Three-Dimensional FDTD Modeling of a Ground-Penetrating Rada(2)

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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