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Received November 12, 2019, accepted November 29, 2019, date of publication December 10, 2019,
date of current version December 23, 2019.
Digital Object Identifier 10.1109/ACCESS.2019.2958631
Suppression of the Attitude Error With a
Modified Iterative Algorithm for Apparent
Resistivity Imaging in GAFDEM Survey
CHANGSHENG LIU , LILI KANG , WENJIE ZHU , HAIGEN ZHOU ,
MING ZHANG , AND JIE LIANG
College of Instrumentation and Electrical Engineering, Jilin University, Changchun 130012, China
Key Lab of Geo-Exploration Instrumentation (Ministry of Education), Jilin University, Changchun 130012, China
Corresponding author: Haigen Zhou (zhouhaigen@jlu.edu.cn)
This work was supported in part by the National Natural Science Foundation of China under Grant 41904159, and in part by the Natural
Science Foundation of Jilin Province under Grant 20170101085JC.
ABSTRACT The ground–airborne frequency-domain electromagnetic (GAFDEM) survey is a fast method to
detect the deep underground structure in areas with difficult access. However, the suspended coil sensor in the
survey system experiences attitude changes, which inevitably yield attitude error on the measured magnetic
field and result in false apparent resistivity imaging. Due to the separated system structure, the attitude error
in GAFDEM survey is significantly different from that in traditional airborne helicopter frequency-domain
electromagnetic survey. In order to improve the detection accuracy, a modified iterative algorithm is proposed
to suppress the attitude error for apparent resistivity imaging. Both simulation and practical experiment
are conducted to verify the usefulness of the correction method. The simulation results indicate that the
correction procedure is important and effective to reduce the attitude error in layered earth model. The field
experiment results show that the corrected apparent resistivity imaging section is more consistent with the
high-density resistivity topography and more reasonable than the uncorrected apparent resistivity imaging
result obtained by conventional method. Consequently, the proposed suppression approach can reduce the
attitude error to obtain more accurate apparent resistivity imaging results in GAFDEM survey, which may
effectively promote the developments and applications of GAFDEM method and systems.
INDEX TERMS Attitude error, apparent resistivity imaging, GAFDEM, modified iterative algorithm.
I. INTRODUCTION
The ground–airborne frequency-domain electromagnetic
(GAFDEM) survey is a recently developed fast semi-
airborne method for geophysical subsurface explorat-
ion [1]–[3]. It mainly uses vertical magnetic fields of different
frequencies in the air to detect an underground structure [4].
The vertical magnetic fields are excited by a controlled
electrical source on the ground and collected by a horizontal
coil sensor suspended under an airborne platform [5]. The
typical source–receiver distance is approximately 2–10 km
and the typical height of the coil ranges from 10 m to
100 m according to ground obstacles [6]. Due to the sep-
arated structure, the GAFDEM system can excite strong
The associate editor coordinating the review of this manuscript and
approving it for publication was Mohammed Bait-Suwailam .
electromagnetic field without the limitation of the weight
and power of transmitter [7], [8], and detect the areas with
large source-receiver distance quickly [9]–[11]. Thus, the
GAFDEM survey is suitable for deep underground structure
exploration in areas with difficult access on the ground.
In practical applications, the GAFDEM survey usually
uses the apparent resistivity imaging to give a quick overview
of underground electrical structures [4], [12], [13]. In the
process of apparent resistivity imaging, the theoretical verti-
cal magnetic field response of a uniform half-space is used
to fit the observed data. This imaging process is based on
the assumption that the coil keeps horizontal throughout
the flight. However, because of the various forces acting
on the survey system (e.g., gravity, lift, drag, cable pull,
and wind), the suspended coil sensor experiences attitude
changes [14], [15], which inevitably yield attitude error
179898 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see http://creativecommons.org/licenses/by/4.0/ VOLUME 7, 2019
C. Liu et al.: Suppression of the Attitude Error With a Modified Iterative Algorithm
(i.e., the differences between the measured responses and the
straight-and-level flight responses) on the measured magnetic
field and may result in false apparent resistivity imaging
results. Therefore, it is necessary to suppress the attitude error
to improve the imaging accuracy.
