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8/9/2019 The Design of Hardware and Signal Processing for a Stepped Frequency Continuous Wave Ground Penetrating Rad…
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101
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-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005
Conductivity in mS/m
γ p
(! *819 !( ( (
( (
=?
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0.906 0.908 0.91 0.912 0.914 0.916 0.918-0.42
-0.415
-0.41
-0.405
-0.4
-0.395
-0.39
Real part of zp
I m a g i n e r y p a r t o f z p
(! *809 ( "
0 (
0 ' (( ,0@0 . ( ++
( ( () (
0 ( ,0B ' (
N0
( ) (
( (0
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"
=@
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100
101
102
1
1.5
2
2.5
Conductivity in mS/m
d p
( m )
100
101
102
10-1
100
101
Conductivity in mS/m
s p
( m )
d1=1m
d2=2.4m
100
101
102
-2
-1
0
1
2
Conductivity in mS/m
τ p
( r a d )
100
101
102
-0.15
-0.1
-0.05
0
0.05
Conductivity in mS/m
γ p
(! *849 !( ( (
( (
=%
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0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95-0.85
-0.8
-0.75
-0.7
-0.65
-0.6
-0.55
-0.5
-0.45
-0.4
-0.35
Real part of zp
I m a g i n e r y p a r t o f z p
(! *8?9 ( "
A-
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100
101
102
10-6
10-4
10-2
100
Conductivity in mS/m
d p
e r r o r ( m )
0.01m0.02m0.03m0.06m0.1m
100
101
102
10-4
10-2
100
102
104
Conductivity in mS/m
s p
e r r o r ( m )
100
101
102
10-6
10-4
10-2
100
102
Conductivity in mS/m
t p e r r o r ( r a
d )
100
101
102
10-5
100
Conductivity in mS/m
γ p
e r r o r
(! *8)@9 ( (
(
A$
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100
101
102
10-10
10-5
100
105
Conductivity in mS/m
d p
e r r o r ( m )
0.05m0.2m0.5m2m5m
100
101
102
10-5
100
105
Conductivity in mS/m
s p
e r r o r ( m )
100
101
102
10-6
10-4
10-2
100
102
Conductivity in mS/m
t p e r r o r ( r a
d )
100
101
102
10-8
10-6
10-4
10-2
100
Conductivity in mS/m
γ p
e r r o r
(! *8))9 ( (
(
A,
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%(! ! ! !
() ()
,0$= ( (
0 . ' # (5(
(
,0>0,0
10-1
100
101
102
10-10
10-5
100
105
Conductivity in mS/m
d p
e r r o r ( m )
-2-0.8
00.82
10-1
100
101
102
10-10
10-5
100
105
Conductivity in mS/m
s p
e r r o r ( m )
10-1
100
101
102
10-10
10-5
100
105
Conductivity in mS/m
t p e r r o r ( r a d )
10-1
100
101
102
10-10
10-5
100
Conductivity in mS/m
γ p
e r r o r
(! *8)/9 ( (
%(! !
