Three-Dimensional FDTD Modeling of a Ground-Penetrating Rada

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING,VOL.38,NO.4,JULY20001513 Three-Dimensional FDTD Modeling of a

Ground-Penetrating Radar

Levent Gürel,Senior Member,IEEE,and U?g ur O?g uz

Abstract—The finite-difference time-domain(FDTD)method

is used to simulate three-dimensional(3-D)geometries of realistic

ground-penetrating radar(GPR)scenarios.The radar unit is mod-

eled with two transmitters and a receiver in order to cancel the

direct signals emitted by the two transmitters at the receiver.The

transmitting and receiving antennas are allowed to have arbitrary

polarizations.Single or multiple dielectric and conducting buried

targets are simulated.The buried objects are modeled as rectan-

gular prisms and cylindrical disks.Perfectly-matched layer ab-

sorbing boundary conditions are adapted and used to terminate the

FDTD computational domain,which contains a layered medium

due to the ground–air interface.

Index Terms—Finite-difference time-domain method(FDTD),

ground-penetrating radar(GPR),perfectly matched layer,sub-

surface scattering.

I.I NTRODUCTION

T HE APPARENT widespread interest in ground-pene-

trating radar(GPR)systems[1]–[3]have also created

the need for a better understanding of subsurface-scattering

mechanisms.Numerical modeling and simulation of GPR

systems have been recognized as the preferred means for

obtaining this understanding.A variety of differential equation

and integral equation-based numerical modeling techniques

have been developed for this purpose.Among these techniques,

the finite difference time domain(FDTD)method[4]has been

distinctively popular[5]–[13]due to its versatility in solving

problems involving arbitrarily complicated inhomogeneities.In

this paper,realistic three-dimensional(3-D)GPR scenarios are

simulated using the FDTD method and the perfectly-matched

layer(PML)[14]–[19]absorbing boundary conditions.

The geometry of the simulated problem is shown in Fig.1.

The ground-air interface lies at a constant-

1514IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING,VOL.38,NO.4,JULY

2000

(a)

(b)

Fig.2.(a)Transmitter-receiver (TR)and (b)transmitter-receiver-transmitter

(TRT)configurations of the radar unit and the definition of the direct (D ,D

),reflected (G ,G ),and scattered (S ,S )signals.

4)As an alternative to the time windowing,if

the

signal can be magnified to a level that allows comfortable

detection even in the presence of

the

is located exactly in the middle of two identical transmitters

(out of phase.In this configuration,the two

direct

signals

or

(2)

,component of the electric

field,depending on the choice of polarization.Thus,discrete

values

GüREL AND O?GUZ:MODELING OF A GROUND-PENETRATING RADAR1515 of time,this is called an A-scan,and the resulting data is de-

noted

as

direction,the collected B-scan data is

denoted

as

(6)

denotes the data collected on a rectangular grid of discrete points

on a

constant

1GHz for the pulse in(1).Sampling intervals in space

and time are selected

as 4.5ps,re-

spectively,which satisfies the Courant stability condition.The

transmitting and receiving antennas of the radar units shown in

Fig.3are separated by two cells(5mm).The computer used in

these simulations was a Digital AlphaServer4100.

A.Conducting Prism

The four GPR models are first tested on a simple scenario.