In conventional airborne electromagnetic method, the atti-
tude error in frequency-domain helicopter electromagnetic
(HEM) systems had been well studied by Yin and Fraser [16]
and Fitterman and Yin [17]. They showed that the attitude
error in HEM systems contains two parts: one is the geometric
part, which is dependent only on the sensor’s attitude, and
the other is the inductive part, which depends not only on the
attitude of the sensor but also on the system frequency and
the earth’s electrical properties. They also demonstrated that
the majority of the attitude error results from the geometric
effect rather than from the inductive effect in the general case
of HEM systems when the separation between transmitting
and receiving coils is much smaller than the flight altitude.
In this situation, the inductive effect can be ignored and the
attitude error can be corrected by using a simple geometric
factor to obtain sufficient imaging accuracy, without requir-
ing information about the earth’s electrical properties.
The above correction method is convenient and useful for
HEM systems. Nevertheless, it is not suitable for GAFDEM
system because the transmitting source is no longer a coil
structure and the distance between source and receiver is far
greater than the flight altitude. Then the inductive effect may
also play an important role in the attitude error and it must
be considered in attitude correction. In this paper, a modi-
fied iterative algorithm is proposed to suppress the attitude
error to improve the apparent resistivity imaging accuracy.
In the correction procedure, the observed data is fitted by
the corrected magnetic field with coil’s rotations instead of a
simple vertical magnetic field in conventional method. In the
following parts, we first analyze the characteristics of attitude
error in GAFDEM system, and then verify the usefulness of
the correction method by theoretical simulation and field test.
II. ANALYSIS OF ATTITUDE ERROR
Fig. 1 shows the schematic diagram of the attitude changes of
the receiving coil in GAFDEM system over a layered earth.
We use three coordinate systems, Oxyz,oxyz and ox’y’z’,
to analyze the attitude error. Oxyz is the transmitter coordinate
system. It is built in accordance with the grounded electric
source. Its origin is at the center of the source wire, its
x-axis coincides with the direction of the electric wire, its
y-axis is perpendicular to the x-axis, and its z-axis points
downward. oxyz is the inertial coordinate system, which is
used to describe the initial state when the coil sensor is
completely horizontal. It follows the same axes as Oxyz, but
its origin is at the center of the coil sensor. ox’y’z’ is the coil
coordinate system, which is used to describe the state of the
coil after rotation. It has the same origin as the oxyz, but its
axes follow the coil’s new orientation. The coil rotations can
be decomposed into three parts, namely, yaw with rotation
around the z-axis, roll with rotation around the x-axis, and
FIGURE 1. Attitude changes of coil sensor in GAFDEM system. ϕY,ϕP, and
ϕRare the yaw, pitch, and roll angles, respectively.
pitch with rotation around the y-axis. According to Fitterman
and Yin [17], the separate rotation matrices and the complete
rotation matrix are as follows:
RY=
cos ϕYsin ϕY0
−sin ϕYcos ϕY0
0 0 1
(1)
RP=
cos ϕP0−sin ϕP
0 1 0
sin ϕP0 cos ϕP
,(2)
RR=
1 0 0
0 cos ϕRsin ϕR
0−sin ϕRcos ϕR
,(3)
R=RRRPRY
=
cϕPcϕYcϕPsϕY−sϕP
cϕYSϕPSϕR−sϕYcϕRsϕYsϕPsϕR+cϕYcϕRcϕPSϕR
cϕYsϕPcϕR+sϕYsϕRsϕYsϕPcϕR−cϕYsϕRcϕPcϕR
,
(4)
where cand srefer to cosine and sine functions, respectively.
