Content uploaded by Ming Zhang
Author content
All content in this area was uploaded by Ming Zhang on Apr 13, 2023
Content may be subject to copyright.
Geophysical Prospecting, 2021, 69, 474–490 doi: 10.1111/1365-2478.13059
Improved controlled source audio-frequency magnetotelluric method
apparent resistivity pseudo-sections based on the frequency and
frequency–spatial gradients of electromagnetic fields
Ming Zhang1,2,3, Colin G. Farquharson3and Changsheng Liu1,2∗
1College of Instrumentation and Electrical Engineering, Jilin University, Changchun, 130061, China, 2Key Lab of Geo-Exploration
Instrumentation (Ministry of Education)Jilin University, Changchun, 130061, China, and 3Department of Earth Sciences, Memorial University
of Newfoundland, St. John’s, NL A1C5S7, Canada
Received April 2020, revision accepted November 2020
ABSTRACT
Although most electromagnetic data can be inverted to actual resistivity, ways of
quickly getting a real-time interpretation of a data set are still valuable. Such meth-
ods are useful when we are testing instrumentation or assessing data quality during
a survey, or when we need to get a general understanding of the geological structure
during a field survey. Apparent resistivity is a good way to satisfy these desires. How-
ever, one of the disadvantages of apparent resistivities is that the traditional apparent
resistivity formulations are poor at recognizing boundaries, mainly because abnormal
responses get stretched into deeper parts of the image (a shadow effect). In order to
improve the recognition ability of boundaries, we propose improved apparent resis-
tivity pseudo-sections based on the formulae for the frequency and frequency–spatial
gradients of the fields in the far-field region of frequency-domain controlled-source
audio-frequency magnetotelluric surveys. The new pseudo-sections are found to be
better than those produced from a traditional method when applied to a number of
3-D examples. The performance of this apparent resistivity method is closely related
to using an appropriate transmitter–receiver distance: when a proper value is used,
good results can be obtained in which the horizontal locations of vertical boundaries
and the positions of top and bottom boundaries can be identified clearly. Finally,
the usefulness of the proposed method for practical applications is evaluated with a
field-data example, for which the results of the proposed apparent resistivity imaging
methodarecomparedwithtraditionalapparentresistivities,as well as with theresults
from a 2-D inversion of DC resistivity data from the same survey line and with what
is known about the geology of the area. This comparison demonstrates the improved
capabilities of the new apparent resistivities over traditional approaches, including an
improved capability to accurately reveal the bottoms of targets.
Key words: Apparent resistivity, Audiomagnetotelluric, Controlled source, Electro-
magnetic field, Field gradients, Imaging.
1 INTRODUCTION
The controlled-source audio-frequency magnetotelluric
(CSAMT) method is an electromagnetic (EM) method where
∗E-mail liuchangsheng@jlu.edu.cn
a grounded electric line source is placed far away from the re-
ceiver sites (Bartel and Jacobson, 1987; Ward and Hohmann,
1988; Zonge and Hughes, 1991). The plane-wave approx-
imation is valid when the transmitter is located far enough
away from the receivers (such as at a distance greater than
3–5 skin depths). Under this approximation, magnetotelluric
474 © 2020 European Association of Geoscientists & Engineers
Imaging method based on the electromagnetic field gradients 475
(MT) interpretation techniques can be applied (Goldstein
and Strangway, 1975; Sandberg and Hohmann, 1982; Sasaki
et al., 1992). But sometimes it is inconvenient or impossible
to satisfy the plane-wave, MT condition, e.g. for deep inves-
tigation, the signal strength in the plane-wave region may be
too low, and thus the exploration capability reduced below
what is hoped (Spies, 1989). In order to obtain stronger
fields so as to improve the detection capability at larger
penetration depths, measuring closer to the source should be
considered (Wilt and Stark, 1982). But under this condition,
the measured data are not strictly in the plane-wave region,
so the simple, straightforward MT apparent resistivity is no
longer appropriate.
A large number of receiver sites closely spaced along a
survey traverse are usually used to collect detailed data which
can later be inverted to give a resistivity model of the subsur-
face. With the continuing increase in computing speed and
memory,fitting the large amount of observed data from such a
survey using many iterative forward-modelling (and sensitiv-
ity) calculations in an inversion is not an insurmountable ob-
stacle nowadays (Börner, 2010; Newman,2014). Through in-
version, it is possible to obtain information about the resistiv-
ityofundergroundstructures.But inversion is post-processing
workwhichisoftendonewellaftera survey.Sometimes, when
we are concerned with the correct operation or calibration of
instrumentation or we need to monitor data quality during a
survey,an initial,quickscanof the available dataorareal-time
interpretation of the data in the field can be very important.
The normal ratio and reduced ratio derived from Turam
data are a good example of a quick data-processing and inter-
pretation approach dating from an era when the inversion of
geophysical EM data was not feasible (Parasnis, 1991; Telford
et al., 2013). The Turam electromagnetic method, which has
traditionallybeenusedin metallic ore exploration,usesa fixed
transmitter (either a large loop or long grounded wire) to gen-
erate currents in the subsurface at relatively low frequencies
(often less than 1 kHz), and a roving pair of horizontal receiv-
ing coils (the receiver coils are separated by a fixed distance).
The ratio of the vertical components of the magnetic field at
the two receiver coils and the phase difference between them
are measured. This ratio (difference in logarithms) and phase
difference are sensitive to the presence of any anomalous con-
ductors.
Apparent resistivity is also useful for a quick interpreta-
tion and assessment of data from a survey. On the one hand,
apparent resistivity can reflect the actual changes of subsur-
face resistivity better than the raw electromagnetic data; on
the other hand, it can provide an indication of the subsur-
face structure more quickly than can be obtained using inver-
sion. Apparent resistivity images can also be used to estimate
an initial model for subsequent inversion (Kruk et al., 2000).
There are several methods for calculating apparent resistiv-
ity for geophysical electromagnetic methods (Wenner, 1915;
Rust,1938; Cargniard,1953;Kunetz,1972; Vozoff,1972;He,
2018). However, those most commonly used do not always
exhibit the best behaviour (Spies and Eggers, 1986). One of
the typical disadvantages is that the images or pseudo-sections
made from the apparent resistivity values are unable to pre-
cisely indicate the locations and size of a target. This is espe-
cially so when considering the locations of the top and bottom
of a target. This is because of the shadow effect which smears
features in the pseudo-sections that are due to shallow struc-
tures, which, as a result, makes the size of an anomaly in the
apparent resistivity pseudo-section much larger than the real
size of a target (Yan and Fu, 2004; Lei et al, 2017).
