Behaviour of Electromagnetic Waves in Different Media and Structures

108
To avoid the influence of air-gap to the testing result, a rock sample holder is make as
shown in fig. 3.
The practical testing equipment including a VNA is shown in Fig. 4.
In equation (17) and (18), because the Bessel function has oscillating property, the main
difficulty focuses on the Bessel function with integral variable. Obviously these nonlinear
equations have no analytical solution. So we uses numerical solution here. A big number
(12500) is used for the positive infinite of the upper limit during the numerical intergal. The
value of the big number is determined by different testing of many conditions.
2.3 Calibration
The calibration in this measurement includes two steps, one is the transmission line
calibration, and the other is the probe calibration.
2.3.1 Transmission line calibration
The VNA is a exact device and is connected to coaxial probe through a coaxial cable.
According to the operation requirement of the network analyzer, the coaxial line is
calibrated using calibrating kits. The detailed operation process as follows.
1.
VNA parameters setting. The frequency range is between 1MHz-1GHz in this test
according to our request. Power can be selected by our need, for example, 0dBm. Large
power is believed to sense large sample volume. We choose 1000 sampling points here.
2.
Calibration process. We use single port calibration here because we only measure S11.
The calibration kits which including the device SHORT, LOAD, and OPEN are used to
calibrate the VNA. After this process, the reference plane for VNA is at the end of the
coaxial cable. However, because the reflection surface is on the flange surface, not the
end of the cable, further calibration is still needed.
2.3.2 Probe calibration

Γ can be calculated
through equation (17) or (18). Through measuring the reflection coefficient of three kinds of
materials
m
Γ , the three equations about
d
e ,
r
e ,
s
e can be obtained. There are three variables
and three equations, the error coefficients
d
e ,
r
e ,
s
e can be obtained.
Short-circuit, and air are ideal calibration materials. The third material must have known
permittivity. The de-ionized water is selected as the third calibration material here. When it
is of short-circuit,
a
-1Γ= ; when the calibration material is air, the reflection coefficient of
every frequency can be calculated through equation (17) or (18), because the permittivity of
air is 1. According to the same theory, the reflection coefficient of de-ionized water can be
calculated. Here, the reflection coefficient of water is obtained through the Cole-Cole
formula.

Wide-band Rock and Ore Samples Complex Permittivity Measurement


Γ , the reflection coefficient
of de-ionized water
water _ a
Γ and
water _ m
Γ and the reflection coefficient of short-circuit
short _ a
-1Γ= and
short _ m
Γ into the equation (19) separately. We get,

air _ a water _ a air _ a
s
water_a air_a water_a water_a air_a
CC-
e
CC -
Γ+Γ +Γ
=
ΓΓ+Γ +Γ Γ
(21)
where,
water _ m
-A
C
A-B
Γ
=
,
air _ m


()
md
a
sm d r
-e
e-ee
Γ
Γ=
Γ+
(24)
Equation (24) determines the second step calibration. Fig. 7 shows the comparison among
results before and after calibration for PTFE and de-ionized water, separately. Fig. 5. Reflection coefficient before and after calibration
It can be seen that the real part of PTFE measured can be calibrated to around but different
from 1.

Behaviour of Electromagnetic Waves in Different Media and Structures

110
2.4 Inversion calculation and error evaluation
If the permittivity of a material measured is known, the interface reflection coefficient (or
admittance) can be calculated. This process is a forward one. The reverse process can be
solved numerically. The following equation can be obtained from equation (18),

()
()
()

(26)
Because it is a complex calculation, the objective function is defined as

() ( ) ()
22
mc mc
faRe- Im-ε= Γ Γ + Γ Γ

(27)
α is a weighting coefficient in this equation,
m
Γ and
c
Γ are measured and the calculated
reflection coefficients. The real part and the imaginary part should be treated equally to
avoid that the large part dominates over the small part too much. This is the typical
optimization problem. Here, ε can be thought as a complex-single variable. But the most
mathematical software optimization tool can not process complex variable optimization
question. So the complex permittivity is divided to real part and imaginary part. The
variable x is a vector array, where,
()
1
xRe=ε,
()
2
xIm=ε. The selection of weighting
coefficient is based on the numerous tests.
We solve the optimization process using the simplex method. The value of
()
f ε after the

Behaviour of Electromagnetic Waves in Different Media and Structures

112

Fig. 9. Permittivity of the air
The relative error is 0.7692%. Because the air is a kind of calibration material, the
permittivity of air calculated should be theoretical value 1.The relative error is below 0.8%.
It proves the validity of inversion process.
The measured permittivity for methanol is displayed in Fig. 10. Fig. 10. Permittivity of methanol
The measured permittivity for methanol is compared with the theoritical values which is
calculated by the debye equation or cole-cole equation (Jordan et al., 1978) as shown in Fig.
10. The measured data is accetable except that they have clear difference with the theotitical
ones at high frequency range. The reducement of this error could be the future topic.
3. Measured results and analysis
342 rocks and ores sample within 31 categories from 6 mines are measured and analyzed in
this part by using open-coaxial probe technique. The photos for these rocks and ores
samples are shown in Fig. 11.