After coil’s rotations, the measured magnetic field (Br) can
be calculated by:
Br=R·[Bx,By,Bz]T·[0,0,1]T
=Bx(cϕYsϕPcϕR+sϕYsϕR)
+By(sϕYsϕPcϕR−cϕYsϕR)+BzcϕRcϕP,(5)
where [Bx, By, Bz] are the three component magnetic fields at
observation point before rotation. For a 1D layered isotropic
earth, the three component magnetic fields at point (x,y,z) in
transmitter coordinate system can be written as [18]:
Bx= −µ0IL
4π·y
R·Z∞
0
(rTM −rTE)·eu0zλJ1(λR)dλ , (6)
By=µ0IL
4πZ∞
0e−u0z+rTEeu0zλJ0(λR)dλ
+µ0IL
4π
x
RZ∞
0
(rTM −rTE)·eu0zJ1(λR)dλ, (7)
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C. Liu et al.: Suppression of the Attitude Error With a Modified Iterative Algorithm
Bz=µ0IL
4π
y
RZ∞
0e−u0z+rTEeu0zλ2
u0
J1(λR)dλ, (8)
where, R=(x2+y2)1/2,u2=λ2-k2,k2=-iωσ +
ω2µε, and J0and J1are the zero and first order Bessel
functions, respectively. Idenotes the transmitter current, and
Lrepresents the length of the transmitter wire. rTE and rTM
indicate electromagnetic wave’s reflection factors defined by
Ward and Hohmann [19]. In our analysis, these formulas are
calculated by using Matlab program with Hankel integral
transformation.
Similar to Yin and Fraser [16], the ratio of the magnetic
response when the coil sensor rotates to that when the coil
keeps horizontal is used to analyze the attitude error. For want
of a better expression, we define the ratio as a correction
factor Ra. From (8), we obtained the correction factor follows:
Ra=Br(ϕY, ϕP, ϕR)Br(0,0,0)
=Txz(cϕYsϕPcϕR+sϕYsϕR)
+Tyz(sϕYsϕPcϕR−cϕYsϕR)+cϕRcϕP,(9)
where Txz =Bx/Bzand Tyz =By/Bz. The correction factor
can also be divided into two parts: the geometric part RG
aand
the inductive part RI
a, which are defined as follows:
RG
a=cϕRcϕP,(10)
RI
a=Txz(cϕYsϕPcϕR+sϕYsϕR)+Tyz (sϕYsϕPcϕR−cϕYsϕR).
(11)
It can be seen that the geometric part depends on ϕRand
ϕPand that the inductive part depends not only on the three
rotation angles but also on the location of the coil, the survey
frequency and the earth’s electrical properties, which are
implicit in Txz and Tyz.
To understand the behavior of the correction factor,
we examined a special case of formula (10) and (11) with
rotations limited to roll and pitch (ϕR=0) based on a
homogeneous half-space model. Fig. 2 shows the modulus of
RG
aand RI
awhen rotation angles increase from 0 to 20 degrees.
The calculation parameters are shown in table 1. In Fig. 2(a),
the modulus of RG
avaries approximately from 1 to 0.89. The
influences of roll and pitch are symmetric. As the angles
increase, the modulus of RG
adecreases. In Fig. 2(b), the influ-
ences of roll and pitch are very different. With the increase
of roll, the modulus of RI
aincreases obviously from 0 to 7.
However, with the increase of pitch, the modulus of RI
aonly
decreases slightly. The modulus of RI
ais more sensitive to the
roll angle compared with pitch angle. As a result, the modulus
of RI
ahas a larger range of variation than that of RG
a, and
their variation features are quite different from each other.
However, the modulus values of RI
aand RG
aare very different
from 1 in most situations, which means that both geometric
and inductive parts can cause obvious differences between
the measured data and the theoretical vertical magnetic field
after coil’s rotations. Thus, it is important to suppress the
attitude error to improve survey accuracy. Moreover, both the
geometric effect and the inductive effect should be considered
in the process of attitude error correction.
TABLE 1. Calculation Parameters for figure 2.
FIGURE 2. Modulus of (a) RG
a, (b) RI
aversus roll and pitch rotation angles.
Calculation parameters are given in table 1.
III. CORRECTION OF ATTITUDE ERROR
Based on the analysis above, a modified iterative algorithm
is proposed to suppress the attitude error in GAFDEM sur-
vey for apparent resistivity imaging. In traditional algo-
rithm, it is assumed that the coil sensor is completely
horizontal and acquires a purely vertical magnetic field.