In gravity and magnetic surveys, spatial gradients of the
fields have played an important role in boundary recognition
(Peter, 1965; Helmut,1970;Butler, 1984).Inrecent years, sim-
ilar approaches have also been applied to EM data, especially
to marine EM data, and show improved boundary recogni-
tion ability (Djeddi et al., 1998; MacGregor and Sinha, 2000;
He et al., 2008; Dell’Aversana, 2010; Meju, 2019). Drawing
lessons from this, Zhang et al. (2020) proposed that measure-
ments of the gradients of the electromagnetic fields in CSAMT
surveys should be made, and presented a forward-modelling
studyoffrequency-domain, controlled-sourceelectromagnetic
gradients. Zhang et al. considered the spatial gradients in the
horizontal directions when acquiring data over a grid or along
a line in order to provide horizontal resolution, and a fre-
quency gradient when measuring with multiple frequencies to
provide depth resolution. The characteristics of the above gra-
dients were analysed, and the results showed that the spatial
gradient is able to indicate accurately the horizontal positions
of the sides of a target, and the frequency gradient is able
to indicate the vertical locations of the top and bottom of a
target more accurately than the electromagnetic field compo-
nents themselves. However, it was also shown that the spatial
gradient can have a non-zero value in homogeneous regions
that is similar in form to the anomaly caused by an isolated
target in a heterogeneous region, thus diminishing to some ex-
tent the ability of the spatial gradient to delineate targets.
In order to improve the boundary recognition ability of
apparent resistivity and to give more accurate information
about underground structure quickly, an improved CSAMT
apparent resistivity pseudo-section approach based on the fre-
quency and frequency–spatial gradients of electromagnetic
© 2020 European Association of Geoscientists & Engineers, Geophysical Prospecting,69, 474–490
476 M. Zhang, C.G. Farquharson and C. Liu
Figure 1 Background interference response. (a) Excurves with respect to x-offset. (b) Exxcurves with respect to x-offset. (c) Diagram showing
the angle α.(d)Exxcurves with respect to α. The green,orange and red lines in panels (a), (b) and (d) represent the responses at receiver sites
along the survey lines y=6000 m, y=8000 m and y=10,000 m, respectively.
fields is proposed here. The frequency and frequency–spatial
gradients of the electric field presented by Zhang et al. (2020)
are used for this apparent resistivity method. When the spatial
gradient has a non-zero value over homogeneous regions, this
will introduce a bias or background offset to the apparent re-
sistivity. Thus, a technique of removing this non-zero value is
first explored to avoid this issue. Then the apparent resistivity
method is introduced in detail. Finally, we apply the apparent
resistivity method to synthetic data sets from several typical
3-D models and to a real data set to assess the performance of
the method.
2 ANALYSIS OF THE BACKGROUND
INTERFERENCE CHARACTERISTICS AND
A TECHNIQUE FOR SUPPRESSING IT
In this paper, we define the non-zero values of the spatial
gradient over uniform regions as background interference.
These non-zero values are caused by the relative locations of
the transmitter and receiver sites because of the fact that the
along-line electric field component Exvaries with the source–
receiver distance, even for a homogeneous earth model. To
characterize this background interference, a homogeneous
earth model with resistivity of 100 m is considered as an
example. An electrical source with a length of 1 km and a
moment of 40,000 Am is arranged along the x-direction with
its midpoint at x=0m,y=0mandz=0 m. Identical
source parameters and source locations are used for all exam-
ples in this paper. COMSOL Multiphysics modelling software
wasusedtocomputetheresponsesforthehomogeneousearth
model (Butler and Zhang, 2016). The variations of Exand the
along-line gradient, Exx, with respect to the x-offset of the
receiversitesalongthreesurveylines (y=6000 m, y=8000 m
and y=10,000 m) at a frequency of 128 Hz, are shown
Figure 1(a, b).
From Figure 1(a) it can be seen that the value of Ex
changes if the source–receiver distance changes (e.g. as the
source–receiver distance increases, the amplitude of Exde-
creases). From Figure 1(b), it can be seen that the spatial gra-
dient curve for a homogeneous earth model has two anoma-
lous extreme values, which are at positions similar to those
of the spatial gradient over a 3-D target where the conductiv-
ity is more than (or less than) that of the homogeneous half-
space (Zhang et al., 2020). This similarity would be confusing
and could lead to a misidentification of a target in a region
that is in fact homogeneous. Thus, distinguishing between
© 2020 European Association of Geoscientists & Engineers, Geophysical Prospecting,69, 474–490
Imaging method based on the electromagnetic field gradients 477
backgroundinterferenceand a real anomaly causedbyatarget
isimportant.In Figure 1(b), the interference extrema positions
xbof the three curves are different. For the curves for the y=
6000 m survey line, the extrema positions are located at xb1 =
−2500 m and xb2 =2500 m, for the y=8000 m survey line,
the extrema positions are xb1 =−3150 m and xb2 =3150 m,
and for the y=10,000 m survey line, the extreme positions
are xb1 =−4000 m and xb2 =4000 m. It can be seen that
as the y-offset of the survey line increases, the extrema posi-
tions xbof the background interference also increase, meaning
that xbis proportional to the y-offset of a survey line. In or-
der to analyse the relationship between the y-offset and the
extrema positions, the angle between xand yis defined as α
=arctan(x/y) as shown in Figure 1(c). The Exxcurve with
respect to αis shown in Figure 1(d). It can be seen that the ex-
trema values of the background interference occur when α=
±21° (tan α=±0.38). By considering different survey lines,
different resistivities, source lengths and frequencies (the re-
sults of which are not shown here), we conclude that the ex-
trema of the background interference always appear at α=
±21°. This can be used as a tool to identify the background
interference.
Even though the background interference can be identi-
fiedfromthecharacteristicsmentioned above, it would bebet-
ter if this interference can be suppressed as much as possible
or eliminated from the spatial gradient curve. Similar inves-
tigations to those described above show that the background
interferenceatdifferent frequencies has similar values(i.e.spa-
tialgradientvalue).Takingadvantage of this property,we pro-
pose a method to suppress the background interference that
uses the frequency difference of the spatial gradient (i.e. the
frequency–spatial gradient given by equation (1)). From mod-
elling, it is found that when the frequency varies from 10 to
8192Hz,which is a commonrangeusedin the field,thehigher
the frequency, the closer are the background interference val-
ues at two adjacent frequencies. Consequently, the better the
suppression effect will be.
The normalized frequency difference of the spatial gra-
dient, i.e. the frequency–spatial gradient, of receiver site jon
survey line iis intended to suppress unwanted effects and is
defined as
Exzx(i,j,fk)=[Exx(i,j,fk)−Exx(i,j,fk−1)]
lg(fk/fk−1),(1)
where fk,fk−1are two neighbouring frequencies, lg is
log10,Lxis the distance between two neighbouring sites,
the zin the superscript of Eindicates different depths
as different frequencies fare associated with different
depths z,Exx(i,j,fk)isthespatialgradientofsitejon
survey line iwhen the frequency is fkwhich is defined
as Exx(i,j,fk)=[Ex(i,j,fk)−Ex(i,j−1,fk)]/Lx,
and Exx(i,j,fk−1) is defined as Exx(i,j,fk−1)=
[Ex(i,j,fk)−Ex(i,j−1,fk)]/Lx.
To illustrate the conclusion mentioned above and demon-
strate the effect of the suppression, a 100 m homogeneous
earth model is considered along with frequencies 8, 16, 32,64,
128 and 256 Hz. The absolute values of Exx(background
interference) for line y=−8500 m are shown in Figure 2(a).
