1. Subsurface Imaging with Ground Penetrating Radar
Carey M. Rappaport
CenSSIS
Dept. Elect. and Comp. Engineering
Northeastern University
April 2011
© Carey Rappaport 2011

2. Propagation Characteristics in Real Soil
Concepts of dielectric constant, electrical conductivity
Velocity, attenuation, dispersion, reflection and refraction at interfaces
Moisture and density dependence
Nonmetallic target scattering in lossy media
Rough surface effects

3. Wave and Helmholtz Equation: Lossy Media (Soil, Water, Tissue)
The electric field for a wave traveling in linear, homogeneous, non-dispersive, and lossy medium is given by:
 2E -   E/  t -   2E/  t2 = 0
 = conductivity (S/m), ranging from ~ 0 to 107
For time harmonic wave, the Helmholtz Equation remains:
2E + k2E=0
But the dispersion relation is modified by :
k =   [00 ’(1 - j tan)] =  - j 
With Loss Tangent defined by:
tan =  / ( ’0)

4. Electromagnetic Waves in Lossy Media
Propagation (Wave) Number
Slightly lossy medium
Very lossy medium
Velocity
Impedance
Slightly lossy medium
Very lossy medium

5. Propagation in Soil is Frequency Dependent
Frequency f (1 MHz – 10 GHz)
Dielectric constant ’ (1 – 25)
Electrical conductivity  (0.0001— 1)
Wave Number, k (meters-1)

6. Exact derivation of Wave Numbers in Lossy Media
Starting from scalar Helmholtz Eqn.
where the complex wave number is:
Separate into real and imaginary components (k = b – j a)
Solve for the quadratic equations for b and a

7. Decibel Scale 1/10 power  10log10(1/10) = -10 dB.
The decibel (dB) is a logarithmic transformation of ratios of amplitudes or powers. A power ratio R corresponds to r = 10log10R (dB). An amplitude ratio R corresponds to 20log10R (dB).
1/10 power  10log10(1/10) = -10 dB.
1/2 power  10log10(1/2) = -3 dB.
1/10 amplitude  20log10(1/10) = -20 dB.
1/2 amplitude  20log10(1/2) = -6 dB.
An intensity attenuation by a factor exp(-a) is equivalent to -4.3a dB .
The decibel changes multiplication into addition
When a wave is transmitted through a cascade of two media resulting in intensity reduction by factors R1 and R2, the overall reduction is a factor R = R1R2.
The change in dB units is r = r1+ r2.
If the rate of attenuation of a medium is a dB/m, a distance z (m), corresponds to
attenuation of az (dB).
Courtesy of B. Saleh, BU

8. Logarithms Without Calculators
Log 5 = Log 10/2 = Log 10 – Log 2 = 0.7
Log 3 ~ Log 101/2 = ½ Log 10 = 0.5-
Log 4 = Log 22 = 2 Log 2 = 0.6
Log 6 = Log (2 X 3) = Log 2 + Log 3 = 0.8
Log 8 = Log 23 = 3 Log 2 = 0.9
Log10 e = 1/ Loge 10 = 1/2.302

9. Penetration Depth v. Frequency for Various Dielectric Materials
Penetration Depth d10
= Distance for the power to drop by a factor of 10 (—10 dB)
(19%) (26%)

10. Wavelengths for Various Dielectric Materials

11. Fields for Different Soil Types
f =2.5 GHz
Dry Sand
YPG
Saturated Sand
A.P. Hill
Bosnian (Alicia); 25% moisture

12. Exercise: Microwave Penetration in Soil
Determine the loss in dB for a wave at 300 GHz penetrating 1.0 mm into uniform soil and then reflecting back out for a) Yuma and b) AP Hill Soil
Hint: Extrapolate the loss curves from previous slide.

