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

Subsurface Imaging with Ground

Penetrating Radar

Carey M. Rappaport CenSSIS

Dept. Elect. and Comp. EngineeringNortheastern University

April 2011

© Carey Rappaport 2011

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

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

2E + k2E=0

k = [00 ’(1 - j tan)] = - j

For time harmonic wave, the Helmholtz Equation remains:

= conductivity (S/m), ranging from ~ 0 to 107

But the dispersion relation is modified by :

tan = / ( ’0)

With Loss Tangent defined by:

00 '

1'

jjk

Slightly lossy medium

1' 0

Very lossy medium 1' 0

'2/

2/'/

0

0

c/'

' 0

2/

v /, 2 ,Velocity

Impedance00 '1

1

'=

j

Propagation (Wave) Number

/2depthskin

Electromagnetic Waves in Lossy Media

00 '21

'

jSlightly lossy

medium

2

(1 j)Very lossy medium

'

tan10

j

ftjxfjfj eetxE 2)]()([),(

Frequency f (1 MHz – 10 GHz)

Dielectric constant ’ (1 – 25)

Electrical conductivity (0.0001— 1)

Wave Number, k (meters-1)

Propagation in Soil is Frequency Dependent

Exact derivation of Wave Numbers in Lossy Media

xx E

z

E 22

2

zyx EEEUUkz

Uor ,or ,,02

2

2

tan1''

2

2

000

22 jc

jk

Starting from scalar Helmholtz Eqn.

where the complex wave number is:

'2

222

c

02

2

2

c

Separate into real and imaginary components (k = – j )

21

2

0

1'

12

'

c

21

2

0

1'

12

'

c

Solve for the quadratic equations for and

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 additionWhen 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).

Decibel Scale

Courtesy of B. Saleh, BU

Logarithms Without Calculators

• Log 10 = 1.0• Log 1 = 0• Log 2 ~ 0.3 • 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

Penetration Depth v. Frequency for Various

Dielectric MaterialsPenetration Depth d10

= Distance for the power to drop by a factor of 10 (—10 dB)

(19%) (26%)

Wavelengths for Various Dielectric Materials

Wavelength:

= 2/

Fields for Different Soil Types

0 5 10 15 20-1

0

1

0 5 10 15 20-1

0

1

0 5 10 15 20-1

0

1

0 5 10 15 20-1

0

1

0 5 10 15 20-1

0

1

Distance (cm)

Dry Sand

YPG

Saturated Sand

A.P. Hill

Bosnian (Alicia); 25% moisture

f =2.5 GHz

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.

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 DepthRadar 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 m -368

A P Hill 40.0 m -500

Wire on Flat Ground:Bosnian Soil 26% Moisture

E-field parallel to wire

H-field parallel to wire

Difference

Wire on Rough Ground:Bosnian Soil 26% Moisture

(Ez) no wire

E-field parallel to wire (Ez)

Modeling Soil Media for Electromagnetic Wave

Propagation

• Type of models• Simulated wave response

Summary of Dielectric Mixing Models Source: Kansas Geological

Survey, 2001Category 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.

Fourier Transform

dftfjfYty

dttfjtyfY

)2exp()()(

)2exp()()(

t f

t 1/t

• Short pulse in time transforms into broadband frequency signal

• Long pulse in time transforms into narrow frequency signal

Temporal Dispersion

• Pulses in time are composed of many frequencies (Fourier relationship)

• Most real material has frequency-dependent dielectric parameters

00 /' j• 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

)()()( ED )(*)()( tEttD

• Because of dispersion, multiplication in frequency domain becomes temporal convolution in the time domain

Dispersion of a Pulse 3 Fourier Components of Pulse at t0

• Each component travels at a different velocity (dispersion)

• Amplitude of component lessens in time (loss)

Same components at t>t0

Modeling Dispersion for Easy Transformation to Time

Domain

v

N

p p

p

j

A

100 1

'

N=2

Standard (2nd Order) Debye Model: simple form for complex permittivity, easily transformed to time domain differential equation

N

p p

p

j

A

12200

0

'

2

Lorentz Model: 2nd order when N = 1

01

100 1

'

jj

A

For 2202 / and A

[Cole-Cole Model is more accurate, not easily converted to time domain]

js

1

''' 00

1002222 '00

AjEjD pp 22

Lorentz

Conversion of Dispersion Models to Time Domain

110001010 1'11 jAjjjEjjD

Replace by D/E and multiply through by denominator

tj

Convert to time domain with

Et

EA

t

E

t

D

t

D

0011002

2

102

2

1 ''