The absolute values of the normalized frequency difference of
the spatial gradient, Exzx(i.e. background interference after
suppression), are shown in Figure 2(b).
From Figure 2(a) it can be seen that, for a uniform earth
model with a resistivity of 100 m and a receiver 8500 m
away from the source, the curves of Exxvalues at different
frequencies basically coincide except at the lowest frequency
(8 Hz). After the suppression, results of which are shown in
Figure 2(b), the background interference is less than 0.3 ×
10−15 V/m2/lgHz for frequencies higher than 8 Hz. This illus-
trates that the higher the frequency, the more successful the
effect of suppression will be.
The results and analysis mentioned above are based on a
homogeneous earth model. To further analyse the characteris-
tics of background interference and evaluate the background
interference suppression effect, a 3-D earth model is consid-
ered. The parameters of the model and survey geometry are
as follows. A survey line is set at y=−8500 m. The target is
a rectangular prism with dimensions 1000 ×1000 ×300 m.
The centre of the target is at x=0m,y=−8500 m, z=
−750 m. The background resistivity is set to 100 m, and
the target resistivity is set to 1 m. A frequency of 10 Hz
was considered. COMSOL Multiphysics modelling software
was used to compute the responses for the 3-D model. The
accuracy of the modelling was verified by comparing results
from COMSOL with the results from the second example of
Jahandari and Farquharson (2014). The background inter-
ference removal effect for this 3-D earth model is shown in
Figure 3.
From the comparison of Figure 3(a, b), it can be seen that,
unlike Exx, which has background values that are compara-
ble to the anomalous region, the value of Exzxis much less
than the values in the anomalous region, which demonstrates
that the background interference suppression has been effec-
tive. In the neighbourhood of the target, the locations of the
extrema for both Exxand Exzxoccur at similar positions
of x=−500 m and x=500 m.
© 2020 European Association of Geoscientists & Engineers, Geophysical Prospecting,69, 474–490
478 M. Zhang, C.G. Farquharson and C. Liu
Figure 2 Background interference removal effect for a homogeneous earth model. (a) Exxcurves. (b) Exzx curves.
3 DEFINITION OF APPARENT RESISTIVITY
USING GRADIENTS OF
ELECTROMAGNETIC FIELDS
Whenwedoasurvey in the far-field region,theapparentresis-
tivity can be given by (Constable and Srnka, 2007; He, 2018;
Meju, 2019)
ρai,j,f=2πr3
j
Pe(3cos2αj−2)Ex(i,j,f),(2)
where Perepresents the moment of the source, and rjindicates
the source–receiver distance of site jon survey line i.Wede-
rive an apparent resistivity using the field gradients based on
equation (2) that we then use within the far-field region. The
derivation of the apparent resistivity is as follows.
The difference in the apparent resistivity in equation (2)
between two adjacent sites, which is identified as the trans-
verse resistivity variation and denoted by ρax,canbeex-
pressed as
ρaxi,j,f=2πr3
j
Pe(3cos2αj−2)Ex(i,j,f)
Figure 4 The geometry of the EM gradient method.
−2πr3
j−1
Pe(3cos2αj−1−2)Ex(i,j−1,f).(3)
Since the source is at the origin, from the diagram of the
geometryoftheelectromagnetic(EM) gradient method shown
in Figure 4, it can be seen that the source–receiver distance can
Figure 3 Background interference removal effect for the 3-D earth model. (a) Exxcurve. (b) Exzx curve.
© 2020 European Association of Geoscientists & Engineers, Geophysical Prospecting,69, 474–490
Imaging method based on the electromagnetic field gradients 479
be expressed as
rj=L2
y+L2
xj,(4)
where Lyis the ycoordinate of the survey line i,andLxj is
the xcoordinate of the site jon survey line i. The difference
between the source–receiver distances of two adjacent survey
points is
r=rj−rj−1=L2
y+(Lxj−1+Lx)2−L2
y+L2
xj−1,(5)
where Lxis the distance between two neighbouring
sites. Suppose there are nsurvey points on a survey
line which satisfy a condition of
max(|Lx1|,|Lx2|,|Lx3|...|Lxj|...|Lxn|)≤|Ly|.Thisas-
sumption limits the survey area to a region which is formed
by two ‘rays’ that start at the midpoint of the long-wire source
and bevelled at angles of ±45° with the line perpendicular to
the source passing through its midpoint. Under this assump-
tion, we can give bounds for r:
0≤|r|≤L2
xj−1+(Ly+Lx)2−L2
y+L2
xj−1.(6)
In a practical survey, typically the measurement spacing
alongasurveylineisquiteclose because we are always keen to
get good resolution along the chosen line. This means that the
condition Lx<<Lyis usually satisfied, which in turn means
Ly+Lx≈Ly. Replacing the term Ly+Lxby Lyin equation
(6), one can obtain
L2
xj−1+(Ly+Lx)2−L2
y+L2
xj−1
∼
=L2
xj−1+L2
y−L2
y+L2
xj−1=0.(7)
Hence,
r∼
=0.(8)
Given that r∼
=0, equation (5) reduces to
rj∼
=rj−1.(9)
Similarly,
3cos2αj−2∼
=3cos2αj−1−2.(10)
Combiningequation(3)withequations(9)and(10)gives
ρaxi,j,f∼
=2πr3
j
Pe(3cos2αj−2)Exx(i,j,f)Lx.(11)
In order to verify the correctness of the above approxi-
mation, the transverse resistivity variation along survey line y
=10 km for a homogeneous earth model (resistivity of the
earth region is set to 100 m) for a frequency of 100 Hz is
Figure 5 Curves of transverse resistivity variation and its approxi-
mate values along survey line y=10 km for a 100 m homogeneous
earth model and 100 Hz. The black dotted curve and the green solid
curve represent the transverse resistivity variation curves computed
by equation (3) and the approximate transverse resistivity variation
curves computed by equation (11), respectively.
calculated using equations (3) and (11). The values are shown
in Figure 5 by the black dotted and green solid curves, respec-
tively. It can be seen that the transverse resistivity variation
curves computed by equation (3) basically coincide with the
approximate curves computed by equation (11) from Lx =
−10 km to Lx =10 km, which verifies the correctness of the
above approximation in this area. It can also be observed that
the curves begin to separate beyond this area, which means
the approximation used for apparent resistivity is no longer
accurate, thus indicating the limitations of the survey area for
which the method is applicable.
In an analogous manner to the above derivation, the dif-
ference of the apparent resistivity between two adjacent fre-
quencies, which we define as the vertical resistivity variation
and denote by ραz, can be expressed as
ραzi,j,fk∼
=2πr3
j
Pe3cos2αj−2Exzi,j,fk
×lgfk/fk−1,(12)
where Exz(i,j,fk) is the frequency–spatial gradient of site
jon survey line iwhen the frequency is fk, which is defined
as Exz(i,j,fk)=[Ex(i,j,fk)−Ex(i,j,fk−1)]/lg(fk/fk−1).