13. Extrapolated Penetration Depths at 300 GHz (Terahertz range)
Return signal power (in dB) from a radar source incident on a metallic target buried a depth D in lossy soil: -20 D/d
Soil Type
d=Penetration Depth
Radar Return (dB)
(D = 1 mm)
Yuma PG
55.7 cm
-0.036
Dry Sand
4.57 cm
-0.44
Wet Sand
0.31 cm
-6.5
Bosnian soil
54.3 mm
-368
A P Hill
40.0 mm
-500

14. Wire on Flat Ground: Bosnian Soil 26% Moisture
H-field parallel to wire
Difference
E-field parallel to wire

15. Wire on Rough Ground: Bosnian Soil 26% Moisture
(Ez) no wire
E-field parallel to wire (Ez)

16. Modeling Soil Media for Electromagnetic Wave Propagation
Type of models
Simulated wave response

17. Summary of Dielectric Mixing Models Source: Kansas Geological Survey, 2001
Category
Method
Types
Advantages
Disadvantages
References
Phenomeno-logical
Relate frequency dependent behavior to characteristic relaxation times.
Cole-Cole; Debye, Lorentz
- Component properties/geometry relationships unnecessary
- Dependent on frequency-specific parameters.
Powers, 1997;
Ulaby 1986; Wang, 1980.
Volumetric
Relate bulk dielectric properties of a mixture to the dielectric properties of its constituents.
ComplexRefractive Index (CRI); Arithmetic average; Harmonic average; Lichetenecker-Rother;
- Volumetric data relatively easy to obtain.
- Do not account for micro-geometry of components, -Do not account for electrochemical interaction between components.
Alharthi 1987; Birchak 1974; Knoll, 1996; Lange, 1983; Lichtenecker 1931; Roth 1990; Wharton 1980.
Empirical and Semi-empirical
Mathematical relationship between dielectric and other measurable properties.
Logarithmic; Polynomial.
- Easy to develop quantitative relationships, -Able to handle complex materials in models.
- No physical justification for the relationship, -Valid only for the specific data used to develop the relation may not be applicable to other data sets.
Dobson 1985; Olhoeft 1975; Topp 1980; Wang 1980.
Effective medium
Compute dielectric properties by successive substitutions.
Bruggeman-Hanai-Sen (BHS)
- Accurate for known geometries.
- Cumbersome to implement, - Must choose number of inputs, initial material, and order and shape of replacement material.
Sen 1981; Ulaby 1986.

18. Fourier Transform
Short pulse in time transforms into broadband frequency signal
Long pulse in time transforms into narrow frequency signal t
1/t t f

19. Temporal Dispersion
Pulses in time are composed of many frequencies (Fourier relationship)
Most real material has frequency-dependent dielectric parameters
If material has constant loss, it is strongly dispersive
Each frequency component travels at a different velocity and with a different decay rate
Amplitude of each frequency component lessens by a different amount with distance
Because of dispersion, multiplication in frequency domain becomes temporal convolution in the time domain

20. Dispersion of a Pulse 3 Fourier Components of Pulse at t0
Same components at t>t0
Each component travels at a different velocity (dispersion)
Amplitude of component lessens in time (loss)

21. Modeling Dispersion for Easy Transformation to Time Domain
Standard (2nd Order) Debye Model: simple form for complex permittivity, easily transformed to time domain differential equation v
N=2
For
Lorentz Model: 2nd order when N = 1
[Cole-Cole Model is more accurate, not easily converted to time domain]

22. Conversion of Dispersion Models to Time Domain
Replace e by D/E and multiply through by denominator
Convert to time domain with
Debye
Lorentz
Convert to time domain with

23. Modeling Dispersion for Easy Transformation to Time Domain
Z-Transform model keeps real permittivity constant, and matches conductivity to measured values in terms of Z-1 [4 Zero Model]
e’ = Constant,
, Z = e jwDt
Since Z-1 transforms to unit time delay, application to FDTD is simple

24. Dielectric Constant and Conductivity for Puerto Rican Clay Loam (1
Dielectric Constant and Conductivity for Puerto Rican Clay Loam (1.2 g/cc) -1 9 10
Rappaport
Debye
10% 8
data -2 7 5%
10% 10 6
2.5% ’  5% -3 5 10 4
2.5% -4 3 10
500
1000
500
1000
Frequency (MHz)
Frequency (MHz)