Debye

tj

Convert to time domain with

EAt

E

t

ED

t

D

t

Dpp 1

2002

2

02

2

2

00''2'2

Modeling Dispersion for Easy Transformation to Time

Domain

Since Z-1 transforms to unit time delay, application to FDTD is simple

)()()(

)()(

ZEZZJ

ZEZD Av

)3()2()()(

)2

3()

2(

)()(

3210

1

ttEbttEbttEbtEb

ttJa

ttJ

tEtD Av

Z-Transform model keeps real permittivity constant, and

matches conductivity to measured values in terms of Z-1 [4 Zero Model]

’ = Constant, Z = e jt11

33

22

1102/1

1

Za

ZbZbZbbZ

Frequency (MHz)0 500 1000

3

4

5

6

7

8

9

Frequency (MHz)

’

0 500 100010

-4

10-3

10-2

10-1

RappaportDebyedata

2.5%

5%

10%

2.5%

5%

10%

Dielectric Constant and Conductivity for Puerto Rican Clay Loam (1.2 g/cc)

7 7.5 8 8.5 9 9.5

0

10

20

30

40

50

60

Log Frequency

(1/m

)

7 7.5 8 8.5 9 9.5-3

-2.5

-2

-1.5

-1

-0.5

0

Log Frequency

- (

1/m

)

RappaportDebyedata

2.5%

5%

10%

2.5%

5%

10%

Real and Imaginary Wave Number for Puerto Rican Clay Loam (1.2g/cc)

Wave Propagation Variation as a Function of Clay Loam Moisture

Transverse Position (cm)

De

pth

(cm

)

Transmitter Receiver

Non-Metallic Mine

60 80 100 120 140 160 180

40

30

20

10

0

-10

-20

-30

-40

Rough Surface Test Geometry

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Time (ps)

Re

lativ

e A

mp

litud

eNon-Metallic Mine Scattered Field 10

cm Deep - Smooth Surface

------- Air Dry Sand Non-Dispersive Loam 20% moistureDispersive Loam 20% moisture

++++++ooooooxxxxxx

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Time (ps)

Re

lativ

e A

mp

litud

eNon-Metallic Mine Scattered Field

(about 10 cm burial) - Rough Surface

------- Air Dry Sand Non-Dispersive Loam 20% moistureDispersive Loam 20% moisture

++++++ooooooxxxxxx

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-0.1

-0.05

0

0.05

0.1

Re

lativ

e A

mp

litud

e

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-0.04

-0.02

0

0.02

0.04

0.06

Time (ps)

Re

lativ

e A

mp

litud

e

Non-Dispersive Loam 20% moistureDispersive Loam 20% moisture

Non-Metallic Mine Scattered Field 10 cm depth a) Flat Surface, b) Rough Surface

80 cm

Square Target

Air

Soil d

11.28 cm

20 cm

60 cm

Circular Target

Air

Soil d

10 cm

20 cm

60 cm10 cm

80 cm

Sandy soil: s = 2.5, s = 0.01Target: m = 2.9, m = 0.004

Shape Determination of Buried Non-Metallic Targets, Multiple Single-Frequency

Observations

Different Buried Test Target Shapes

Heig

ht

(cm

)

Horizontal Position (cm)

-10 -5 0 5 10

-15

-10

-5

0Square

-20-10 -5 0 5 10

-15

-10

-5

0Circle

-20-10 -5 0 5 10

-15

-10

-5

0Diamond

-20

Blob

-10 -5 0 5 10

-15

-10

-5

0

-20-10 -5 0 5 10

-15

-10

-5

0Star

-20

Scattered Field - Real Part

500 MHz, depth = 5 cm


Heig

ht

(cm

)

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

Circle

-40 -20 0 20 40-60

-40

-20

0

20

Diamond

-40 -20 0 20 40-60

-40

-20

0

20

Square

-40 -20 0 20 40-60

-40

-20

0

20

Star

-40 -20 0 20 40-60

-40

-20

0

20Blob

-40 -20 0 20 40-60

-40

-20

0

20

Scattered Field - Real Part

1000 MHz, depth = 5 cm

-0.2

-0.1

0

0.1

0.2


Heig

ht

(cm

)