In this case, we use the term ‘vertical’ as different frequencies
are associated with different depths, z. Combining equations
(1), (11) and (12), the vertical–transverse joint resistivity
variation, denoted by ραzx, can be derived easily and is
© 2020 European Association of Geoscientists & Engineers, Geophysical Prospecting,69, 474–490
480 M. Zhang, C.G. Farquharson and C. Liu
Figure 6 (a) The survey geometry, (b) ραzxcalculated using equation (13, (c)) the pseudo-section for ρgradient calculated using equation (14),
and (d) the pseudo-section for ραcalculated using equation (2), respectively, for the homogeneous half-space. The red line indicates the source
and the black dots the survey line. (e–h) The same, but for the conductive target (the location of which is shown in panel e). (i–l) The same,
but for the resistive target. The white rectangular box indicates the actual locations of the target, and the white solid lines indicate the actual
horizontal boundaries of the target.
given by
ραzxi,j,fk∼
=2πr3
j
Pe3cos2αj−2
×Exzx i,j,fklgfk/fk−1Lx.(13)
Differences of the apparent resistivity can be calculated
usingtheabove equation.Ifthe apparent resistivity ofacertain
reference point is known, which is recorded as ρα(i,j0,f0),the
apparent resistivity of site jLat the depth corresponding to
frequency f0can be obtained by taking into account the finite
differences along the line and down through the frequencies
using the equation
ρgradient i,jL,fK
=ρi,j0,f0+
L
l=12πr3
jl
Pe3cos2αjl−2Exxi,jl,f0)Lx
+
K
k=12πr3
jL
Pe3cos2αjL−2Exzi,jL,fklgfk/fk−1,(14)
where l=1, 2, 3,…,Land k=1, 2, 3,…,K. The approx-
imate value of the apparent resistivity of a certain reference
point could be obtained from geological information or bore-
hole data. Calculating the apparent resistivity from Exusing
equation (2) is another possibility.
4 THREE-DIMENSIONAL MODEL TRIALS
4.1 Properties of apparent resistivity calculated by field
gradients
In order to illustrate the advantages of the apparent resistivity
calculated from field gradients, especially its ability to delin-
eate boundaries of a target, we consider an earth model with a
3-D conductive target and an earth model with a resistive tar-
get (as well as the corresponding homogeneous background
model). The top views of the three earth models are shown in
Figure 6(a, e and i), respectively. The parameters of the mod-
els are as follows. The survey line is y=−8500 m. The target
© 2020 European Association of Geoscientists & Engineers, Geophysical Prospecting,69, 474–490
Imaging method based on the electromagnetic field gradients 481
is a rectangular prism of dimensions 1000 ×1000 ×300 m.
Thecentreofthetargetisatx=0m,y=−8500 m, z=
−950 m. The background resistivity is 100 m. In model 1,
the resistivity of the target is 100 m (i.e. a homogeneous
earth model); in model 2, its resistivity is 1 m (i.e. a con-
ductive target); and in model 3, its resistivity is 10,000 m
(i.e. a resistive target). The vertical–transverse joint resistiv-
ity variation, ραzx, is calculated from the field gradients us-
ing equation (13). The apparent resistivity based on the field
gradients is calculated using equation (14). The traditional
controlled-source audio-frequency magnetotelluric (CSAMT)
apparent resistivity based on the original field component is
calculated using equation (2). The vertical–transverse joint re-
sistivityvariationandapparentresistivity are all calculated for
atotalof26 frequencies ranging from 5 to100Hz.The appar-
ent resistivity pseudo-sections along the y=−8500 m profile
are shown in Figure 6. To construct these pseudo-sections, the
frequencies were converted to apparent depths using the skin-
depth equation, δ=503 ×(ρ/f)1/2, with ρset to 100 m. The
results for the homogeneous earth model, which are shown in
Figure 6(b, c and d), act as a comparison with the results for
the 3-D models. ρazxshown in Figure 6(b) is calculated us-
ing equation (13), ρgradient shown in Figure 6(c) is calculated
using equation (14), ραshown in Figure 6(d) is calculated us-
ing equation (2). The differences between the various types of
apparent resistivity for the 3-D earth models and the homo-
geneous model illustrate how the targets and background are
manifest in the pseudo-sections.
From Figure 6(f, j), it can be seen that ρazxhas two ex-
trema values at positions x1=−500m and x2=−500m (in-
dicated by the two white lines on Figure 6(f and j). The true
locations of the lateral boundaries of the target are at x1=
−500m and x2=−500m, as shown in Figure (e, i). When the
resistivity varies from high to low as one moves along the sur-
vey line, ραzxhas a negative extremum value: when the resis-
tivity varies from low to high, ραzxhas a positive extremum
value. Thus, the resistivity of a target relative to the back-
ground can be recognized by the sign of ραzx. By comparing
Figure 6(b and f), it can be seen that the extremum value for
the conductive target is larger than that for the resistive target.
This means that ραzxis more sensitive to a conductive target
compared with a resistive target if the other parameters of a
model are the same. From the preceding examples and anal-
ysis, we therefore conclude that ραzxis able to accurately
reveal and delineate the lateral extents of a target.
In Figure 6(c), it can be seen that, at greater appar-
ent depths, there are artefacts in the apparent resistivity
pseudo-sectionforthehomogeneousearthmodel,which is the
background apparent resistivity interference discussed above.
Anomalies in the apparent resistivity pseudo-sections for the
3-D models are clearly visible (indicated by the white rectan-
gular boxes in Fig. 6(g, k). However, other anomalies caused
by the background apparent resistivity interference, which are
similar both in amplitude and position in the pseudo-section
as the ones for a homogeneous earth model, are also visible.
From the comparison of Figure 6(g and h), it can be
seen that the bottom boundary of the target at a depth of
1100 m cannot be discerned from the apparent resistivity
pseudo-sectioncreatedfromthefieldcomponentfortherange
of frequencies used due to the shadow effect which stretches
the shallow apparent resistivity anomalies to depth. In con-
trast, the approximate locations of the top and bottom of the
target can be discerned in the pseudo-section created from the
field gradients (Fig. 6g calculated using equation (14)). Also,
the depth stretching due to the shadow effect has clearly been
reduced.Comparable results fortheresistivetarget can be seen
in Figure 6(k and l). By using the proposed apparent resistivity
imaging method, the size of an anomaly in the apparent resis-
tivity pseudo-section can be reduced, making it closer to the
true size of a target. This can be seen from Figure 6(g), where
the bottom of the anomaly is located at z=−1500 m, which
is only 400 m deeper than the true location of the bottom of
the target (z=−1100 m). Moreover, with a 100 mback-
ground resistivity, we get an apparent resistivity of 86 mfor
the conductive body using the field component (Fig. 6h cal-
culated using equation (2)) whereas an apparent resistivity of
78 m using the field gradients (Fig. 6g), which means the
proposed imaging method is better able to estimate the true
resistivities of targets. The same is true for a resistive target
(Fig. 6k and l).
We next assess the performance of the apparent resis-
tivity calculated using field gradients when multiple targets
are present. Three 3-D earth models, each with two targets,
are considered. The apparent resistivity pseudo-sections are
shown in Figure 7. The top views of the three models are
shown in Figure 7(a, e and i). The parameters of the mod-
els are as follows. The survey line is y=−8500 m. The size of
both targets is 600, 1000 and 600 m in the x,yand zdirec-
tions, respectively. The coordinates of the boundaries of the
two targets are x=−450 and −1050 m (the first target) and
x=450 and 1050 m (the second target), y=−8000 and
−9000 m (both targets), and z=−600 and −1200 m (both
targets). The background resistivity is 100 m. In model 1,
both of the targets are conductive, with a resistivity of 1 m.