25. Real and Imaginary Wave Number for Puerto Rican Clay Loam (1.2g/cc)60
Rappaport
Debye
10% 50
data
-0.5
2.5% 5% 40 -1 5%
 (1/m) 30
- (1/m)
-1.5
2.5% 20 -2
10% 10
-2.5 -3 7
7.5 8
8.5 9
9.5 7
7.5 8
8.5 9
9.5
Log Frequency
Log Frequency

26. Wave Propagation Variation as a Function of Clay Loam Moisture

27. Rough Surface Test Geometry
Transmitter
Receiver
Non-Metallic Mine 60 80
100
120
140
160
180 40 30 20 10
-10
-20
-30
-40
Depth (cm)
Transverse Position (cm)

28. Non-Metallic Mine Scattered Field 10 cm Deep - Smooth Surface
0.4
Air
Dry Sand
Non-Dispersive Loam 20% moisture
Dispersive Loam 20% moisture
++++++
oooooo
xxxxxx
0.3
0.2
0.1
Relative Amplitude
-0.1
-0.2
-0.3
-0.4
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Time (ps)

29. Non-Metallic Mine Scattered Field (about 10 cm burial) - Rough Surface
0.4
Air
Dry Sand
Non-Dispersive Loam 20% moisture
Dispersive Loam 20% moisture
++++++
oooooo
xxxxxx
0.3
0.2
0.1
Relative Amplitude
-0.1
-0.2
-0.3
-0.4
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Time (ps)

30. Non-Metallic Mine Scattered Field 10 cm depth a) Flat Surface, b) Rough Surface
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
-0.1
-0.05
0.05
0.1
Relative Amplitude
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
-0.04
-0.02
0.02
0.04
0.06
Time (ps)
Relative Amplitude
Non-Dispersive Loam 20% moisture
Dispersive Loam 20% moisture

31. Shape Determination of Buried Non-Metallic Targets, Multiple Single-Frequency Observations
Sandy soil: es = 2.5, ss = 0.01
Target: em = 2.9, sm = 0.004
Circular Target
Square Target
Air
Air
20 cm
20 cm d d
Soil
Soil
11.28 cm
10 cm
10 cm
60 cm
60 cm
80 cm
80 cm

32. Different Buried Test Target Shapes
Height (cm)
Horizontal Position (cm)
-10 -5 5 10
-15
Square
-20
Circle
Diamond
Blob
Star

33. Scattered Field - Real Part
500 MHz,
depth = 5 cm
Horizontal Position (cm)
Height (cm)
-0.06
-0.04
-0.02
0.02
0.04
0.06
Circle
-40
-20 20 40
-60
Diamond
Square
Star
Blob

34. Scattered Field - Real Part
1000 MHz,
depth = 5 cm
-0.2
-0.1
0.1
0.2
Horizontal Position (cm)
Height (cm)
Square
-40
-20 20 40
-60
Circle
Diamond
Star
Blob

35. Surface Field - Magnitude
500 MHz, depth = 5cm
1000 MHz, depth = 5cm
0.04
0.05
square
0.04
circle
0.035
diamond
star
0.03
blob
square
circle
diamond
star
blob
Intensity
0.03
0.02
0.025
0.01
0.02
-40
-20 20 40
-40
-20 20 40
Horizontal Position (cm)

36. Scattered Field - Aspect Ratio Dependence
Circle, r = 5.64 cm
-20 20 40
-40
-60
10 x 10 cm
-20 20 40
-40
-60
-0.08
-0.06
-0.04
-0.02
0.02
0.04
Sandy Soil
e = 2.5, s = 0.01
freq = 500 MHz depth = 5 cm
-20 20 40
-40
-60
7.5 x 13.3 cm
-20 20 40
-40
-60
5 x 20 cm
-20 20 40
-40
-60
2.5 x 40 cm
Height (cm)
-20 20 40
-40
-60
13.3 x 7.5 cm
-20 20 40
-40
-60
20 x 5 cm
-20 20 40
-40
-60
40 x 2.5 cm
Horizontal Position (cm)

37. Distinguishing Shapes of 3D Buried Objects under Rough Surfaces: Geometry
Point Source
10 cm
Rough Surface
5 cm
Soil
Mine
4 cm
10 cm