A perfectly conducting prism of

2121cells

(5.25

4

cm

)a t a f i x e d e l e v a t i o n o f t e n c e l l s(2.5c m)o v e r t h e

g r o u n d

()a n d s t o p s e v e r y

2

7

5

a n

d).O n t h e o t h e r h a n d,G P R

r e s p o n d o n l y w h e n t h e r a d a r u n i t i s v

p r o d u c i n g a l o c a l i z e d r e s p o n s e.T h e

t u d e a n d t h e r a n g e o f t h e f o u r G P R m o

i z a t i o n o f t h e a n t e n n a s a n d c a n b e u s e

i n a p o l a r i z a t i o n-e n r i c h e d G P R s y s t

F i g.5(a)–(d)s h o w s t h e r e s u l t s o b t

m o d e l s w h e n t h e r a d a r u n i t t r a v e l s o n

t e r e d w i t h r e s p e c t t o t h e b u r i e d p r i

s

l i n e).T h e s e r e s u l t s d i s p l a y s i

c o m p a r e

d t o F i g s.4(a)–(d),n a m

e l y,

r e m a r k a b l y w e a k e r s i g n a l s,w h e r e a s

c o n s i

d

e r a b l y l a r g e r s i g n a l s.T h e d e

b y G P R1a n d G P R3i s d u e t o t h e s y m m e

r a t i o n.W h e n t h e s e t w o G P R m o d e l s t r

c e n t e r e

d w i t h r

e s p e c t t o t h e b u r i e d p

t h e r a d a r u n i t c o i n c i d e s w i t h t h e s y m

o b j e c t.T h a t i s,t h e s c a t t e r e r a l s o b e

s p e c t t o t h e r e c e i v e r.T h e r e f o r e,t h e

t w o t r a n s m i t t e r s a n d s c a t t e r e d b y t h

o u t a t t h e r e c e i v e r l o c a t i o n.I f t h e s

e v e n n u m b e r o

f c e l l s i n t h e

1516IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING,VOL.38,NO.4,JULY2000

(a)(b)

(c)(d)

Fig.5.Simulation results of a perfectly conducting rectangular prism buried

five cells(1.25cm)under the ground.The ground model has a relative

permittivity of =2.The simulations are carried out using(a)GPR1,

(b)GPR2,(c)GPR3,and(d)GPR4.The radar unit travels on a linear path that

is almost centered with respect to the buried object.

there is no exact symmetry in the problem.However,except for

a one-cell-wide portion of it,the conducting prism is symmet-

rical with respect to the symmetry plane.Therefore,the signals

reflecting from those symmetrical parts cancel each other and

produce a weak scattered signal at the receiver.

The differences between Figs.4and5demonstrate that the

choice of the path of measurement has a significant effect on the

results.In order to further illustrate this effect and the symme-

tries in the problem,the radar units are moved on a two-dimen-

sional grid,as opposed to a linear path.For each discrete radar

position on the two-dimensional(2-D)grid,an A-scan measure-

ment is performed,and the energy of the received A-scan signal

is computed as

(8)

where

-polarized and

-polarized configuration contain both GPR1and GPR2results,

and the

and constant-

direction or GPR4units moving in the

and

GüREL AND O ?GUZ:MODELING OF A GROUND-PENETRATING RADAR

1517

(a)

(b)

Fig.7.Energy diagrams measured by (a)x -polarized and (b)z -polarized TRT radar units moving on a 2-D grid.A perfectly conducting disk is buried five cells (1.25cm)under the ground with a relative permittivity of =2.

(e.g.,),the receiver collects an ignorable amount of energy everywhere on the path.On the other hand,GPR1pro-duces localized responses on a linear path,but these responses contain detectable levels of energy even if the path itself is away from the target

(e.g.,).

Each configuration with a different polarization has an advan-tage to it,and all of the results mentioned previously lead to the conclusion that multiple radar units with polarization persity and multidimensional scans can facilitate the detection of the buried targets.

B.Conducting Disk

The 2-D scan of the previous section is repeated for a per-fectly conducting disk with a radius of 10.5cells (2.625cm)and a height of 16cells (4cm)buried five cells (1.25cm)under the ground.The relative permittivity of the ground is again selected

as

21

5.25)is buried four cells (1cm)under the ground-air inter-face,and the radar unit travels on

the

and linear path.The length of the horizontal axes of the plots in Fig.8are not chosen equal for the purpose of presenting all of the significant (nonzero)features of the data in the minimum amount of space.In Fig.8(a),the results of the simulations of GPR1with a ground model