In model 2, both of the targets are resistive, with a resistiv-
ity of 10,000 m. In model 3, one target is conductive (with a
© 2020 European Association of Geoscientists & Engineers, Geophysical Prospecting,69, 474–490
482 M. Zhang, C.G. Farquharson and C. Liu
Figure 7 (a) Plan view of survey geometry and model, (b) ραzxcalculated using equation (13), (c) the pseudo-section for ρgradient calculated
using equation (14), and (d) the pseudo-section for ραcalculated using equation (2), respectively, for the model with two conductive targets. The
red line indicates the source and the black dots the survey line. (e–h) The same for the model with two resistive targets. (i–l) The same for the
model with one conductive target and one resistive target. The white rectangular box indicates the actual locations of the target, and the white
solid lines indicate the actual horizontal boundaries of the target.
resistivity of 1 m), and the other is resistive (with a resistivity
of 10,000 m).
From Figure 7(b, f and (j), which is generated using equa-
tion (13), it can be seen that ραzxhas four extrema values
(indicated by the four white lines in each panel). These lo-
cations match the true locations of the sides of the targets
(x1=−1050m, x2=−450m, x3=450m and x4=1050m;
see Fig. 7a, e, i). This shows that ραzxcan accurately reveal
the lateral boundaries of multiple targets no matter whether
the targets are more conductive or resistive than the back-
ground. In Figure 7(c, g and k),which is generated using equa-
tion (14), the actual locations of the tops and bottoms of the
multipletargetsmarkedbythe white rectangles (indicating the
true outline of the targets) are revealed by the pseudo-sections
of the apparent resistivity calculated from the field gradients.
By comparison, Figure 7(d, h and l),which is calculated using
equation(2),shows that,althoughthe approximate horizontal
locations of the sides of the two targets can be seen, the bot-
tom boundaries of the targets are not evident (in the range of
frequencies for either type of target). It is therefore clear that
the proposed apparent resistivity imaging method works well
for approximately identifying the base of a target when there
are multiple targets, with this being true for both conductive
and resistive targets.
4.2 Relationship between the false anomaly of the apparent
resistivity and source–receiver distance
In this section, we consider the relationship between the
false interference anomaly appearing in the apparent resis-
tivity pseudo-sections calculated using equation (14) and the
source–receiver distance. Three earth models, each with a sin-
gle conductive target, but with different source–receiver dis-
tances, are considered. The results are shown in Figure 10.
For these three examples, all parameters are the same except
the relative positions of the source and survey line. The plan
© 2020 European Association of Geoscientists & Engineers, Geophysical Prospecting,69, 474–490
Imaging method based on the electromagnetic field gradients 483
Figure 8 Apparent resistivity pseudo-sections for a 3-D target for different source–receiver distances. (a) Plan view of survey geometry and
model, (b) ραzxcalculated using equation (13), (c) the pseudo-section for ρgradient calculated using equation (14), and (d) the pseudo-section
for ραcalculated using equation (2) respectively,for a source–receiver distance of 4500 m . (e–h) The same, but for a source–receiver distance
of 6500 m. (i–l) The same, but for a source–receiver distance of 8500 m. The white rectangular box indicates the actual locations of the target,
and the white solid lines indicate the actual horizontal boundaries of the target.
views are shown in Figure 8(a, e and i). The parameters are as
follows. The line source with a length of 1 km and a moment
of 40,000 Am is oriented in the x-direction, with its midpoint
at x=0m,y=0mandz=0 m. The size of the target is
again 1000 ×1000 ×300 m. The background resistivity is
100 m. The target resistivity is set to 1 m. In the first of the
three cases, the centre of target is at x=0m,y=−4500 m,
z=−950 m. In the second case, the centre of the target is at
x=0m,y=−6500 m, z=−950 m. And for the third case,
the centre of the target is at x=0m,y=−8500 m and z=
−950 m. The survey line for each case passes over the centre
of the target and is oriented in the y-direction.
The true locations of the lateral boundaries of the target
(x1=−500m and x2=500m) can be seen in the plan views
in Figure 8(a, e and i). From Figure 8(b, f and j), it can be
seen that ραzxhas two extrema values at the positions in-
dicated by the two white lines in each panel. These locations
match well with the true locations. It can also be seen that
the lateral boundaries of the target are apparent in ραzxfor
thedifferentsource–receiverdistances,with the locationofthe
extrema of ραzxnot changing with the source–receiver dis-
tance. This indicates that the ability of the proposed apparent
resistivity for identifying the lateral boundaries of a target are
not affected by changes in the source–receiver distances for
the ranges tested.
From Figure 8(c, g and k), it can be seen that as the
source–receiver distance increases, the background apparent
resistivity interference moves deeper down in the apparent re-
sistivity pseudo-section. Also, the bottom of the anomaly in
the pseudo-section due to the target appears at deeper appar-
ent depths. For Figure 8(c, g and k), the tops of the anomalies
are all located at about z=−800 m, whereas the bottoms of
the anomalies are located at about z=−900 m,z=−1200 m
and z=−1500 m, respectively. The bottom of the real tar-
get is located at z=−1100 m. This means the vertical ex-
tent of the anomaly is 200 m smaller than the true extent of
© 2020 European Association of Geoscientists & Engineers, Geophysical Prospecting,69, 474–490
484 M. Zhang, C.G. Farquharson and C. Liu
Figure 9 Apparent resistivity pseudo-sections for different depths to the top of a target. (a) Side view of the target, (b) ραzxcalculated using
equation (13), (c) the pseudo-section for ρgradient calculated using equation (14), and (d) the pseudo-section for ραcalculated using equation (2),
respectively, for a depth-to-top of 600 m. (e–h) The same, but for a depth-to-top of 800 m. (i–l) The same, but for a depth-to-top of 1000 m.
The white rectangular box indicates the actual locations of the target, and the white solid lines indicate the actual horizontal boundaries of the
target.
the target for the closest source–receiver separation (Fig. 8c),
and the bottom of the anomaly is totally covered by the deep
interference, 100 m bigger for the intermediate source–
receiver distance (Fig. 8g), and 400 m bigger for the furthest
source–receiver distance (Fig. 8k). Thus,it can be inferred that
when the source–receiver distance is too small, the anomaly
will be covered, and when the source–receiver distance is too
large, the anomaly for the target will extend too deep. This
means it is important to choose a proper source–receiver dis-
tance for a survey. We consider how to determine an appro-
priate source–receiver distance for an anticipated 3-D earth
model in the following section.
