
associated with the lowest frequency will be about
4,500 m for this model. Based on the theory presented in
Appendix A, we find that the limiting offset in the far-
field is about 40,500 m for Ex and about 58,500 m for
Hy. Thus, for each offset considered here, not all the
frequencies fulfill the far-field condition.
The apparent resistivity was calculated from both
the electric-component equation (Eq. (2)) as shown in
Fig. 3(a), and the two-component Cagniard formula
(Eq. (3)) as shown in Fig. 3(b). At high frequencies,
corresponding to a far-field situation, both sets of curves
(electric-component and the ratio apparent resistivity)
coincide. However, at lower frequencies, when the
intermediate field region of the transmitter is reached,
the two curves start to diverge at the various source-
receiver offsets. With a further decrease in frequency
(reaching the low-frequency band or near-field region),
the apparent resistivity curve associated with Eq. 3
increases linearly with frequency and exhibits a steep
slope (Fig. 3(b)), which again indicates a loss of
resolution. In contrast, the single-component apparent
resistivity curves increase with a relatively small slope
(Fig. 3(a)) and finally maintain a stable value, which
reflects the correct change in conductivity. From this
example, it is evident that the single-component
apparent resistivity equation (Eq. (2)) is superior to
the ratio apparent resistivity equation (Eq. (3)), espe-
cially when the receiver is close to the source. Similar
findings were obtained for other models.
Apart from the theoretical considerations made
evident in our synthetic model studies, there are other
factors that need to be considered in practical field
surveys. Because of the different responses to noise and
the different data quality between the electric and
magnetic fields, the ratio apparent resistivity equation
may exhibit a distortion in terms of magnitude, shape
and phase, which results in an overall loss of the
resolving power in the near-field region.
Phase Conversion
Not only the amplitude, but also the phase of
the apparent resistivity will vary when the electrical
properties of the subsurface changes. The following
relation between the amplitude of the complex apparent
resistivity and the phase is derived by Kaufman and
Keller (1983):
Ys~1
p
ð?
0
d ln rv�� ��
dvln
vzvk
v{vk
��������dv ð4Þ
where vk denotes an adjacent frequency.
Figure 3. The apparent resistivity versus frequency
curves demonstrating the resolution for both the single
component (b) and the Cagniard ratio apparent resistivity(a) for various source-receiver distances (r = 2,000 m,
6,000 m and 10,000 m).
49
Xue et al.: Discovery of a Coal Deposit using Modified CSAMT
From Eq. (4), it follows that the phase curve is
related to the slope of the apparent resistivity curve. It is
therefore possible to remove the static shift between
apparent-resistivity curves according to the phase curve.
Equation (4) can be further simplified as follows
(Kaufman and Keller, 1983):
Ys & 450+450 ln rs
lnvð5Þ
According to Eq. (5), the apparent phase is a function of
the rate of change of the frequency. Therefore, it is
possible to obtain the apparent phase from the
knowledge of the apparent resistivity. The phase
conversion method using the single-component appar-
ent resistivity is an efficient way to solve the static shift
problem. For special cases, like a geological stratum
consisting of an embedded thin layer, it is not possible to
use the amplitude curve of the apparent resistivity.
However, the alternative use of the phase curve may
distinguish the thin layer. Also, when the geological
stratum is buried in a highly resistive basement, it is also
not possible to use the amplitude curve for distinguish-
ing the basement. This is because of the limited electrode
separation and no significant difference in electrical
properties. However, again the converted phase curve
shows a better performance under such conditions.
To demonstrate the feasibility of the converted
phase approach, a simple synthetic model with the
following electrical properties was considered: r1 5 10
V?m, r2 5 400 V?m, r3 5 10 V?m, d1 5 10 m, d2 5
100 m, and r 5 2,000 m. Figure 4 shows a plot of the
converted phase curve (asterisk line) together with the
theoretical apparent phase curve (solid line) for 26
sampled frequencies between 0.125 Hz and 4,096 Hz. It
is clear that no visible differences appear between the
two curves. This supports the use of the converted phase
curve since it exhibits the same resolving power as its
theoretical counterpart. However, a basic condition is
that measurements are carried out for a sufficient
recording time.