Hence, Bz(ρ(i)
a,R,ω) is used to match the measured mag-
netic field (Bm) based on the quasi static approximation
of (6):
Bz=µ0IL
2π·y
RZ∞
0
λ2
λ+u1
eλzJ1(λR)dλ(12)
where u1=(λ2+k2
1)1/2, and k2
1=-iµω/ρa,ρais the
apparent resistivity. The iterative algorithm starts with the
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C. Liu et al.: Suppression of the Attitude Error With a Modified Iterative Algorithm
TABLE 2. Calculation Parameters for figure 3.
initial value ρ0
a=ρ0, following (13):
ρ(i)
a=ρ(i−1)
a+1ρ(i−1)
a=ρ(i−1)
a
+
Bzρ(i)
a,R, ω−Bzρ(i−1)
a,R, ω
B0
zρ(i−1)
a,R, ω,(13)
and continues until Bzmeets:
Bm(ρ, R, ω)−Bzρ(i)
a,R, ω
Bz(ρ, R, ω)
< ε, (14)
where εrepresents the fitting tolerance error. It is set to be
10−4–10−2, in accordance with the signal-to-noise ratio.
In the modified iterative algorithm, we use Br(ρ(i)
a,R,ω)
to match the measured magnetic field (Bm) based on for-
mula (5). The modified iterative algorithm also starts with the
initial value ρ0
a=ρ0.But it follows
ρ(i)
a=ρ(i−1)
a+1ρ(i−1)
a=ρ(i−1)
a
+
Brρ(i)
a,R, ω−Brρ(i−1)
a,R, ω
B0
rρ(i−1)
a,R, ω,(15)
and continues until Brmeets:
Bm(ρ, R, ω)−Brρ(i)
a,R, ω
Br(ρ, R, ω)
< ε (16)
Fig. 3 gives a block diagram summarizing the key steps in
the attitude correction. In the modified algorithm, both the
geometric effect and inductive effect are corrected because
Brcontains rotation angles and three-component magnetic
fields. Thus, the modified iterative algorithm can obtain
more accurate imaging results compared with the traditional
method. We use a three-layer earth model to illustrate the
effectiveness of the correction method. The resistivity and
thickness of each layer are [100, 10, 100] ·m and [500,
100, ∞] m, respectively. The measurement point is set as
[100, 4000, -20] m and the coil sensor’s attitude angles are
[5, 5, 20] ◦. All the assumptions are list in table 2.
Fig. 4(a) shows the response amplitudes at different fre-
quencies before and after coil sensor’s rotations. The response
amplitude after the coil sensor’s rotations present obvious
deviations to that without attitude changes, especially at
the high frequency range. Fig. 4(b) shows the corrected,
uncorrected, and raw apparent resistivity. The raw apparent
FIGURE 3. Block diagram of the attitude correction.
FIGURE 4. Simulation results: (a) response amplitude, (b) apparent
resistivity, (c) relative error between corrected apparent resistivity and
apparent resistivity without attitude changes.
resistivity means the apparent resistivity obtained by the mag-
netic data without coil’s attitude changes. The raw apparent
resistivity present an obvious three layer structure with a top
layer of 100 ·m at high frequencies (fhrange), a transition
layer with sunken apparent resistivity values at the medium
frequencies (fmrange), and a bottom layer of about 65 ·m at
low frequencies (flrange). The uncorrected apparent resistiv-
ity presents obvious misfits to the raw apparent resistivity and
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C. Liu et al.: Suppression of the Attitude Error With a Modified Iterative Algorithm
FIGURE 5. Overview of the survey map and the GAFDEM survey system.
the misfit at fhrange increases when the frequency increases.
The maximum misfit is about 3 times of the raw apparent
resistivity. These misfits will lead to a fault explanation of
the subsurface structure. However, the corrected apparent
resistivity curve coincides with the raw apparent resistivity
very well in the whole frequency band. Fig. 4(c) presents
the relative error between the raw and corrected apparent
resistivity. The relative error at low frequencies and high
frequencies is close to 0. The maximum error occurred in
the medium frequency band is less than 4%. Therefore, this
correction method is effective to suppress the attitude error
and improve the accuracy of apparent resistivity.