4.3 The sensitivity of the apparent resistivity to the top and
bottom boundary positions of the target
In order to evaluate the sensitivity of the apparent resistivity
to the vertical locations of the top and bottom of a target,
two groups of models are designed. The first group is used to
evaluate the sensitivity to the top boundary of the target and
the second group is used to evaluate the sensitivity to the bot-
tom boundary. As mentioned above, since the source–receiver
distance can influence the size of the anomaly in the pseudo-
section,the proper source–receiver distanceisselectedfor each
model to achieve the best imaging performance. In the three
3-D models for the first group, the positions of the top bound-
aries of the target are different and the positions of the bottom
boundariesareallthesame.The section views of the three 3-D
earth models are shown in Figure 9(a, e and i). The parame-
ters are as follows. The survey line is y=−8500 m. (This
is the best source–receiver distance for these three 3-D earth
models.) The background resistivity is equal to 100 m. The
target resistivity is 1 m. The positions of the bottom bound-
ariesofthetargetsareallz=−1300 m. The depths to the
tops of the targets are 600 m (for a target size of 1000 ×1000
×700 m), 800 m (target size of 1000 ×1000 ×500 m), and
© 2020 European Association of Geoscientists & Engineers, Geophysical Prospecting,69, 474–490
Imaging method based on the electromagnetic field gradients 485
Figure 10 Apparent resistivity pseudo-sections for different depths-to-bottom of a target. (a) A side view of the model, (b) ραzxcalculated using
equation (13), (c) the pseudo-section for ρgradient calculated using equation (14), and (d) the pseudo-section for ραcalculated using equation (2),
respectively,for a target thickness of 300 m. (e–h) The same, but for a target thickness of 400 m. (i–l) The same, but for a target thickness of
500 m. The white rectangular box indicates the actual locations of the target, and the white solid lines indicate the actual horizontal boundaries
of the target.
1000 m (target size of 1000 ×1000 ×300 m) in the three
models.
From the comparison of Figure 9(b, f, j), it can be seen
that ραzxalways has two extrema values at the positions
x1=−500m and x2=−500m for all three different depths
of the top boundary, which means that the ability of ραzxto
locate the lateral extents of a target is not affected by the vari-
ation of the top boundary (i.e. burial depth). However, ραzx
is sensitive to the depth to the top of a target in that the values
of ραzxdecrease as the target moves deeper.
The vertical positions of the tops and bottoms of the tar-
gets, the true positions of which are marked by the white
rectangles in Figure 9(c, g and k), are reproduced well in
the apparent resistivity pseudo-sections. It can be seen that
the apparent resistivity calculated using the field gradients
is sensitive to the depth of the top boundary of a target.
In contrast, as can be seen from Figure 9(d, h and l), the
apparent resistivity calculated using the original component
Exis not sensitive to the bottom boundary of the target, al-
though it is somewhat sensitive to the depth of the top of the
target.
Similar results were obtained for the second group of
three models, for which the top boundaries of the target are
all the same, but the depths to the bottom boundary of the
target are different. The section views of the three models are
shown in Figure 10(a, e and i), and the parameters of the mod-
els are as follows. The depth to the top boundary of the tar-
gets (i.e. buried depths) is z=−800 m. The background resis-
tivity is 100 m. The target resistivity is 1 m. For the first
model, the depth to the bottom boundary of the target is z
=−1100 m (and thus the thickness of the target is 300 m),
the source–receiver distance is 6500 m (6500 m is the best
value for this model), and the survey line is y=−6500 m. For
the second scenario, the depth to the bottom boundary is z
=−1200 m (giving a target thickness of 400 m), the source–
receiver distance is 7500 m (which is the most appropriate
source–receiver distance for this example), and the survey line
is y=−7500 m. In the third scenario, the bottom boundary
© 2020 European Association of Geoscientists & Engineers, Geophysical Prospecting,69, 474–490
486 M. Zhang, C.G. Farquharson and C. Liu
of the target is at z=−1300 m (for a thickness of 500 m), the
source–receiver distance is 8500 m (again, the best source–
receiver distance for this scenario) and the survey line is y=
−8500 m.
From Figure 10(b, f and j), it can be seen that the two
extrema of ραzxoccur at the true locations of the sides of the
target (x1=−500m and x2=−500m) for all three different
depths to the bottom of the target, which means the ability of
ραzxto recognize the locations of the sides of a target is not
affected by the variation in the depth to the bottom boundary
of a target. As the bottom of a target gets deeper (and hence
the thickness of the target increases), the extreme values of
ραzxincrease, meaning that ραzxis sensitive to the size of
the target.
From Figure 10(c, g and k), it can be seen that the tops
of the anomalies in the pseudo-sections for the apparent resis-
tivities computed using the field gradients stay the same and
the bottoms of the anomalies move deeper as the target thick-
ness increases. This means that all these boundary locations
of the anomalies correspond well with the true locations of
the tops and bottoms of the targets (indicated with the white
rectangles in Fig. 10c, g and k). In other words, the appar-
ent resistivity calculated from the field gradients is sensitive to
the location of the bottom of a target. In contrast, it can be
seen from Figure 10(d, h and l) that the tops of the targets are
also clearly and accurately located in the apparent resistivity
pseudo-sectionscalculated using thefield components,butthe
bottoms of the targets are not. This again verifies that the ap-
parent resistivity calculated using the field gradients generates
pseudo-sections that are better representations of the subsur-
face than the apparent resistivities calculated using the field
component.
5 PRACTICAL SURVEY
In order to further assess the performance and demon-
strate the effectiveness of the improved controlled-source
audio-frequency magnetotelluric (CSAMT) apparent resis-
tivity pseudo-sections method based on the gradients of
frequency-domain controlled-source electromagnetic fields in
a practical survey, we present a real data example from
the coal mining area of Xi’an District, Liaoyuan City, Jilin
Province, China. Liaoyuan City is located in the south of Jilin
Province (Fig. 11a), and the survey area is located immedi-
ately to the northwest of Liaoyuan City. Figure 11(b) shows
the regional geology of the survey area. The main rocks in the
survey area, including the main coal-bearing strata, are Juras-
sic in age. Coal mining has been occurring in this area since
1911, and, as a result of this mining, the original stability of
the rock mass has been weakened. This has resulted in the dis-
placement and deformation of the rock strata, and when the
movement and damage near a stope extends out far enough,
it can reach to the surface, leading to problems such as sur-
face deformation, cracks and subsidence. Figure 11(c) shows
six main subsidence areas in the survey area according to the
geological data.
In the coal mining areas, the disused goafs, which tend to
be the centres and root cause of subsidence, are mostly filled
with water. The electrical resistivity of these water-filled goafs
tends to be relatively low (less than 5 m), whereas the coal
seams themselves are more resistive (higher than 5 m). Elec-
trical and electromagnetic methods therefore offer a means of
detecting and delineating the old underground workings and
hence areas of further potential subsidence. Figure 11(d) in-
dicates the probable existing subsidence or areas where new
subsidence might occur in the future inferred from the DC
resistivity results with areas of resistivity lower than 5 m.
From this panel, the relative position of the line of electrodes
fortheDCresistivity survey (shown by thereddottedline), the
electromagnetic (EM) gradient survey line (shown by the or-
ange solid line) and the existing subsidence areas can be seen.