Square

-40 -20 0 20 40-60

-40

-20

0

20Circle

-40 -20 0 20 40-60

-40

-20

0

20Diamond

-40 -20 0 20 40-60

-40

-20

0

20

Star

-40 -20 0 20 40-60

-40

-20

0

20Blob

-40 -20 0 20 40-60

-40

-20

0

20


Inte

nsi

ty

-40 -20 0 20 400

0.01

0.02

0.03

0.04

0.05

1000 MHz, depth = 5cm

square

circle

diamond

star

blob

-40 -20 0 20 400.02

0.025

0.03

0.035

0.04

500 MHz, depth = 5cm

square

circle

diamond

star

blob

Surface Field - Magnitude


-0.08-0.06-0.04-0.0200.020.04

Circle, r = 5.64 cm

Sandy Soil = 2.5, = 0.01freq = 500 MHz depth = 5 cm-20 0 20 40

0

-20

-40

-60-40

20

-20 0 20 40

0

-20

-40

-60

7.5 x 13.3 cm20

-40 -20 0 20 40

0

-20

-40

-60

5 x 20 cm20

-40 -20 0 20 40

0

-20

-40

-60

2.5 x 40 cm

-40

20

-20 0 20 40

0

-20

-40

-60

13.3 x 7.5 cm20

-40 -20 0 20 40

0

-20

-40

-60

20 x 5 cm20

-40 -20 0 20 40

0

-20

-40

-60

40 x 2.5 cm

-40

20

-20 0 20 40

0-20

-40

-60

10 x 10 cm20

-40

Heig

ht

(cm

)

Scattered Field - Aspect Ratio Dependence

Distinguishing Shapes of 3D Buried Objects under Rough Surfaces:

Geometry

Point Source

Rough Surface

Mine

10 cm

4 cm

5 cm

10 cm

Soil

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

Target

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

(back view)

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

Targets

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

Targets

Soil Packing Affects Greatly Scattering: 3D FDFD with Short

Cylindrical Target

Relative Height 30

TNT in 26% moist Bosnian soil at 960 MHz


Non-Metallic Target

Soil

Air

-20 -15 -10 -5 0 5 10 15 20

Dep

th (

cm)

-5

0

5

10

15

20

25

30

35

Surface Scattering Clutter Increases with Frequency. Example: 4 GPR Freq., PRCL 10%

moisture, 1.4 g/cc

Mine scattered field: smooth surface

Scattered field: rough surface with mine

Scattered field: rough surface only

Mine scattered field: rough surface

Display Format for each of Four Frequencies

480 MHz


Dep

th (

cm)


-20 -10 0 10 20

0

10

20

30

-0.2

-0.1

0

0.1

0.2


Dep

th (

cm)


-20 -10 0 10 20

0

10

20

30

-0.2

-0.1

0

0.1

0.2


Dep

th (

cm)


-20 -10 0 10 20

0

10

20

30

-0.2

-0.1

0

0.1

0.2


Dep

th (

cm)


-20 -10 0 10 20

0

10

20

30

-0.2

-0.1

0

0.1

0.2

Am

plitu

de R

elative to Incid

ent

Am

plitu

de R

elative to Incid

ent

Am

plitu

de R

elative to Incid

ent

Am

plitu

de R

elative to Incid

ent

960 MHz


Dep

th (

cm)


-20 -10 0 10 20

0

10

20

30

-0.2

-0.1

0

0.1

0.2


Dep

th (

cm)


-20 -10 0 10 20

0

10

20

30

-0.2

-0.1

0

0.1

0.2


Dep

th (

cm)


-20 -10 0 10 20

0

10

20

30

-0.2

-0.1

0

0.1

0.2


Dep

th (

cm)


-20 -10 0 10 20

0

10

20

30

-0.2

-0.1

0

0.1

0.2A

mp

litud

e Relative to In

ciden

tA

mp

litud

e Relative to In

ciden

t

Am

plitu

de R

elative to Incid

ent

Am

plitu

de R

elative to Incid

ent

1920 MHz


Dep

th (

cm)


-20 -10 0 10 20

0

10

20

30

-0.1

-0.05

0

0.05

0.1


Dep

th (

cm)


-20 -10 0 10 20

0

10

20

30

-0.1

-0.05

0

0.05

0.1


Dep

th (

cm)


-20 -10 0 10 20

0

10

20

30

-0.1

-0.05

0

0.05

0.1


Dep

th (

cm)


-20 -10 0 10 20

0

10

20

30

-0.1

-0.05

0

0.05

0.1A

mp

litud

e Relative to In

ciden

tA

mp

litud

e Relative to In

ciden

t

Am

plitu

de R

elative to Incid

ent

Am

plitu

de R

elative to Incid

ent

3840 MHz


Dep

th (

cm)


-20 -10 0 10 20

0

10

20

30

-0.05

0

0.05


Dep

th (

cm)