IV. FIELD SURVEY
In order to further verify the usefulness of the correction
method, we process the GAFDEM data collected in a field
survey near Liaoyuan City, Jilin Province, China. Fig. 5 gives
the overview of the survey map and GAFDEM survey system.
The red line is the source line with a length of 2 km. The
yellow line is the survey line with a length of 1.7 km. The
distance between the source line and the survey line is approx-
imately 3.0 km. The GAFDEM survey system contains two
parts: the transmitting system on the ground and the receiving
system in the air. The transmitting system mainly includes a
high power transmitter, a current logger and grounded wires.
The receiving system mainly includes a rotorcraft, a receiver
and a coil sensor. In addition, an attitude sensor with an
accuracy of 0.1 degrees is installed on the coil sensor. The
red triangle represents the position of the transmitter, and
the Yellow asterisk represents the take-off position of the
rotorcraft.
In this survey, the GAFDEM system operated at 64, 128,
256, 512, and 1024 Hz with currents of 31, 30, 45, 25, and
22 A, respectively. The rotorcraft flew at a height of 50 m
at 8 m/s. The separation between the coil sensor and the
rotorcraft is 15 m. Fig. 6(a) presents the three rotation angles
of the coil sensor recorded at one flight. At the beginning and
end of the survey line, the attitudes present large deviations
because the speed changes significantly when the rotorcraft
starts and stops. The yaw presents large deviations due to
the strong wind during the flight. Fig. 6(b) shows the raw
magnetic data which were processed every 10 s and normal-
ized by the current at each frequency. The raw magnetic data
present relevant deviations as the attitudes, especially the yaw
attitudes.
Before our survey, comprehensive exploration had been
conducted to study the coalmine goafs in the survey area [20].
Therefore, the underground electrical structure is relatively
clear. Fig. 7(a) shows the previous resistivity cross section
of the high-density resistivity (HDR) method at the same
position as GAFDEM survey, which was obtained by a 2D
inversion software named RES2DINV. In Fig. 7(a), the resis-
tivity value varies from 10 ·m to 150 ·m. There are two
obvious conductive anomalies at 0-400 m and 700-1250 m in
179902 VOLUME 7, 2019
C. Liu et al.: Suppression of the Attitude Error With a Modified Iterative Algorithm
FIGURE 6. GAFDEM data in Liaoyuan survey: (a) attitude data,
(b) measured magnetic data.
FIGURE 7. Results of Liaoyuan survey: (a) resistivity cross section
obtained by high-density resistivity method, (b) uncorrected apparent
resistivity cross section, (c) corrected apparent resistivity cross section
obtained by GAFDEM survey.
the survey line. They are separated by an inclined resistive
region. At 1300-1700 m, the electrical structure is resistive.
Its resistivity value varies approximately from 50 ·m to
150 ·m. These features provide good comparison informa-
tion for our results.
Fig. 7(b) shows the uncorrected apparent resistivity cross
section in GAFDEM survey using traditional algorithm. The
apparent resistivity value varies from 1 ·m to 1000 ·m.
Its range is much larger than that in HDR method. The cross
section also presents two obvious conductive anomalies. The
left conductive area is at 0–600 m and the right conductive
area is at 800–1600 m. They are much wider than that in
Fig. 7(a). In addition, there is an obvious resistive layer in
the shallow part at 400-1700m. Fig. 7(c) shows the cor-
rected apparent resistivity cross section in GAFDEM survey
using modified algorithm. It is interesting to see that the
corrected apparent resistivity is smaller than the raw apparent
resistivity, ranging from 1 ·m to approximately 200 ·m.
Moreover, the corrected cross section also highlights the two
conductive bodies encircled by the black lines, which are at
100-400 m and at 900-1300 m, respectively. Besides, the area
of the shallow resistive layer decreases. These features make
Fig. 7(c) similar to Fig. 7(a).