Case Study from Coal Exploration
Survey Environment and Electromagnetic Disturbances
The case study is taken from the Yangqu County,
located in the northern part of Taiyuan City in the
Shanxi Province in China. From earlier investigations,
this particular region was considered to contain no
significant coal deposits. This conclusion was partly
based on the finding of Cenozoic gray-green rock in one
of the drilled holes, which lead to the wrong conclusionthat this stratum belongs to the Benxi group. However,
because of energy shortages, the authors were invited to
conduct a modified CSAMT survey in this region to
further assess its coal potential.
The survey area is located in the northern part of
the Taiyuan basin in the piedmont hills, which are fully
covered by loess with a thickness between 300–400 m
and in the center of a syncline with preserved coalseams. The geological strata are from the Ordovician,
Carboniferous-Permian and Cenozoic ages. The Car-
boniferous strata mainly contain the coal seams, which
have an average thickness of 6.7 m as revealed by
borehole records.
The survey region is shown in Fig. 5, where the
upper left corner of the map is a picture of the area, the
lower left map shows the location within China, and thelower central map is of Shanxi Province. The main part
of the figure describes the outlay of the survey, including
22 south to north directed survey lines at 100-m line
Figure 4. Comparison between true (calculated frommodel) and converted phase curves.
Figure 5. The lower left panel is a map of China; the
lower middle panel shows the Shanxi Province and the
location of Yangqu County; the upper left panel is a photo
of the field area; and the middle panel shows the outlay of
the survey.
50
Journal of Environmental and Engineering Geophysics
interval and observation points at every 50 m. The
survey area covered a total of 15 km2. From previous
drilling and well logs, the main electrical parameters for
the survey region were obtained (see Table 1). It can be
seen from Table 1 that the shallow strata show low
resistivity, the coal seam has a relatively high resistivity,
and the basement of the coal layers shows the highest
resistivity. These observations can be used to determine
the lower depth of the coal seam.
As advocated for in this paper, the CSAMT survey
was carried out measuring only a single component (Ex)
of the electrical sensors. An equatorial dipole array was
exploited with r 5 3,000 m, AB 5 1,000 m and MN 5
200 m. The frequencies used are listed in Table 2.
Data Processing and Interpretation
To analyze the processed data properly, modeling
of some typical strata was performed prior to the field
surveys. The model results are shown in Fig. 6, which
gives the characteristic shape of the apparent resistivity
curve for two different scenarios:
N H curve (Q + N strata overlying O2 strata) shown in
Fig. 6(a)
N HA curve (same as H, but with a layer of P + C in
between) shown in Fig. 6(b).
At first glance, these two curves look very similar inshape, but there are obvious differences: 1) the ratio
between the maximum and minimum value is different,
with that in Fig. 6(a) being the largest, which again
means that a large geo-electric difference exists between
the basement and the overburden; and 2) the frequency
number corresponding to the minimum value of
resistivity is different, with that of Fig. 6(a) representing
the largest frequency (see Table 2 for conversion), whichagain corresponds to a shallow burial depth of the
basement. Correspondingly, the burial depth of the
basement in Fig. 6(b) is deeper, which may represent
the case of a possible coal deposit.
In general, if the basement of the coal seam is the
Ordovician grey rock, then it can be regarded as the
standard electrical basement stratum because of its wide
distribution and high resistivity. However, if the
geological section contains the Carboniferous-Permian
coal seams, then the CSAMT apparent resistivitysounding curves often exhibit an HA pattern (Fig. 6(b)).
Conversely, when the sounding curve displays an H type
pattern (Fig. 6(a)) then coal is absent. Such features can
be regarded as the basic principle with which to
recognize the presence of coal in the stratigraphic
section. In this survey region, two types of sounding
curves can be recognized: one is the H pattern (Fig. 6(a))
and the other is the HA pattern (Fig. 6(b)). The formerindicates the presence of coal beneath the Cenozoic; the
latter indicates that the thick Cenozoic is directly in
contact with the Ordovician limestone and there are no
embedded Permo-Carboniferous strata.
Now, let us turn to the actual measurements
obtained. Figure 7(a) shows the ensemble of apparent
resistivity versus frequency sounding curves for line 14.
In this figure, the curves corresponding to small station
numbers (2–14) exhibit the H-type pattern, whichindicates that there are no subsurface buried coal seams;
however, at larger station numbers (18–42) the HA
Table 1. Main electrical parameters for the surveyregion.
Geological age Rock type Resistivity
Quaternary Loess, clay, silt 16–50 V?m
Tertiary Sand clay 40–100 V?m
Carboniferous
Permian
Mudstone, pink
sandstone, coal, thin
limestone
70–360 V?m
Ordovician Thick limestone .500 V?m
Table 2. Frequency conversion table.