Figure 11(e) shows the arrangement of source and survey line
for the EM gradient survey. A DC resistivity survey using a
Wenner array configuration was also done in the area.From
the diagram of the Wenner array configuration shown in Fig-
ure 11(f), it can be seen that the minimum and maximum elec-
trode spacing of the Wenner array was 10 and 60 m,respec-
tively, and hence the depth to which the configuration can see
is approximate 200 m.
Based on the locations of the main areas of subsidence
outlined by obvious surface expressions of subsidence and
knowledge of the geology of the area (Fig. 11c), and inferred
from the DC resistivity survey results (Fig. 11d), a survey ge-
ometry for the EM method was chosen with a survey line that
passes across two suspected water-filled goafs (Fig. 11e). The
length of the survey line was about 1200 m. The northern-
most end of the survey line was close to a major highway. The
geological conditions in this area are stable and belong to the
late Jurassic Liaoyuan formation. The middle part of the sur-
vey line passes through two known areas of water-filled mine
workings. DC resistivity data had also been collected along
this survey line. The source–receiver distance for the EM sur-
vey was about 3 km, and the frequencies used were 64, 128,
256, 512 and 1024 Hz.
Figure 12(a) shows the apparent resistivity pseudo-
sectioncalculatedusingequation (14), and Figure12(b)shows
© 2020 European Association of Geoscientists & Engineers, Geophysical Prospecting,69, 474–490
Imaging method based on the electromagnetic field gradients 487
Figure 11 (a) The location of the survey area near Liaoyuan City, Jilin Province,China. (b) Regional geological map of the survey area. (c) Main
areas of subsidence inferred by geological survey results. (d) Areas of subsidence area inferred from DC resistivity results. (e) Arrangement of
source and survey line for the EM gradient survey.(f) The diagram of the Wenner array configuration. The red dashed line and the orange solid
line shown in (d) indicate the line of electrodes for the DC resistivity survey and the line of the EM gradient survey, respectively; they basically
coincide with each other. The survey line shown in (e) is in the same location as the orange solid line in (d). The area between the two grey dashed
lines shown in (f) represents the location where the line of electrodes for the DC resistivity survey coincides with the line of the EM gradient
survey,that is, the location where the orange solid line and the red dotted line shown in (d) coincide with each other. This is also the area shown
in Figure 12.
© 2020 European Association of Geoscientists & Engineers, Geophysical Prospecting,69, 474–490
488 M. Zhang, C.G. Farquharson and C. Liu
Figure 12 Resistivity sections for the EM survey line. (a, b) Apparent resistivity pseudo-sections calculated using Exand Ex, respectively. (c)
Resistivity model constructed via 2-D inversion of the DC resistivity data along the same survey line. The vertical axes of (a, b) show pseudo-
depth, which was calculated using the skin-depth equation.
the apparent resistivity pseudo-section calculated using equa-
tion (2). Figure 12(c) shows the model constructed by the 2-D
inversion of the DC resistivity data along this survey line. In
Figure 12(a, b), the frequencies were converted to apparent
depths using the skin-depth equation, δ=503 ×(ρ/f)1/2, with
p=15 m, so as to facilitate comparison between the appar-
ent resistivity pseudo-sections and the DC resistivity inversion
model.
It can be seen from the apparent resistivity pseudo-
sections in Figure 12 that there are two conductive zones (the
blue areas) under the middle of the survey line, from approx-
imately 200 to 600 m and from 800 to 1200 m, below a
depth of 100 m. The resistivities of both conductive zones
are smaller than 10 m. The resistivity model constructed by
the DC resistivity inversion (Fig. 12c) shows a similar result,
with two conductive zones under the middle part of the sur-
vey. Since this part of the survey line passes over two known
subsidence areas, and since all these three sections give similar
results, it is inferred with some confidence that two water-
filled coal mine goafs exist under this part of the survey line.
For the northernmost end of the survey line, corresponding
to 0–200 m in Figure 12, all three resistivity sections show
resistivities higher than 100 m. Since this part of the survey
line was close to the highway, and geological information sug-
gests that this area comprises the stable late Jurassic Liaoyuan
formation, it is supposed that no water-filled goafs or tun-
nels exist here, which is consistent with the higher resistivi-
ties. Through the above analysis, it can be seen that the ap-
parent resistivity pseudo-sections derived from both the field
gradients data and from the original along-line field compo-
nent correlate well with the DC resistivity inversion results
as well as agreeing with the geological information of the sur-
vey area.
Although the apparent resistivity pseudo-sections calcu-
latedfromthefield gradients (Fig. 12a)andthosecreatedfrom
theoriginalelectricfieldcomponent (Fig. 12b) agree witheach
other in general, there are some differences in the details. For
example, at the site indicated by the black dotted line, the re-
sistivity variation with depth is different. In Figure 12(a), the
approximate location of the bottom of the conductive zone
can be discerned in the pseudo-section created from the field
gradients. In contrast, with the same range of frequencies, the
bottom of the conductive zone cannot be discerned in Fig-
ure 12(b). This is consistent with the synthetic modelling re-
sults shown above, for which the apparent resistivity calcu-
lated using the field component stretches shallow apparent
resistivity anomalies to depth whereas the apparent resistivity
calculated using the field gradients is less susceptible to this
© 2020 European Association of Geoscientists & Engineers, Geophysical Prospecting,69, 474–490
Imaging method based on the electromagnetic field gradients 489
vertical stretching. Since the variation of resistivity with depth
in the DC resistivity inversion results at the same site (repre-
sented by the black dotted line in Fig. 10c) corresponds well
with that of the apparent resistivity pseudo-section calculated
using field gradients, it is supposed that the apparent resistiv-
ity calculated from the field gradients is revealing the bottoms
of targets more accurately.
6 CONCLUSION
We have proposed an improved controlled-source audio-
frequency magnetotelluric (CSAMT) apparent resistivity
pseudo-sections method based on frequency and frequency–
spatial gradients of the fields from the frequency-domain
controlled-source electromagnetic method. The performance
of the proposed method for single and multiple targets was
demonstrated here, with good results for most of the models
considered. We also analysed the artefacts and distortions that
can occur in the apparent resistivity pseudo-sections and how
theyvarywith source–receiver distance,andshowedthat these
issues can be mitigated if an optimal source–sensor separation
can be selected. We also assessed the sensitivity of the new ap-
parent resistivity imaging approach to the depths to the tops
and bottoms of targets, showing that the new apparent resis-
tivityisbetteratresolvingthese features, especially the bottom
of a target, than the traditional apparent resistivity calculated
from the field itself. Furthermore, the practicability of the pro-
posed imaging method for real-life situations was assessed by
its application to field data acquired in the coal mining area of
Xi’an District, Liaoyuan City, Jilin Province, China. Through
comparison of the results of the proposed apparent resistiv-
ity imaging method with those of the traditional method, as
well as DC resistivity inversion results and geological infor-
mation, the applicability of this method to real-life data sets
was demonstrated, including its enhanced ability to identify
the bottoms of targets.
Although the approach is applicable to CSAMT surveys
and can play a useful role in adjusting the operation parame-
ters of instrumentation and in monitoring data quality during
a survey by giving a quick interpretation of the data in the
field, the approach does not replace inversion as the means of
obtainingaccurateinformation(i.e.resistivitiesand depths)of
underground structures. In future work, it would be worth-
while to investigate joint inversion of the initial electromag-
netic (EM) fields and the gradients of the EM fields to assess
whether the inclusion of the gradients can improve the imag-
ing performance.