Based on the results above, it can be seen that the values
of the corrected apparent resistivity are closer to that of the
resistivity in HDR method than the raw apparent resistivity.
Furthermore, the two conductive anomalies shown in cor-
rected apparent resistivity cross section are more coincides
with the resistivity cross section in HDR method. Conse-
quently, the correction procedure is useful for GAFDEM
survey, which can provide a more accurate imaging result for
subsurface structure.
V. CONCLUSION
The attitude error in GAFDEM system is analyzed based on
a layered earth. It contains two parts: the geometric part and
the inductive part. Both the two parts play an important role in
attitude error and should be considered for attitude correction
in GAFDEM survey. These features are quite different from
that in traditional frequency-domain HEM survey. The use-
fulness of the modified iterative algorithm is verified by sim-
ulation and field test. The simulation results of the three-layer
earth show that the corrected apparent resistivity is consistent
with that obtained from the data without attitude changes. The
field test shows that the corrected apparent resistivity imaging
cross section is more similar to the resistivity result in HDR
method compared with the uncorrected apparent resistivity
imaging cross section. Hence, the modified iterative algo-
rithm can reduce the attitude error to improve the apparent
resistivity imaging accuracy. Considering the urgent need
of rapid detection of deep underground structures, this new
correction method may effectively promote the developments
and applications of GAFDEM method and systems.
ACKNOWLEDGMENT
The authors are very grateful to Liaoyuan housing and urban-
rural development bureau and Prof. Z. Zeng for their high-
density resistivity results support.
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CHANGSHENG LIU was born in Hubei, China,
in 1979. He received the B.S. degree from Central
South University, Changsha, China, in 2003, and
the M.S. and Ph.D. degrees from Jilin University,
Changchun, China, in 2005 and 2009, respectively.
He is currently a Professor and the Ph.D. Super-
visor with Jilin University. His research inter-
ests include electromagnetic detection technology,
instruments, and their applications.
LILI KANG was born in Inner Mongolia, China,
in 1993. She received the B.S. and Ph.D.
degrees from Jilin University, Changchun, China,
in 2014 and 2019, respectively. She is currently
an Engineer with the Institute of Geology and
Geophysics, Chinese Academy of Sciences. Her
research interests include data processing and
imaging for geophysical electromagnetic methods.
WENJIE ZHU was born in Henan, China, in 1990.
He received the B.S. degree from Jilin University,
Changchun, China, in 2016, where he is currently
pursuing the M.S. degree in power electronics and
power transmission with the College of Instrumen-
tation and Electrical Engineering. His research
interests include attitude measurement and correc-
tion for ground-airborne frequency-domain elec-
tromagnetic method.
HAIGEN ZHOU was born in Henan, China,
in 1990. He received the B.S. degree in elec-
trical engineering and automation and the Ph.D.
degree in measurement technology and instru-
ments from Jilin University, Changchun, China,
in 2012 and 2017, respectively. He is cur-
rently undertaking Postdoctoral Research with
Jilin University. His research interests include
ground-airborne frequency-domain electromag-
netic method, instruments, and their applications.
MING ZHANG was born in Changchun, China,
in 1989. She received the B.S. and M.S. degrees
from Jilin University, China, in 2011 and 2014,
respectively. She is currently pursuing the Ph.D.
degree in measurement and control technology
and instruments with the College of Instrumen-
tation and Electrical Engineering, Jilin Univer-
sity, and the Ph.D. degree in geophysics with the
Department of Earth Science, Memorial Univer-
sity of Newfoundland, Canada. Her research inter-
ests include forward modeling and the inversion of electromagnetic data for
geophysical prospecting.
JIE LIANG was born in Henan, China, in 1994. She
received the B.S. degree from the Guangdong Uni-
versity of Technology, Guangzhou, China, in 2015,
and the M.S. degree from Henan Normal Univer-
sity, Xinxiang, China, in 2018. She is currently
pursuing the Ph.D. degree in measurement tech-
nology and instruments with the Department of
Instrumentation and Electrical Engineering, Jilin
University. Her research interest includes imaging
methods for use in GAFEM surveys.
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