Wide-band Rock and Ore Samples Complex Permittivity Measurement

113

Fig. 11. Photographs of the rocks and ores samples from 6 metal mines
3.1 Samples from the Changren nickel-copper mine, Jilin, China
Table 1 shows the messages of rocks and ores from the Changren nickel-copper mine, Jilin,
China.
Fig.12 shows marbles permittivities as an example, the solid and the dashed lines denote the

mine

Wide-band Rock and Ore Samples Complex Permittivity Measurement

115
Actually, the pyroxene peridotite, light alterative bornblende pyroxenite are basic rocks and
ultra-basic rock which were ore carrier. When ore’s grade is low, the permittivity represents
the carrier rock’s property. These basic rocks and ultra-basic rock come from tectonic
emplacement. The granitized granite is the host rock which has distinguished lower values.
These measured data show optimistic aspect for borehole radar detection for metal ore-body.
3.2 The samples from the Huanghuagou lead-zinc mine, Chifeng, Inner Mongolian,
China
The table 2 shows the message of rocks and ores from the Huanghuagou Lead-Zinc mine
Chifeng, China. Ores and rocks ranked by permittivity from high to low are high-grade ore,
pyrite, medium-grade ore, dacitoid crystal tuff, low-grade ore, crystal tuff, tuffaceous
breccia, tuffaceous sandstone, and dacite. The high-grade ore, pyrite, and the medium-grade
ore are distinguishable from each other and the others.

Rocks Rock or Ore names Fig. no permittivity Samples number
1 tuffaceous fine-grained sandstone 11(2a) 5-7 5
2 tuffaceous breccia 11(2b) 5-6 5
3 dacitoid crystal tuff 11(2c) 5.5-8 13
4 dacite 11(2d) 5.5-6 10
5 crystal tuff 11(2e) 5-7.5 11
Ores
6 high-grade ore 11(2f) 10-70 11
7 medium-grade ore 11(2g) 10-12 5
8 low-grade ore 11(2h) 5-10 8
9 pyrite 11(2i) 20-40 4
Table 2. Messages of the Huanghuagou lead-zinc mine, Chifeng, Inner Mongolian, China

albitophyre ore is clearly distinguishable from the others in the real part. Other rocks and
ore are ambitious in permittivity.

Rocks Rock or Ore names Fig. no Permittivity Samples number
1 albite rhyolite porphyry (core) 11( 4a) 5-5.5 8
2 breccia porphyry 11(4b) 5-5.5 14
3 quartz albitophyre 11(4c) 5-7.5 11
Ores
4 albitophyre ore 11(4d) 5-10
16(No
：01-09,11-17)
5 malachite oxide ore 11(4e) 5-5.5
14(No.
：01-14)
Table 4. Messages of rocks and ores from the Qunji Copper mine, Xinjiang, China

Wide-band Rock and Ore Samples Complex Permittivity Measurement

117

Fig. 16. Average permittivities of rocks and ores from the Qunji Copper mine, Xinjiang,
China
3.5 Samples from the Musi copper mine, Xinjiang, China
The table 5 shows the messages of rocks and ores from the Musi copper mine, Xinjiang,
China. Ores and rocks ranked by permittivity from high to low are vesicular amygdaloidal
andesite, massive diorite, and andesitic copper ore. The andesitic copper ore is
distinguishable from the others and shows low permittivity characteristic which is opposite
to other mines.
sample sheets are required. Because the sensing range of the probe concentrates mainly at
the center of the probe and the samples measured are no so homogeneous, we use averaging
value from several samples of a rock or ore to reduce the random effect due to their in-