() () )
,0$A
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( (
( (0
10-1 100 101 10210
-10
10-5
100
105
Conductivity in mS/m
d p
e r r o r ( m )
-0.001-0.003-0.01-0.03-0.1
10-1 100 101 10210
-10
10-5
100
105
Conductivity in mS/m
s p
e r r o r ( m )
10
-1
10
0
10
1
10
210
-10
10-5
100
105
Conductivity in mS/m
t p e r r o r ( r a d )
10
-1
10
0
10
1
10
210
-10
10-5
100
Conductivity in mS/m
γ p
e r r o r
(! *8)29 ( (
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' ( ( (1) 6 6
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*818/ -!%
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. ) ( ( (
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& ( ') . ( 1 )
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( :
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600 700 800 900 1000 1100 1200-34.5
-34
-33.5
-33
-32.5
Frequency in MHz
R e c i e v e d S i g n a l P o w e r ( d B m )
600 700 800 900 1000 1100 1200-4
-2
0
2
4
R e c i e v e d S i g n a l P h a s e ( r a d i a n s )
0 1 2 3 4 5 6 7-180
-160
-140
-120
-100
-80
-60
-40
-20
Depth in metres
R e c e i v e d p
o w e r i n d B m
(! *8)39 (5(
7
600 700 800 900 1000 1100 1200-62
-61
-60
-59
-58
Frequency in MHz
R e c i e v e d S i g n a l P o w e r ( d B m )
600 700 800 900 1000 1100 1200-4
-2
0
2
4
R e c i e v e d S i g n a l P h a s e ( r a d i a n s )
0 1 2 3 4 5 6 7-180
-160
-140
-120
-100
-80
-60
-40
-20
Depth in metres
R e c e i v e d p o w e r i n d B m
(! *8)19 (5(
7
B-
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600 700 800 900 1000 1100 1200-95
-90
-85
Frequency in MHz
R e c i e v e d S i g n a l P o w e r ( d B m )
600 700 800 900 1000 1100 1200-5
0
5
R e c i e v e d S i g n a l P h a s e ( r a d i a n s )
0 1 2 3 4 5 6 7-180
-160
-140
-120
-100
-80
-60
-40
-20
Depth in metres
R e c e i v e d p
o w e r i n d B m
(! *8)09 (5(
7
600 700 800 900 1000 1100 1200-126
-124
-122
-120
-118
-116
-114
-112
-110
Frequency in MHz
R e c i e v e d S i g n a l P o w e r ( d B m )
600 700 800 900 1000 1100 1200-4
-3
-2
-1
0
1
2
3
4
R e c i e v e d S i g n a l P h a s e ( r a d i a n s )
0 1 2 3 4 5 6 7-180
-160
-140
-120
-100
-80
-60
-40
-20
Depth in metres
R e c e i v e d p o w e r i n d B m
(! *8)49 (5(
7 "0
B$
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600 700 800 900 1000 1100 1200-170
-160
-150
-140
-130
Frequency in MHz
R e c i e v e d S i g n a l P o w e r ( d B m )
600 700 800 900 1000 1100 1200-4
-2
0
2
4
R e c i e v e d S i g n a l P h a s e ( r a d
i a n s )
0 1 2 3 4 5 6 7-180
-160
-140
-120
-100
-80
-60
-40
-20
Depth in metres
R e c e
i v e d p o w e r i n d B m
(! *8)?9 (5(
7
(
. ((
66 0 . 6
( 0 ) ,0$B 6 ,0$@
++ ( ' ( ( (
) ' . ' 6
0 (5() (
5() 7 O (
' ( ( 7 ++ 6
( ( ( '
' ( 0
,0,- ,0,$ ( / (
++ ( ' ( 6 ( (
0 ( ( N
" (5(0
( ) ( (
B,
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100
101
102
1
1.5
2
2.5
3
3.5
4
Conductivity in mS/m
d p
( m )
100
101
102
10-2
100
102
Conductivity in mS/m
s p
( m )
100
101
102
-3
-2
-1
0
1
2
3
4
Conductivity in mS/m
τ p
( r a d )
d1=1.6m
d2=2.1m
d2=2.2m
100
101
102
-0.4
-0.3
-0.2
-0.1
0
0.1
Conductivity in mS/m
γ p
(! *8*@9 1 (
B=
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100
101
102
10-5
100
Conductivity in mS/m
d p
( m )
d1=1.6m
d2=2.1m
d2=2.2m
100
101
102
10-4
10-2
100
102
Conductivity in mS/m
s p
( m )
100
101
102
10-6
10-4
10-2
100
102
Conductivity in mS/m
τ p
( r a d )
100
101
102
10-6
10-4
10-2
100
Conductivity in mS/m
γ p
(! *8*)9 + ( (
BA
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100
101
102
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
R e l a t i v e e n e r g y i n s i n g u l a r v a l u e s
Number of principle eigenvectors, P