Sample Point No. 1 2 3 4 5 6 7 8
Frequency 2,844 1,280 512 426.67 341.33 256 213.33 170.67
Sample Point No. 9 10 11 12 13 14 15 16
Frequency 128 106.67 85.333 64 53.33 42.667 32 26.667
Sample Point No. 17 18 19 20 21 22 23 24
Frequency 21.333 16 13.33 10.667 8 6.667 5.333 4
Sample Point No. 25 26 27 28 29 30 31 32
Frequency 3.333 2.6667 2 1.6667 1.333 1 0.833 0.6667
Sample Point No. 33 34 35 36 37 38 39 40
Frequency 0.5 0.41667 0.3333 0.25 0.20833 0.15 0.125 0.01
Sample Point No. 41
Frequency 0.08
51
Xue et al.: Discovery of a Coal Deposit using Modified CSAMT
pattern is observed, which indicates that there are coal
seams present. Figure 7(b) shows the apparent resistivity
map along the same line after depth conversion. The
apparent resistivity was transformed into depth accord-
ing to the skin depth equation:
d~503|
ffiffiffir
f
rð6Þ
Correspondingly, Fig. 7(c) represents the sectional map
of the converted phase. From the extension and
variation of the contour map, the coal fault can be
inferred to be of fold type. Combined with drilling
results available in the survey region, the final inter-
preted geological sectional map is as shown in Fig. 7(d).
Two coal bearing strata exist following a synclinal
structure and located in a deeply buried rift basin, which
is cut by two faults, labeled as F4 and F5 in the figure.
Later Drilling Test
Based on the geo-electrical mapping results (see
Fig. 7), a drill hole was selected near station 18 of line 14
(see Fig. 7(c)). The total drilling depth was 678.37 m.
Analyses of the borehole cores verified that two coal
seams are present. The depth of the upper coal stratum
is 566.91 m with a thickness of 5.18 m, while the depth
of the lower coal stratum is 652.52 m with a thickness of
9.65 m. Both coal seams have a small dip (less than 10u).A geological log of the borehole is presented in
Fig. 8(a). The deep sounding curve near the drill hole
is shown in Fig. 8(b).
The CSAMT survey shows that the region
contains a coal bearing structure, and is able to
approximately delineate the boundaries. Subsequent
drilling verified our prediction of the coal structure,
Figure 6. The H (a) and HA (b) pattern of the apparent
resistivity curves. The abbreviations at the bottom are Q +N: Cenozoic Quaternary and Tertiary stratum; P + C:
Permian + Carboniferous strata; and O2: Ordovician strata.
Figure 7. a) Map of apparent resistivity versus frequen-cy (line 14), b) resistivity map after depth conversion, c)
corresponding phase contour map and d) final geological
interpreted section (same abbreviations as used in Fig. 6).
52
Journal of Environmental and Engineering Geophysics
which lies within the Carboniferous and Permian strata.
It is also verified that the coal seams belong to the
Shanxi and Taiyuan groups. The Taiyuan group carriesfour coal layers with a total thickness of 6.27 m. The
coal bearing vicinity covers an area of about 101 km,
from which it is estimated to contain more than 10
billion tons of coal. Other favorable conditions include
the good quality of the coal and the ease of mining
because of an existing transportation network.
Conclusions
In this paper, a simplified use of the CSAMT
technique is advocated involving the use of a single
component (horizontal electric inline). A new formula
was presented for calculating the apparent resistivity
from an E-field component only, which takes into
account the finite size of the antenna. Theoretical
simulations and real applications indicate that the
single-component apparent resistivity provides good
resolution of the subsurface stratum.
The modified CSAMT method was then applied in
the region of the Yanqqu County in China, an area that
was concluded from earlier investigations to most likely
contain no significant coal deposits beneath the Ceno-
zoic sediments. However, based on the new CSAMT
survey it was concluded that significant underground
coal deposits do exist in this area. This was later verified
by drilling, revealing a large coal reserve of more than 10
billion tons.
The main characteristics of the modified CSAMT
method can be summarized as follows:
(i) The transmitter-receiver distance should be de-
creased compared to traditional CSAMT because
the Ex-component more easily fulfills the far-field
condition.
(ii) The sensitivity to a resistive disturbance is higher in
general for the Ex-field than the Hy-field. Thus,
compared to the ratio-derived apparent resistivity,
the apparent resistivity defined by Ex alone will be
more accurate.
