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

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