38. Total Ex Field from an x-Directed Point Source, with a Buried Non-Metallic Square Target

39. Total Ex Field from x-Directed Point Source, with a Buried Non-Metallic Square Target (back view)

40. Comparison of Total Ex Field for Buried Non-Metallic Square and Circular Targets

41. Comparison of Scattered Ex Field for Buried Non-Metallic Square and Circular Targets

42. TNT in 26% moist Bosnian soil at 960 MHz
Soil Packing Affects Greatly Scattering: 3D FDFD with Short Cylindrical Target
Relative Height 30
TNT in 26% moist Bosnian soil at 960 MHz

43. Transverse Position (cm)
Surface Scattering Clutter Increases with Frequency. Example: 4 GPR Freq., PRCL 10% moisture, 1.4 g/cc -5
Air 5 10
Depth (cm)
Soil 15
Non-Metallic Target 20 25 30 35
-20
-15
-10 -5 5 10 15 20
Transverse Position (cm)

44. Display Format for each of Four Frequencies
Scattered field:
rough surface with mine
Mine scattered field:
smooth surface
Scattered field:
rough surface only
Mine scattered field:
rough surface

45. 480 MHz Mine scattered field: smooth surface
Transverse Position (cm)
Depth (cm)
Mine scattered field: smooth surface
-20
-10 10 20 30
-0.2
-0.1
0.1
0.2
Scattered field: rough surface with mine
Scattered field: rough surface only
Mine scattered field: rough surface
Amplitude Relative to Incident

46. 960 MHz Mine scattered field: smooth surface
Scattered field: rough surface with mine
0.2
0.2
0.1
0.1 10 10
Depth (cm)
Depth (cm)
Amplitude Relative to Incident
Amplitude Relative to Incident 20 20
-0.1
-0.1 30 30
-0.2
-0.2
-20
-10 10 20
-20
-10 10 20
Transverse Position (cm)
Transverse Position (cm)
Scattered field: rough surface only
Mine scattered field: rough surface
0.2
0.2
0.1
0.1 10 10
Depth (cm)
Depth (cm)
Amplitude Relative to Incident
Amplitude Relative to Incident 20 20
-0.1
-0.1 30 30
-0.2
-0.2
-20
-10 10 20
-20
-10 10 20
Transverse Position (cm)
Transverse Position (cm)

47. 1920 MHz Mine scattered field: smooth surface
Transverse Position (cm)
Depth (cm)
Mine scattered field: smooth surface
-20
-10 10 20 30
-0.1
-0.05
0.05
0.1
Scattered field: rough surface with mine
Scattered field: rough surface only
Mine scattered field: rough surface
Amplitude Relative to Incident

48. 3840 MHz Mine scattered field: smooth surface
Transverse Position (cm)
Depth (cm)
Mine scattered field: smooth surface
-20
-10 10 20 30
-0.05
0.05
Scattered field: rough surface with mine
Scattered field: rough surface only
Mine scattered field: rough surface
Amplitude Relative to Incident

49. Short Pulse GPR Interaction with Rough, Dispersive Ground / Mine
Modulated Gaussian Pulse Plane Wave
30o
Air
Soil

50. PMN-1A Non-Metallic AP Mine Geometry
From MineFacts, version 1.2, National Ground Intelligence Center

51. Snapshot of Total Time Domain E-Field (with Target)
Air
Soil

52. Snapshot of Background Time Domain E-Field
Soil
Air

53. Snapshot of Scattered Time Domain E-Field (Mine Only)
Soil
Air
Mine

54. Effect of Rough Ground of Bistatic GPR Signals
Transmitter
Receiver
Rough Ground (cm)
Height (cm)
-12 12 -
-24 24
-48 48
Mean Height variation h= 6cm
Correlation distance between surface peaks lc= 15cm
Time Step (t = 20ps)
Signal Amplitude
0.5
-0.5
0.0
100
200
300

55. Rough Ground Clutter Signal Characterization
Signals from rough ground vary considerably
Pulse shape depends on roughness and TR position
Peak depends on particular TR position
Overall amplitude varies
Monte Carlo simulation can model following relevant features
2D FDTD model
Real measured impulse GPR excitation and dispersive soil
500 different rough surface realizations