(iii) Measuring Ex is easier to realize compared to
mounting a magnetic probe to measure the
magnetic field.
(iv) Ex is very sensitive to the transverse change of the
geo-electric properties of the Earth, which leads to
static shifts. Hence, this modified CSAMT method
is suitable for 1-D layered Earth models.
(v) The Ex-field has poor penetration in resistive
layers, which limits the detection depth.
Acknowledgment
This research was financially supported by the Major
State Basic Research Program of the People’s Republic of
China (2012CB416605). The authors would like to thank the
Natural Science Foundation of China for support (grants
No. 41174090 and 41174108), the open Fund of the Key
Figure 8. The geological log (a) and deep sounding curve
(b) near the drill hole (same abbreviations as used in
Fig. 6).
53
Xue et al.: Discovery of a Coal Deposit using Modified CSAMT
Laboratory of Mineral Resources, Chinese Academy of
Sciences, as well as Major National Research Equipment
Development Project (ZDYZ2012-1-05-04).
References
Bartel, L.C., and Jacobson, R.D., 1987, Results of a
controlled-source audio frequency magnetotelluric sur-
vey at the Puhimau thermal area, Kilauea Volcano,
Hawaii: Geophysics, 5, 665–77.
Boschetto, N.B., and Hohmann, G.W., 1991, Controlled
source audio frequency magnetotelluric responses of
three-dimensional bodies: Geophysics, 56, 255–64.
Boerner, D.E., Wright, J.A., Thurlow, J.G., and Reed, L.E.,
1993, Tensor CSAMT studies at the Buchan’s mine in
central New Foundland: Geophysics, 58, 12–9.
Cagniard, L., 1950, Procedure for geophysical prospecting:
French patent No. 1025683.
Chen, C.S., 1993, Application of CSAMT method for gold
copper deposits in Chinkuashih area, Northern Taiwan:
TAO, 4, 339–50.
Cagniard, L., 1953, Principle of magneto-telluric method, a
new method of geophysical prospecting: Ann. de
Geophys., 9, 95–125.
Chen, M.S., and Yan, S., 2005, Analytical study on field zones,
record rules, shadow and source overprint effects in
CSAMT exploration: Chinese J. Geophys. (in Chinese),
48, 951–958.
Christensen, N.B., 2000, Difficulties in determining electrical
anisotropy in subsurface investigations: Geophys.
Prosp., 48, 1–19.
Di, Q.Y., Wang, M.Y., Shi, K.F., and Zhang, G.L., 2002,
CSAMT research survey for preventing water-bursting
disaster in mining: Proceeding of the SEGJ Conference,
Tokyo.
Goldstein, M.A., 1971, Magneto-telluric experiments employ-
ing an artificial dipole source: Ph.D. thesis, University of
Toronto, Toronto.
Goldstein, M.A., and Strangway, D.W., 1975, Audio-frequen-
cy magnetotellurics with a ground electric dipole source:
Geophysics, 40, 669–83.
Hosseini, K., Montazeri, A., Alikhanian, H., and Kahaei,
M.H., 2008, New classes of LMS and LMF adaptive
algorithms. Information and Communication Technol-
ogies: From theory to applications: ICTTA, 3rd
International Conference on 05/2008, doi: 10.1109/
ICTTA.2008.4530045.
Kaufman, A., and Keller, G.V., 1983, Frequency and transient
sounding, Elsevier Science Publishers, B.V. 110–115,
213–226.
Nabighian, M.N., 1979, Quasi-static transient response of a
conducting half-space: Geophysics, 44, 1700–1705.
Ranganayaki, R.P., Fryer, S.M., and Bartel, L.C., 1992,
CSAMT surveys in a heavy oil field to monitor steam
drive enhanced oil recovery process: in Expanded
Abstracts, 62nd Annual International Meeting, Society
of Exploration Geophysicists, 1384.
Routh, P.S., and Oldenburg, D.W., 1999, Inversion of
controlled source audio frequency magnetotellurics data
for a horizontally layered Earth: Geophysics, 64,
1689–97.
Sandberg, S.K., and Hohmann, G.W., 1982, Controlled-
source audio-magnetotellurics in geothermal explora-
tion: Geophysics, 47, 100–116.
Spies, B.R., 1989, Depth of investigation in electromagnetic
sounding methods: Geophysics, 54, 872–888.