ACKNOWLEDGEMENTS
The paper is financially supported by Key Technology Re-
searchandDevelopmentProgramofJilinProvince(GrantNo.
20150204021GX), the Natural Science Foundation of Jilin
Province (Grant No. 20170101085JC) and Chinese Scholar-
ship Council (Grant No.201706170173). The authors would
like to thank all members in the EM group of the Key Lab
of Geo-Exploration Instrumentation who provided assistance
for the field test and we are very grateful to Liaoyuan housing
and urban–rural development bureau for providing geological
information and Professor Zhaofa Zeng for their high-density
resistivity results support.
DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available
from the corresponding author upon reasonable request.
ORCID
Ming Zhang https://orcid.org/0000-0003-0459-2018
REFERENCES
Bartel, L.C. and Jacobson, R.D. (1987) Results of a controlled-source
audio frequency magnetotelluric survey at the Puhimau thermal
area, Kilauea Volcano, Hawaii. Geophysics, 52(5), 665–677.
Börner, R.U. (2010) Numerical modelling in geo-electromagnetics:
advances and challenges. Surveys in Geophysics, 31(2), 225–245.
Butler, D.K.(1984) Microgravimetric and gravity gradient techniques
for detection of subsurface cavities. Geophysics,49(7), 1084–1096.
Butler, S. L. and Zhang, Z. (2016) Forward modeling of geophysi-
cal electromagnetic methods using Comsol. Computers and Geo-
sciences, 87, 1–10.
Cagniard, L. (1953) Basic theory of the magneto-telluric method of
geophysical prospecting. Geophysics, 18(4), 605−635.
Constable, S. and Srnka, L.J. (2007) An introduction to marine
controlled-source electromagnetic methods for hydrocarbon explo-
ration. Geophysics, 72, WA3–WA12.
Dell’Aversana, P. (2010) Accurate detection of resistivity anomalies
using the symmetry attribute and inversion of marine CSEM data.
The Leading Edge, 29, 662–671.
Djeddi, M., Baker, H.A. and Tabbagh, A. (1998) Interpretation of
VLF-EM anomalies of 3D structures by using linear filtering tech-
niques. Annali di Geofisica, 41, 151–163.
Goldstein, M. A. and Strangway, D. W. (1975) Audio-frequency mag-
netollurics with a grounded-electric dipole source. Geophysics,
40(4), 669−683.
He, J.S. (2018) Combined application of wide-field electromagnetic
method and flow field fitting method for high-resolution explo-
ration: a case study of the Anjialing No. 1 Coal Mine. Engineering,
4(5), 667–675.
© 2020 European Association of Geoscientists & Engineers, Geophysical Prospecting,69, 474–490
490 M. Zhang, C.G. Farquharson and C. Liu
He, Z.K., Strack, K., Yu, G. and Wang, Z.G. (2008) On reservoir
boundary detection with marine CSEM. Applied Geophysics,5,
181–188.
Helmut, L. (1970) Remarks on the use of the magnetic gra-
diometer in oil exploration. Geophysical Prospecting, 18(1), 119–
133.
Jahandar, H. and Farquharson, C.G. (2014) A finite-volume solution
to the geophysical electromagnetic forward problem using unstruc-
tured grids. Geophysics, 79(6), 287–302.
Kruk,J.,Meekes, J.,Berg, P.M. and Fokkema,J.T.(2000) An apparent-
resistivity concept for low-frequency electromagnetic sounding
techniques. Geophysical Prospecting, 48(6), 1033–1052.
Kunetz, G. (1972) Processing and interpretation of magnetotelluric
soundings. Geophysics, 37, 1005–1021.
Lei, D., Fayemi, B. and Yang, L.Y.(2017) The non-static effect of near-
surface inhomogeneity on CSAMT data. Journal of Applied Geo-
physics, 139, 306–315.
MacGregor, L. and Sinha,M. (2000) Use of marine controlled-source
electromagnetic sounding for sub-basalt exploration. Geophysical
Prospecting, 48, 1091–1106.
Meju, M.A. (2019) A simple geological risk-tailored 3D CSEM multi-
attributes analysis and quantitative interpretation approach. Geo-
physics, 84(3), E155–E171.
Newman, G.A. (2014) A review of high-performance computational
strategies for modeling and imaging of electromagnetic induction
data. Surveys in Geophysics, 35(1), 85–100.
Parasnis, D.S. (1991) Large-layout harmonic field systems. In:
Nabighian, M.N. (Ed.) Electromagnetic Methods in Applied Geo-
physics: Volume 2, Application, Parts A and B.Tulsa:SEG,pp.271–
284.
Peter, H. (1965) Gradient measurements in aeromagnetic surveying.
Geophysics, 30(5), 891–902.
Rust, W.M. (1938) A historical review of electromagnetic prospecting
methods. Geophysics,3,1–6.
Sandberg, S.K. and Hohmann, G.W. (1982) Controlled-source audio-
magnetollurics in geothermal exploration. Geophysics, 47, 100–
116.
Sasaki, Y., Yoneda, Y. and Matsuo, K. (1992) Resistivity imaging
of controlled-source audio frequency magnetotelluric data. Geo-
physics, 57(7), 952–955.
Spies, B.R. (1989) Depth of investigation in electromagnetic sounding
methods. Geophysics, 54(7), 872–888.
Spies, B.R. and Eggers, D.E. (1986) The use and misuse of apparent
resistivity in electromagnetic methods. Geophysics, 51(7), 1462–
1471.
Telford, W.M., Geldart, L.P. and Sheriff, R.E. (2013) Applied Geo-
physics. Cambridge University Press.
Vozoff, K. (1972) The magnetotelluric method in the exploration of
sedimentary basins. Geophysics, 37, 98–141.
Ward, S.H. and Hohmann, G.W. (1988) Electromagnetic theory for
geophysical applications. In: Nabighian, M.N. (Ed.) Electromag-
netic Methods in Applied Geophysics: Volume 1, Theory.Tulsa:
SEG, pp. 130–311.
Wenner,F. (1915) A method of measuring earth resistivity. Bulletin of
the US Bureau of Standards, 12, 469–478.
Wilt, M. and Stark, M. (1982) A simple method for calculating ap-
parent resistivity from electromagnetic sounding data. Geophysics,
47(7), 1100–1105.
Yan,S. and Fu, J.M.(2004) An analytical method to estimate shadow
and source overprint effects in CSAMT sounding. Geophysics,
69(1), 161–163.
Zhang, M., Farquharson, C.G. and Liu, C.S. (2020) Response char-
acteristics of gradient data from the frequency domain controlled-
source electromagnetic method. Journal of Applied Geophysics,
172, 103873.
Zonge, K.L. and Hughes, L.J. (1991) Controlled source audio-
frequency magnetotellurics. Society of Exploration Geophysicists,
2, 713–809.
© 2020 European Association of Geoscientists & Engineers, Geophysical Prospecting,69, 474–490