of 2are given.The relative permittiv-ities of the targets are 1,4,8,and 16.In this figure,the largest reflections are obtained from the dielectric prism with relative permittivity of 16,and the smallest reflection is obtained from the dielectric prism with relative permittivity of 1.Therefore,Fig.8demonstrates that as the contrast between the ground and the target increases,scattered fields observed at the receiver get larger in amplitude.Each simulation result given in Fig.8displays two separate major reflections from the buried target,originated by the upper and lower faces of the dielectric prism.Fig.8(a)demonstrates that if the permittivity of the target is larger than the permit-tivity of the ground,the second reflected signal is stronger than the first.That is,the reflection from the lower face of the target is larger than that from the upper face.However,if the ground is denser than the target,then the reflection from the upper face of the target is stronger.This is due to the larger reflections encoun-tered while passing from a denser medium to a rarer one,mainly caused by total internal reflections.As the buried object be-comes denser to make the permittivity contrast larger,stronger total internal reflections cause multiple reflections,which be-come visible in Fig.8(a)as late-time effects following the two major reflections.Fig.8(b)and (c),where the relative permittivities of the ground models are selected as 4and 8,respectively,lead to similar observations,namely,the maximum scattered fields are due to the largest target-background permittivity contrasts,and the dominant scattered waveforms from targets denser than the background are due to the reflections from the bottom of the target.In order to investigate the effects of a different polarization,the simulations of Fig.8(b)are repeated with a GPR2radar unit traveling on

the linear path.Fig.8(d)shows

that,even though the features of the waveforms are quite dif-ferent,the observations made previously concerning the depen-dence of the magnitude of the waveforms on the permittivity contrast and dominant latter reflections due to the targets denser than the background are also valid for GPR2.

1518IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING,VOL.38,NO.4,JULY2000

(a)

(b)

(c)

(d)

Fig.8.B-scan results of a dielectric rectangular prism buried four cells(1cm)under the ground.The results are obtained with(a)GPR1and relative permittivities =2and =1,4,8,16,(b)GPR1and relative permittivities =4and =1,2,8,16,(c)GPR1and relative permittivities = 8and =1,2,4,16,and(d)GPR2and relative permittivities =4and =1,2,8,16.GPR1travels on the y=061and z=101linear path,and GPR2travels on a linear path that is almost centered(y=0)with respect to the buried prism.

D.Multiple Targets

The previous sections demonstrate that GPR1and GPR3pro-

duce localized responses to nearby targets,whereas GPR2and

GPR4respond to distant targets as well.The sensitivities of

GPR1and GPR3to nearby targets can be beneficial for the de-

tection of two closely buried objects.In order to investigate this

situation,Fig.9presents the simulation results of a scenario,

where two conducting prisms of2116cells(5.25

4cm

GüREL AND O ?GUZ:MODELING OF A GROUND-PENETRATING RADAR

1519

(a)

(b)

(c)(d)

Fig.9.Simulation results of two perfectly conducting rectangular prisms buried five cells (1.25cm)under the ground and separated by 20cells (5cm).The ground has a relative permittivity of =4.The simulations are carried out using (a)GPR1,(b)GPR2,(c)GPR3,and (d)GPR4.The path of the radar unit is offset by ten cells (y =101)from the symmetry plane (y =0)of the buried objects.All B-scan results and all energy plots are normalized with respect to their maxima in

(a).

(a)(b)

Fig.10.Simulation results of two objects buried five cells (1.25cm)under the ground and separated by 20cells (5cm).The results are obtained with GPR1.The ground has a relative permittivity of =4.The objects are (a)a cavity (air bubble)with =1and a dielectric object with =8,and (b)a cavity and a perfectly conducting object.All plots are independently normalized with respect to their own maxima.

targets are buried 20cells (5cm)apart and five cells (1.25cm)

under the ground,which has a relative permittivity

of

4.Fig.10(a)depicts that GPR1clearly detects the two objects,

even though the energy peak produced by the cavity is much

smaller than that of Fig.9(a)for a conducting object,and the

energy produced by the dielectric object is even smaller.It is

also observed that the waveforms reflected from the cavity

and the dielectric object have their own characteristics,as

displayed in Fig.8.In the second simulation,the dielectric

prism is replaced by a conducting prism.Fig.10(b)shows that

the objects are again visible,although the cavity is a weaker

scatterer compared to the conducting object.Note that the same cavity is the stronger scatterer in Fig.10(a)compared to the dielectric object.IV .C ONCLUDING R EMARKS The power and flexibility of the FDTD method are combined with the accuracy of the PML absorbing boundary conditions to simulate realistic GPR scenarios.Three-dimensional (3-D)ge-ometries containing models of radar units,buried objects,and surrounding environments are simulated.In this paper,the radar unit is modeled as a TRT configuration,and the transmitting and

1520IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING,VOL.38,NO.4,JULY 2000receiving dipole antennas are allowed to have different polariza-

tions.The buried objects are modeled as rectangular prisms and

cylindrical disks with arbitrary conductivities and permittivities.