Tikhonov, A.N., 1950, On determining the electrical charac-
teristics of the deep layers of the Earth’s crust: Doklady,
73, 295–297.
Wannamaker, P.E., 1997, Tensor CSAM T survey over the
Sulphur Springs thermal area, Valles Caldera, New
Mexico, USA, Part E: Implications for structure of the
western equations: Geophysics, 62, 451–65.
Zonge, K.L., Ostrander, A.G., and Emer, D.F., 1986, Con-
trolled-source audio-frequency magnetotelluric measure-
ments: in Magnetotelluric methods, Vozoff, K. (ed.), Soc.
Expl. Geophys., Geophysics Reprint Series, 5, 749–763.
Zonge, K.L., and Hughes, L.J., 1991, Controlled source
audiomagnetotellurics: in Electromagnetic Methods in
Applied Geophysics, Volume 2, Application, Part B:
Nabighian, M.N. (ed.), Society of Exploration Geo-
physicists, Tulsa, OK, 713–809.
APPENDIX A
ELECTRIC FIELD COMPONENT VERSUS
MAGNETIC FIELD COMPONENT IN CSAMT
Let I ,L,r represent current, wire length and
separation, respectively. The electric field Ew(v) and
magnetic field Hr(v) responses in case of the CSAMT
method can then be written as (Cagniard, 1950, 1953):
Ew(v)~I :l
2ps
1
r31{3 sin2 wze{ikr 1zikrð Þ� �
ðA-1Þ
Hr(v)~I :l
4ps
1
r2sinw 6I1
ikr
2
� �K1
ikr
2
� ��
zikr I1ikr
2
� �K0
ikr
2
� �{I0
ikr
2
� �K1
ikr
2
� � �:
For the far-field, Eqs. (A-1) and (A-2) can be
simplified as follows:
Ew(v)&I :l
ps
1
r3sinw ðA-3Þ
Hr(v)&I :l
4pffiffiffiffiffiffiffiffiffiffismvp
1
r3sinwe
{ip
4 ðA-4Þ
Next, we rewrite Eq. (A-1) in an alternative form:
Ew(v)~I :l
2ps
1
r3F (ikr) ðA-5Þ
(A-2)
54
Journal of Environmental and Engineering Geophysics
where
F (ikr)~1{3 sin2 wze{ikr(1zikr) ðA-6Þ
We also have:
{ikr~({1{i)p, p~r
dðA-7Þ
From use of Euler’s formula, the following relationship
holds:
e{ikr(1zikr)~e{pe{ip(1zpzip)
~e{( cos p{i sin p)(1zpzip)ðA-8Þ
A direct comparison between Eqs. (A-1) and (A-3)
shows that the factor e{ikr(1zikr) is a near-field term.
Thus the smaller this factor is in value, the better the far-
field assumption. If we let e{ikr(1zikr)ƒ0:02, the
following condition follows from Eq. (A-8):
p§9 ðA-9Þ
which again implies that if r§9d, the electric field
component measured by the CSAMT method can be
regarded as a far-field mode.
Carrying out the same analysis for the magnetic
field component in Eqs. (A-2) and (A-4), the condition
in Eq. (A-9) is replaced by:
p§13 ðA-10ÞTable A-1 computes the far-field mode limitations
as given by the induction number for the electric and
magnetic field components (dividing the near-field
factor into four range intervals). It follows from this
table that the far-field requirements are easier fulfilled
for the electric field component than the magnetic field
component (less strict bounds). Thus, for a given source-
receiver distance, the number of frequencies not
suffering from the far-field limitation is larger in the
case of the electric field as compared with the magnetic
field. This observation suggests that using only the
electric component allows a decrease in the source-
receiver distance, and thereby reduces the acquisition
costs. This is a practical benefit for use of the electric
component in our modified CSAMT technique.
APPENDIX B
DERIVATION OF THE ELECTRIC FIELD FOR A
FINITE LENGTH OF DIPOLE SOURCE
For a true electric dipole source, it is assumed that
the length of the source line AB is infinitesimal. This is
reasonable when the offset between transmitter and
receiver is sufficiently long when compared to the length
AB. However, the point source approximation breaks
down at modest offsets and errors are incurred in the data
interpretation. A better approach is to derive a formula
that takes into account the finite length of the current
dipole AB. We can sub-divide the transmitting antenna
AB into many small segments, as shown in Fig. 2, for
which it is reasonable to apply a dipole formula to
calculate the response, and then sum over each small
segment’s contribution to obtain the final result.