Wide-band Rock and Ore Samples Complex Permittivity Measurement

119
homogeneity. It is shown that permittivity of metal ore is higher than other rocks, and high-
grade ore is distinguishable from surrounding rocks. These measurements provide insights
into the wide-frequency permittivity of metal ores and rocks, and also provide basis for
electromagnetic exploration by borehole radar.
There are still couple of problems with the current research. The sizes of the flange, the
aperture of the probe, sheet sample thickness, are not optimized yet. The sensing area for
the current probe is small for the inhomogeneous rocks and ores. These are all future works
for us.
5. Acknowledgment
This research is supported by the National Natural Science Foundation of China (Grant No
40874073 and 41074076), and by the National High-Tech R&D Program 863 (Grant No
2008AA06Z103)
6. References
Blackham, D.V. & Pollard, R. D. (1952). An improved technique for permittivity
measurements using a coaxial probe.
IEEE Transactions on Instrumentation and
Measurement
, Vol. 46, No. 5, (Sept., 1997), pp.1093-1099, ISSN 0018-9456
Coutanceau-Monteil, N., & Jacquin, C. (1960). Improvements of the coaxial line technique
for measuring complex dielectric permittivity of centimetric samples in the 20 to
1000 MHz range: application to sedimentary rocks.
Log Analyst, Vol. 34, No. 5,
(September-October, 1993), PP. 21-33, ISSN 1529-9074

Microwave Theory and Techniques
, Vol. 35, No. 10, (1987), pp. 925-928, ISSN 0018-
9480

Behaviour of Electromagnetic Waves in Different Media and Structures

120
Nelson, S.O & Bartley, P. G. (1952). Open-ended coaxial line permittivity measurements on
pulverized materials.
IEEE Transactions on Instrumentation and Measurement, Vol. 47,
No.1, (Jan., 1998), pp. 133-137, ISSN 0018-9456
Nicolson, A. M. & Ross, G. (1952). Measurement of intrinsic properties of Materials by time
domain techniques.
IEEE Trans on Instrument & Measurement, Vol. IM-19, No. 4,
(November 1970), pp. 377-382, ISSN 0018-9456
Nyshadham, A.; Sibbaldcl, C. L. & Stuchly, S. S. (1963). Permittivity measurements using
open-ended sensors and reference liquid calibration an uncertainty analysis.
IEEE
Transactions on Microwave Theory and Techniques
, Vol. 40, No. 2, (Feb., 1992), pp. 305-
314, ISSN 0018-9480
Roberts, S. R. & Hippel, A. Von. (1930). A new method for measuring dielectric constant and
loss in the range of centimeter wave.
Journal of Applied Physics, Vol. 17, No. 7, (July,
1946), pp. 610-616, ISSN 0021-8979
Shen, L. C. (1961). A laboratory technique for measuring dielectric properties of core
samples at ultrahigh frequencies.
Society of Petroleum Engineers Journal, Vol. 25 No.
4, (April, 1985), pp. 502-514, ISSN 0197-7520
Shi, X. D. & Shen, L. C. (1958). Dielectric properties of reservoir rocks at very-high

7
Detection of Delamination in Wall Paintings by
Ground Penetrating Radar
Wanfu Wang
Dunhuang Academy
People's Republic of China
1. Introduction
Wall painting is an important part of cultural heritage. Generally speaking, painting on the
wall of buildings or rocks, and those on the wall of caves are called wall paintings. But
painting on the rock face is called rock painting. Wall painting on the building can be
approximately classified into drawing murals, relief frescoes, mosaic murals and etcetera
material paintings. Chinese ancient wall paintings can be generally distinguished according
to different drawing site, such as palace paintings, temple paintings, grotto frescoes, coffin
chamber murals, residential paintings and so on. Most of the paintings, including grotto
frescoes, palace paintings or temple paintings, have several hundred years, or even several
thousand years of history. During this time, under the influence of environmental factors
(light, temperature, humidity, wind, sand and so on), biotic factors (micro-organism, insect),
painting support walls and materials, architectural composition and human factor, wall
paintings have undergone various kinds of diseases and damage. The most common
painting diseases are delamination, flaking, disruption, smoking, pollution, deep-loss, paint-
losses, cracks-hatch, mechanical-damage and so on.
Delamination is the loss of adhesion between layers in the support (wall, rock mass or
others) and plaster stratigraphy, causing separation between plaster and suport.
Delamination can occur between plaster layers, plaster and support. Generally,
delamination causes painting surface crack and protrusion, even leads to painting losses
because of gravity force from wall painting itself.
Literally speaking, Tibet is a region with abundance of cultural relics. According to an
incomplete statistics, there are more than 2,000 ancient architectures all over the region,
among which 3 are included in the world heritage list, 27 are national key preservation
units, 55 are provincial level ones and 96 are city or county level ones. A primary survey

structured wall paintings in those sections suffer distortion and breach under the pressure
of vertical shearing stress, showing the unequal distribution of different interface stress
upon different materials. The load of the building and roofing on beams and purlines
transfers through those frameworks to walls. The wall painting plasters leaning against
walls are directly connected to roofing. During the drying process, different materials
displaying dissimilar contraction rates are easy to form gaps around the combining parts of
those materials, which, in combination with the transmission of forces, contributes to the
formation of the delamination.
Secondly, the cause comes to the layout of the architecture and the effects brought by both
natural and human activity vibration. The structures of ancient Tibetan architecture mainly