σm=1 mS/mσ
m=5 mS/m
σm
=10 mS/m
σm
=20 mS/m
σm
=30 mS/m
σm
=40 mS/m
(! *8**9 (5(
' 1( 4 &1 &0
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0 7 )
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,0,= 6 ,0,? ( (( 6
( ) ( (
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0 *
0 ( 6
BB
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( ( (
0 ( ( (
( (0
600 700 800 900 1000 1100 1200
-34
-32
-30
Frequency in MHz
R e c i e v e d S i g n a l P o w e r ( d B m )
600 700 800 900 1000 1100 1200
-5
0
5
R
e c i e v e d S i g n a l P h a s e ( r a d i a n s )
0 1 2 3 4 5 6 7-180
-160
-140
-120
-100
-80
-60
-40
-20
Depth in metres
R e c e i v e d p o w e r i n d B m
(! *8*/9
7
,0,@ ( (
( (0
,0,% ) (0
*808/ (
& &1 &) ) ( 4)
( 10 1(
( ++ ( 7 O )
( ( (
( ((
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600 700 800 900 1000 1100 1200-50
-48
-46
-44
-42
-40
-38-36
-34
Frequency in MHz
R e c i e v e d S i g n a l P o w e r ( d
B m )
600 700 800 900 1000 1100 1200-4
-3
-2
-1
0
1
23
4
R e c i e v e d S i g n a l P h a s e ( r a d
i a n s )
0 1 2 3 4 5 6 7-180
-160
-140
-120
-100
-80
-60
-40
-20
Depth in metres
R e c e i v e d p o w e r i n d B m
(! *8*29
7
B?
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600 700 800 900 1000 1100 1200-80
-60
-40
Frequency in MHz
R e c i e v e d S i g n a l P o w e r ( d
B m )
600 700 800 900 1000 1100 1200-5
0
5
R e c i e v e d S i g n a l P h a s e ( r a d
i a n s )
0 1 2 3 4 5 6 7-180
-160
-140
-120
-100
-80
-60
-40
-20
Depth in metres
R e c e i v e d p o w e r i n d B m
(! *8*39
7
B@
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600 700 800 900 1000 1100 1200-150
-100
-50
Frequency in MHz
R e c i e v e d S i g n a l P o w e r ( d
B m )
600 700 800 900 1000 1100 1200-5
0
5
R e c i e v e d S i g n a l P h a s e ( r a d
i a n s )
0 1 2 3 4 5 6 7-180
-160
-140
-120
-100
-80
-60
-40
-20
Depth in metres
R e c e i v e d p o w e r i n d B m
(! *8*19
7
B%
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600 700 800 900 1000 1100 1200-180
-160
-140
-120
-100
Frequency in MHz
R e c i e v e d S i g n a l P o w e r ( d
B m )
600 700 800 900 1000 1100 1200-4
-2
0
2
4
R e c i e v e d S i g n a l P h a s e ( r a d
i a n s )
0 1 2 3 4 5 6 7-180
-160
-140
-120
-100
-80
-60
-40
-20
Depth in metres
R e c e i v e d p o w e r i n d B m
(! *8*09
7
>-
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10-2
100
1
1.5
2
2.5
3
3.5
4
Imag(εr)
d p
( m )
10-2
100
10-2
100
102
Imag(εr)
s p
( m )
10-2
100
-3
-2
-1
0
1
2
3
Imag(εr)
τ p
( r a d )
d1=1.6m
d2=2.1m
d2=2.2m
10-2
100
-0.4
-0.3
-0.2
-0.1
0
0.1
Imag(εr)
γ p
(! *8*49 1 ( (
(
>$
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100
101
102
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
R e l a t i v e e n e r g y i n s i n g u l a r v a l u e s
Number of principle eigenvectors, P
Im(εr)=-0.01
Im(εr)=-0.1
Im(εr)=-0.2
Im(εr)=-0.4
Im(εr)=-0.6
Im(εr)=-0.8
(! *8*?9
66 0 ,0,= 6 ,0,?
(
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,0,% ) # &?
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T X
R X
0.3m
Antennas
Pipe
x
z
(! *8/@9 +( ' ((
-0.12
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Azimuth position in meters
D e p t h i n m e t e r s
0.2 0.4 0.6 0.8 1 1.2
0
0.5
1
1.5
2
2.5
3
3.5
4
(! *8/)9 ( ( (
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) '/
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200 300 400 500 600 700 800 900 1000 1100 1200-60
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0.01
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0.2
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0.5
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