In Fig. 2, r is the distance from the field
(observation) point to the central point of AB. r9 is the
distance from the field point to the small segment (x, x +dx) along AB, and a is the angle between the vectors AB
and r9. Note that:
cos2 a~x2
r’2~
x2
x2zr2and r’~
ffiffiffiffiffiffiffiffiffiffiffiffiffiffir2zx2
p: ðB-1Þ
Nabighian (1979) introduced an expression for the
electric field for an infinitesimal dipole source in a
homogeneous half-space:
dEx(v)~I :dx
2ps
1
(r2zx2)3=2
3x2
r2zx2{2
� �: ðB-2Þ
Inserting Eq. (B-1) into (B-2), the electric field
contribution from each small segment (dipole) along
the dipole AB can be written as:
dEx(v)~I :dx
2psr’2{2z(ikr’z1)e{ikr’z
3x2
r’2
� �: ðB-3Þ
Applying the trigonometric relation cos2a 5 2cos2a-1,
we have:
Table A-1. Far-field mode limitation of electric and magnetic field components.
e{ikr(1zikr)ƒ0:02 e{ikr(1zikr)ƒ1 e{ikr(1zikr)ƒ5 e{ikr(1zikr)ƒ10
Ew(v) r§9d r§7d r§5d r§4dHr(v) r§13d r§9d r§7d r§5d
55
Xue et al.: Discovery of a Coal Deposit using Modified CSAMT
dEx(v)~I :dx
2psr’32(ikr’z1)e{ikr’z3 cos 2a{1�
: ðB-4Þ
For a horizontally layered media, the far-field expression
( kr’j jww1) is similar to the one for a homogeneous half
space, in such case the exponential term (e-ikr9) in Eq. (B-
4) can be neglected and we obtain the far-fieldexpression:
dEx(v)~Idx
4psr03(3 cos 2a{1)
~I :dx
2ps
1
(r2zx2)3=2
3x2
r2zx2{2
� �:
ðB-5Þ
The total x-component of the electric field isobtained as the summation over each small segment
contribution along the transmitting antenna AB. The
integrated result of Eq. (B-5) is:
Ex(v)~{Il
psr3
r(8r2zl2)
(4r2zl2)3=2ðB-6Þ
In the central location of AB the electric field generated
by the dipole is:
Ex(v)~{Il
psr3ðB-7Þ
In this case, the apparent resistivity formula is:
rEx (v)~4p:r3
I :l: Ex(v)
3 cos 2a{1
��������2
ðB-8Þ
The electric field generated by a transmitting antenna
with scale length of l has an additional item4r2zl2
r(8r2zl2)
when compared with the electric field generated by a
dipole source (see Eqs. (A-6) and (A-7)). It is clear that
the term4r2zl2
r(8r2zl2)represents a correction factor that
modifies the single-component apparent resistivity when
the transmitter scale is appreciable relative to the
receiver offset. Because the apparent resistivity is
defined by the dipole source, it is reasonable to
introduce the correction term when one calculates the
electric field generated by the transmitting antenna with
a scale length of l. In practical surveying, one multiples
the correction term4r2zl2
r(8r2zl2)with the observed Ex data
and then calculates the apparent resistivity. However,
when the length AB can be neglected (point or dipole
source), the correction term4r2zl2
r(8r2zl2)~1, which means
that there is no need to correct the non-dipole effect in
Eq. (B-7).
Substituting Eq. (B-6) into Eq. (B-8), we obtain
the modified single-component apparent resistivity
formula:
rEx (v)~p:r3
AB:MN: Ex(v)½ � 4r2zl2
r(8r2zl2): ðB-9Þ
In practice, the observed field value is not at a fixed
point, but an average value around this point because
the receiving antenna has a finite length. Such influence
should also be corrected for. Suppose the receiving
antenna has a length of l9, then the observed electric
field (EEx) and the electric field (Ex) at the central
location of the receiving antenna fulfills the following
relation:
Ex(v)~E�
x(v)(4r2l02)3=2
r(8r2zl02): ðB-10Þ
When both the transmitting and receiving antenna are
long, we can combine the above two correction factors
by multiplying them together and obtain the new
apparent resistivity in the equatorial direction:
rEx (v)~p:r3
I :l: �EExj j
(4r2zl2)
r(8r2zl2)
(4r2zl’2)3=2
r(8r2zl’2): ðB-11Þ
56
Journal of Environmental and Engineering Geophysics