56. Monte Carlo Analysis Run many simulations Vary each run
Change geometry
Change signal
Compute statistics
Mean values
Standard deviations
Conclude “typical” behavior
Determine likelihood of given test
Set threshold and count number of occurrences of detection or false alarm --> ROC curve

57. Computational Geometry
Z = 0
Z = 28cm
Transmitter
Receiver
24.5 cm
L = 294 cm
soil
mine
Z = depth

58. Impulse Ground Penetrating Radar Specifications
Relative Amplitude
Time Step (t=20ps)

59. Original Signal Averages Obscure Mine Signal
No Mine
Mine
500 computed signals

60. Physics-based Signal Processing flowchart
Raw Signals
Compute different
velocity in soil, shift
to line up the target
feature
Shifting
Cross-correlate
with reference
Scaling
Shift and scale
raw signals and
take average
Subtract shifted and
scaled average from
each raw signal

61. Ground Clutter Signal Removal
Mine
No Mine

62. Realigning Signals to Presumed Mine Position
No Mine
Mine

63. Average Mine Scattered Signals
h=3cm
lc=10cm
lc=3cm
h=1cm

64. Hypothesis Testing Simply binary hypothesis Likelihood ratio test
H0 : absence of a target at certain depth
H1 : presence of a target at certain depth
Likelihood ratio test
R – individual trial signal,
mi – average of the interested signals,
Qi – inverse of the diagonal matrix of standard deviation of the interested signals
T – Threshold of detection

65. Receiver Operating Characteristic (ROC) Curve
Good detector
Inc .Performance
Random guess
Inc. Threshold

66. Receiver Operating Characteristic (ROC) for Model with Clutter
---- Realigned signals
---- Clutter removed signals
h= 1cm
lc= 10cm
depth=8.5cm

67. ROC Curves of Rough Surfaces
9.8
8.5
6.1
4.8
(h , lc , depth)
(1, 10, 4.8)cm
(1, 10, 6.1)cm
(1, 10, 8.5)cm
(1, 10, 9.8)cm
(3, 10, 8.5)cm
(3,10,8.5)

68. ROC Curves for Mismatched Target Depths
8.5
9.8
4.8
h= 1cm lc= 10cm
Trail depth=8.5cm
test depth= 2.4cm
3.6cm
4.8cm
6.1cm
8.5cm
9.8cm
2.4
6.1
3.6

69. Average of Aligned Background-Subtracted Signals
h= 1cm,lc= 10cm
depth=8.5cm
Multi-Bistatic
Multistatic
T R M
T R M
T R M
T R M
T R M TR M
T R M
T R M
T R M
T R M

70. Trans./Rec. Spatial Effects on Performance
h= 3cm,lc= 10cm
depth=8.5cm
Multi-Bistatic
Multistatic

71. Soil Moisture Change with Wetting
Water movement in a vertical column of a medium is described by the advection-dispersion equation in the z-direction, as:
Where:
 = moisture content
z = depth [L]
D = dispersion coefficient of water [L/t2]
K = hydraulic conductivity [ L/t]
t = time [t]

72. Time Response Due to Saturating Soil Surface

73. Rough Surface with Buried Non Metallic Mine and Point Source Geometry
Ground Surface
Source
Non-Metallic Target
Air
Soil with Varying Moisture Content
Testing geometry
-100
-80
-60
-40
-20 20 40 60 80
100

74. Planar Ground Surface, 5% Uniform Moisture

75. Planar Ground Surface, 20% Uniform Moisture

76. Planar Ground Surface, 5 - 20% Moisture Profile

77. Rough Ground Surface, 5% Uniform Moisture

78. Rough Ground Surface, 20% Uniform Moisture

79. Rough Ground Surface, 5 - 20% Moisture Profile

80. Summary
Realistic soil media complicates the sensing of subsurface objects
Loss affects penetration depth and makes surface clutter more dominant
Rough interfaces produce additive uncertain clutter and distort transmitted signals
Moisture variations cause huge propagation differences
Small contrast differences makes detection/ imaging more challenging
Shapes of underground dielectric object are hard to distinguish
Multistatic wideband GPR can provide much more information than monostatic