Detection of Delamination in Wall Paintings by Ground Penetrating Radar

123
belong to pillar mixed load carrying members. In those architectures, the top of the
architecture serves not only as the roofing of the floor but the platform for its upper floor.
Besides used as passages and aisles, the Buddhist ceremony was also held here. Therefore,
the vibration brought by the human activity is ranked among the causes for the formation of
wall painting crevices and delamination. Each year the renovation of roofing is carried out
regularly, during which a large number of people performing ramming generates strong
vibration when they are ramming a new layer of Argar. This is also a potential threat to the
supporting structure of roofing. In a word, the original layout of the structure leaves wall
paintings open to deterioration, the deterioration of delamination in particular, while the
human activity accelerates this process. The vibration produced by the human activity and
the architecture weight itself are the direct cause of the mural delamination. In addition, the
frequent earthquakes of different magnitudes also impose important effect upon the
architecture, resulting in its distortion and damage.
Thirdly, the roof leakage is anther cause of delamination, which in turn is caused by the
architecture distortion and the malfunction of the Argar layer.
Fourthly, the environment also contributes to the delamination. The surrounding


Behaviour of Electromagnetic Waves in Different Media and Structures

124
antenna at the nominal central frequency of 1.6 GHz, the antenna is gently attached upon a
piece of transparent parchment paper that has been covered on the vanishing surface of wall
paintings, the sampling parameters of time window is set at 4 ns and sampling frequency at
142 GHz, and the signal triggering mode is adopted as distance or time. Having been
processed by the band-pass filter and the filter of subtracting mean trace, the scope of
delamination disease is determined and the thickness of wall painting delamination is
estimated in the radar profile. Fig. 3. Typical plaster section of wall paintings in Potala Palace
2. Detection of delamination in replica plaster
Under ideal condition, the vertical resolution limit is up to 1/10 of electromagnetic
wavelength, but under poor circumstance, the resolution is only 1/3 of characteristic
wavelength. As to the geotechnical detection by ground penetrating radar, it is typically
considered 1/4 to 1/2 of impulsed electromagnetic wavelength as the vertical resolution to
select the appropriate radar antenna. When the characteristic wavelength of electromagnetic
waves is close to the thickness of cavity or delamination, the relative strong echo from the
top or the bottom of cavity in the radar image is easy to identify. Because of the application
of ultra-wideband radio technology, such kind of ground penetrating radar has higher
resolution
[4 ]- [7]
.
Replica of Tibetan wall painting plaster is made, and regular voids at different depth and
with varied size are set inside, then the forward modeling detection is carried out in order to
get appropriate parameters for acquisition of radar data, and to find effective filters for
signal processing.

35000
Amplitude /mV
Time /ns
1.6GHz Antenna
2.3GHz Antenna

Fig. 5. Time domain waveform of carrier-free pulse emitted by GPR antenna

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
0.0
0.2
0.4
0.6
0.8
1.0
Normalized Amplitude
Frequency /MHz
1.6GHz (FFT)
2.3GHz (FFT)
-20dB
2.3GHz (nominal)
-10dB

Fig. 6. Frequency domain spectrum of carrier-free pulse emitted by GPR antenna

Behaviour of Electromagnetic Waves in Different Media and Structures

126
According to the Federal Communications Commission (FCC), the band width of impulse
signal of electromagnetic wave is defined as the range of frequencies in which the signal's

(f
c
) is the peak amplitude at the central
frequency of f
c
.
When
P
dB
(f) is -10 dB, A(f)=10
-1/2
·A
max
(f)≈0.32 A
max
(f). As shown in Fig. 6, when the
normalized amplitude is 0.32, its normalized power is equal to -10 dB.
In Fig. 6, the signals in time domain have been transformed into frequency domain by Fast
Fourier Transform (FFT), the higher bound f
H
and lower bound f
L
of spectral band width of
the electromagnetic wave transmitted by 1.6 GHz antenna is 502 MHz and 2,203 MHz
respectively. As to 2.3 GHz antenna, the higher bound f
H
and lower bound f
L
is 772 MHz
and 3,321 MHz respectively. The relative band width

eff
, possess higher resolution. The simplified equation of the vertical resolution, ΔR,
of the ground penetrating radar can be worked out according to the Rayleigh criterion:

R
2B 2B
Δ= =
r
e
ff
e
ff
c
ε
ν

(3)
where: Δ
R is the vertical resolution of ground penetrating radar, also called as longitudinal
resolution, its unit is m.
υ is the propagating velocity of impulse electromagnetic wave in the
medium, with the unit of m/s.
B
eff
is the effective absolute band width in frequency
spectrum of received signals and its unit is Hz.
c is the traveling speed of electromagnetic
wave in vacuum, its value is about 3.00
×10
8

electromagnetic wave transmitting in the wall painting plaster is 6.62 cm. Then, the
maximum theoretical vertical resolution of λ/8 is about 8 mm.
2.3 Physical modeling experiment
In order to determine the appropriate acquisition parameter of RAMAC GPR, and to
obtain the method of digital signal processing (DSP), regular voids with different depth
and thickness are made in the loam plaster (Fig. 7). The ground penetrating radar
equipped with 1.6 GHz shielded antenna is used to carry out the lab test (Fig. 8, Fig. 9,
Fig. 10, Fig.11). A B C
Δh=5mm
Δh=23mm
Δh=18mm

Fig. 7. Schematic layout of rectangular voids in plaster replica for detection by GPR
In Fig. 7, the length of the delamination parts A, B, and C is 100 mm. Their buried depth h
and thickness Δh is 45 mm & 5 mm, 45 mm & 23 mm and 27 mm & mm respectively. The
relative dielectical constant of the loam plaster is about 1.74, so that the propagation velecity

Behaviour of Electromagnetic Waves in Different Media and Structures

128
of the electromagnetic wave in such medium is 2.27×10
8
m/s, namely 0.227 m/ns or 227
m/μs. It is faster than that of the electromagnetic wave in dry clay.

Distance/m
0

0.0

0.4

0.8

1.2

1.8

2.0
Two-way Travel Time/ns
2.0

1.6

1.2

0.8

0.4

0.0
Depth/m at ν=0.12m/ns
0.00

0.03

0.06


Time/ns
1.2
0.8

0.4

0
Time/ns
1.0
0.8

0.6

0
I.
f
s=141,820MHz II.
f
s=212,730MHz III.
f
s=425,459MHz

Fig. 10. FIR filtered GPR profiles at different sampling frequency


Δ=⋅ =⋅
t
t
t
hc c

(5)
where: Δh is the thickness of the delamination with the unit of m. c is the propagation
velocity of electromagnetic wave in the delaminated area and the value is about 3.00×10
8

m/s. Δt is the two-way travel time when the electromagnetic wave propagates in the
delaminated area and its unit is s.
N
t
is sample number of the lower surface of delamination
in typical trace.
N
0
is sample number of the upper surface of delamination. t is time depth of
the whole trace with the unit of s.
N is sample number of the whole trace.
In equation (5), t is 2.26×10
-9
s. According to the characteristic waveform of delamination B
in time domain, N
t
and N
0
is 179 and 155 respectively, and N is 320. The thickness of the

Depth/mm Thickness/mm
142 213 425
A 45 5 16.5 19.2 15.6
B 45 23 25.4 26.6 26.3
C 27 18 19.1 N/A N/A
Table 1. Interpreted thickness of delamination in comparison to nominal size
2.4 Analysis of typical traces
The typical wave forms (Fig. 11, Fig. 12) of delamination A with the thickness of 5 mm,
delamination B of 23 mm thick and background are extracted from the radar profile. The
comparison and analysis of transformed wave forms in time domain are presented in Fig. 13
and Fig. 14. 0.00.51.01.52.02.53.03.54.0
-35000
-30000
-25000
-20000
-15000
-10000
-5000
0
5000
10000
15000
20000
25000
30000
35000
Amplitude /mV


Fig. 12. Comparison of typical traces after high pass at 1.2 GHz in time domain

Detection of Delamination in Wall Paintings by Ground Penetrating Radar

131

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
0
5000
10000
15000
20000
25000
30000
35000
40000
Instantaneous Amplitude /mV
Time /ns
5 mm Delamination
23 mm Delamination
Background
0.70
1.150.94

Fig. 13. Comparison of instantaneous amplitude after Hilbert transform 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
-3.5

delamination beneath wall painting plaster. As the GPR raw data is processed by applying
filter of finite impulse response (FIR), delamination in wall paintings is characterized as
sudden amplification of negative amplitude in waveform, and the extent of delamination is
proportional to the time difference of two adjacent troughs, representing how serious the
deterioration is.