Multiple-target scenarios are also simulated.

Using the simulation results,the advantages and the disadvan-

tages of both the TRT configuration and various polarizations

of the dipole antennas are demonstrated.The major advantage

of the TRT configuration is the total cancellation of the direct

signals due to the direct coupling from the transmitters to the re-

ceiver and the partial cancellation of the reflected signals from

the ground-air interface.Cancellation of these signals greatly

facilitates the detection of the buried objects.GPR models with

different antenna polarizations are shown to possess specific ad-

vantages,leading to the conclusion that polarization-enriched

GPR systems should be preferred for better detection perfor-

mance.

The simulations reported in this paper are carried out using

a lossless homogeneous medium of arbitrary permittivity to

model the ground.The performance of GPR systems with

different configurations and polarizations over lossy and

inhomogeneous ground models,including surface roughness,

are also under study [20].

A PPENDIX

PML A BSORBING B OUNDARY C ONDITION FOR L AYERED

M EDIA

The PML absorbing boundary condition is a nonphysical ma-

terial boundary surrounding the computational domain.For a

lossless and homogeneous medium,the matching conditions de-

fined in the literature,e.g.,[14]–[19],ensure a reflectionless

transition to the PML region regardless of frequency and angle

of incidence.However,subsurface-scattering problems involve

layered media.For example,GPR simulations involve at least

two layers (two half-spaces),one of which is the air

(),and

the other of which is the ground

().The ground medium

can also be layered in itself.

Referring to the simple example depicted in Fig.11,the

matching condition for air is given

by

(10)

At the air-ground interface (ab in Fig.11),the FDTD equa-

tions yield an effective permittivity

of

plane of the PML region (bc in

Fig.11),the conductivity values

(,

that (13)

where

and from (9)and (10)into (13),we

obtain

GüREL AND O?GUZ:MODELING OF A GROUND-PENETRATING RADAR1521

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unpublished.

Levent Gürel(S’87–M’92–SM’97)was born in

Izmir,Turkey,in1964.He received the B.Sc.degree

from the Middle East Technical University(METU),

Ankara,Turkey,in1986,and the M.S.and Ph.D.

degrees from the University of Illinois,Urbana

(UIUC),in1988and1991,respectively,all in

electrical engineering.

He joined the Thomas J.Watson Research Center,

IBM Corporation,Yorktown Heights,New York,in

1991,where he worked as a Research Staff Member

on the electromagnetic compatibility(EMC)prob-lems related to electronic packaging,the use of microwave processes in the manufacturing and testing of electronic circuits,and the development of fast solvers for interconnect modeling.He then became an Associate Professor with the Institute of Higher Education,Ankara,in1993.Since1994,he has been a Faculty Member,Department of Electrical and Electronics Engineering, Bilkent University,Ankara.He was a Visiting Associate Professor at the Center for Computational Electromagnetics(CCEM),UIUC,for one semester in1997.His research interests include the development of fast algorithms for computational electromagnetics(CEM)and the application thereof to scattering and radiation problems involving large and complicated scatterers, antennas and radars,frequency-selective surfaces,and high-speed electronic circuits.He is also interested in the theoretical and computational aspects of electromagnetic compatibility and interference analyses.Ground penetrating radars and other subsurface scattering applications are also among his current research interests.

Dr.Gurel is currently serving as the Chairman of the AP/MTT/ED Chapters of the IEEE Turkey

Section.

U?g ur O?g uz was born in Ankara,Turkey,in1973.He

received the B.Sc.and M.Sc.degrees,both in elec-

trical engineering,from Bilkent University,Ankara,

Turkey,in1994and1997,respectively.

From August1997to October1998,he served in

the Turkish Army as a database manager and system

administrator.Since November1998,he has been a

Research Engineer with the Department of Electrical

and Electronics Engineering,Bilkent University.His

research interests include time-domain methods in

computational electromagnetics and their applica-tions to geophysical problems.

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