-20 -10 0 10 20

0

10

20

30

-0.05

0

0.05


Dep

th (

cm)


-20 -10 0 10 20

0

10

20

30

-0.05

0

0.05


Dep

th (

cm)


-20 -10 0 10 20

0

10

20

30

-0.05

0

0.05

Am

plitu

de R

elative to Incid

ent

Am

plitu

de R

elative to Incid

ent

Am

plitu

de R

elative to Incid

ent

Am

plitu

de R

elative to Incid

ent

30o

Modulated Gaussian Pulse Plane Wave

AirAir

SoilSoil

Short Pulse GPR Interaction with Rough,

Dispersive Ground / Mine

From MineFacts, version 1.2, National Ground Intelligence Center

PMN-1A Non-Metallic AP Mine Geometry

Air

Soil

Snapshot of Total Time Domain E-Field (with Target)

Soil

Air

Snapshot of Background Time Domain E-Field

Soil

Air

Mine

Snapshot of Scattered Time Domain E-Field (Mine Only)

Rough Ground (cm)Rough Ground (cm)

Hei

gh

tH

eig

ht (c

m)

(cm

)

0-12

12

0

--

--24 24-48 48

Transmitter

Receiver

Effect of Rough Ground of Bistatic GPR Signals

0 100 200 300

-0.5

0

0.5

Time Step (Time Step (t = 20ps)t = 20ps)Sig

nal

Am

pli

tud

eS

ign

al A

mp

litu

de 0.5

-0.5

0.0

0.0 100 200 300

Mean Height variationMean Height variation hh= 6cm= 6cm

Correlation distance Correlation distance between surface between surface peakspeaks l lcc= 15cm= 15cm

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

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

Computational GeometryComputational Geometry

Z = 0

Z = 28cm

TransmitterTransmitter ReceiverReceiver24.5 cm

L = 294 cm

soilsoil minemine

Z = depth

Impulse Ground Impulse Ground Penetrating Radar Penetrating Radar

SpecificationsSpecifications

0 100 200 300

-4

-2

0

2

4

-4

-2

0

2

4

Time Step (Time Step (t=20ps)t=20ps)

Rel

ativ

e A

mp

litu

de

Rel

ativ

e A

mp

litu

de

Original Signal Averages Obscure Mine Signal

MineNo Mine

500 computed signals

Raw Signals

Cross-correlatewith reference

Shifting

Scaling

Shift and scale raw signals andtake average

Subtract shifted and scaled average from each raw signal

Compute different velocity in soil, shiftto line up the targetfeature

Physics-based Signal Processing flowchart

MineNo Mine

Ground Clutter Signal Removal

Realigning Signals to Presumed Mine Position

No Mine Mine

Average Mine Scattered Signals

h=3cm

h=1cm

lc=10cm lc=3cm

ROC Curves for Mismatched Target Depths

hh= 1cm = 1cm llcc= 10cm= 10cm

Trail depth=8.5cmTrail depth=8.5cm

test depth= 2.4cmtest depth= 2.4cm 3.6cm3.6cm 4.8cm4.8cm 6.1cm6.1cm 8.5cm8.5cm 9.8cm9.8cm

8.5

9.8

2.46.1

3.6

4.8

Water movement in a vertical column of a medium is described by the

advection-dispersion equation in the z-direction, as:

Where: = moisture contentz = depth [L] D = dispersion coefficient of water [L/t2]K = hydraulic conductivity [ L/t]t = time [t]

)())((

Kdz

d

dz

dD

dz

d

dt

d

Soil Moisture Change with Wetting

Moisture ProfileKsat = 0.2 cm/min

0.00

0.05

0.10

0.15

0.20

0.25

0 10 20 30 40 50 60Depth into Soil (cm)

Mo

istu

re C

on

ten

t (%

)

0.1 Minute

1 Minute

2 Minutes

3 Minutes

4 Minutes

Time Response Due to Saturating Soil Surface

Ground Surface

Source

Non-Metallic Target

Air

Soil with Varying Moisture Content

Testing geometry

-100 -80 -60 -40 -20 0 20 40 60 80 100

-100

-80

-60

-40

-20

0

20

40

60

Rough Surface with Buried Non Metallic Mine and Point Source

Geometry

Planar Ground Surface, 5% Uniform Moisture

Planar Ground Surface, 20% Uniform Moisture

Planar Ground Surface, 5 - 20% Moisture Profile

Rough Ground Surface, 5% Uniform Moisture

Rough Ground Surface, 20% Uniform Moisture

Rough Ground Surface, 5 - 20% Moisture Profile

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

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

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