International Journal on Communications Antenna and Propagation (IRECAP), Vol. xx, n. x June 2010
2D FDTD Simulation to Study Response of GPR Signals in Homogeneous and Inhomogeneous Mediums G.Alsharahi1, A.Faize2, A. Mint Mohamed Mostapha1, A.Driouach1
Abstract–The aims of this paper are the study of response signals of the Ground Penetrating Radar (GPR) and the development of one numerical code in order to improve the efficiency of the simulation and to compare the obtained results by different softwares (GprMax2D/3D and Reflexw).The first software is free while the other is not and it is expensive. The work presented here examines objects buried in homogenous and inhomogeneous dielectrics mediums using 400 MHz and 800Mhz antennas, in order to study the influence the mediums on the detected signals. Copyright © 2016 Praise Worthy PrizeS.r.l. - All rights reserved.
Keywords:2D FDTD, Simulation, Response, GPR signals
I.
Introduction
GPR uses the Geophysical method for the detection of targets buried in the medium. This work will present a study about GPR response signals in different mediums. The GPR response from a particular target or set of targets can be simulated by solving the Maxwell’s equations subject to the geometry of the problem and the initial condition. GPR has been used for the detection and the understanding of metallic and dielectric objects extensively [2-3]. To simulate the GPR signals of the proposed objects, the two used simulators (Reflexw and GprMax2d/3d )[4] require a number of parameters such as the frequency of the used antenna, the geometry of the basement and the dielectric permittivity, the magnetic permeability and the electric conductivity, intervening in simulation environments[5][6][7]. Some studies validating the intrinsic near-field antenna model ranging among the numerical evaluations of real field applications [1] are presented in this work. The modelling and simulation are performed to understand the factors affecting the GPR ability to detect, distinguish and identify the buried objects subsurface or concrete [9][18]. Furthemore, many modelling techniques are proposed by both GprMax2d/3d and Reflexw for the evaluation of GPR systems in terms of their ability to accurately identify the geometry of buried objects when working in critical conditions[8]. The characteristics of GPR are not well known and the proposed model is obtained by using some comparisons among simulations by various softwares on different medium as dry sand, clay wet, concrete and other medium. The simulations are made using FDTD model[10]12]13].
Manuscript received and revised xx 2010, accepted xx 2010
II.
Theoretical Background and Method II.1.
FDTD based modelling and simulation
The Maxwell’s equations in electromagnetic field describe the electric and magnetic fields arising from distributions of electric charges and currents and they can be used to describe all the electromagnetic field. The propagation of electromagnetic fields is-governed by the Maxwell equations[20], ∇xE r, t = −
∂ ∂t
B r, t = −μ
∇xH r, t = J r, t +
∂ ∂t
∂H (r,t)
(1a)
∂t
D r, t = σE(r, t) − ε
∂E (r,t) ∂t
B r, t = −μ. H(r, t) D r, t = −. E(r, t)
(1b) (1c) (1d)
Where B is the magnetic flux density in Vs/ m2, D is the electric flux density in As /m2, H is the magnetic field in A/m, E is the electric field in V/m, J is the electric current dentsity in A/m2 and is the electric load density in As/m3. This equation calculates the field 𝐸𝑦 𝑛+1 Based on Field 𝑛 +1/2
𝐻𝑥 . The same procedure is followed for the expression of each component of the electromagnetic field. This discretization of Maxwell's equations constitutes the basis of the Yee algorithm as shown in figure 1.
Copyright © 2010 Praise Worthy Prize S.r.l. - All rights reserved
G.Alsharahi, A.Faize, A. Mint Mohamed Mostapha , A.Driouach
The scattered field E s , the obstacle , is connected to the equivalent sources by the relation [16]. 𝐸𝑠 = Fig.1. Yee cell in Cartesian coordinates [21]
∇ ∇.𝐴 +𝐾 2 𝐴
𝐻𝑠 = ∇ ∧ 𝐴 +
∇ ∇.𝐹 +𝐾 2 𝐹
=
n−1/2 Hi,j,k
n
+
∆t E y i,j,k +1/2 − E y i,j,k −1/2 . μ i ,j,k ∆z
(2)
(8)
𝑗𝜔 𝜇 0
For the TE mode the 2D FDTD equations Becomes
n+1/2 Hx i,j,k
(7)
𝑗𝜔 𝜀 0
1 A(r ) 4
J (r )Gdv
1 f (r ) 4
M (r )Gdv
(9)
v
(10)
v
n+1
Ey i,j,k
1− =
1+
n
2i,j,k
. Ey i,j,k
σ i,j,k ∆t 2i,j,k ∆t
+
n+1/2
i,j,k
1+
Where: 𝑠′ is the surface of the disperser.
σ i,j,k ∆t
σ i,j,k ∆t
.
n+1/2
Hx i,j,k+1/2 − Hx i,j,k−1/2 ∆z
2i,j,k
(3)
r And r ′ are respectively Field position vectors and sources positions vectors (Fig.2b), is 𝑣′ the volume of the disperser, The three-dimensional Green's function in the vacuum, with R = r − r ′ . A and F, are respectively, the magnetic vector potential and the electric vector potential. Equations (7) and (8) are reduced, in the case of a perfect conductor (Ms is null and Js is a surface current density). II.2.
Mode scan and hyperbola
Scan data can be interpreted as an image of a vertical slice of the basement. It is obtained by the concatenation of a series of A-Scan data recorded by a GPR moving along a measuring line and at a constant height above the ground. Objects fled basement, are marked by the presence of hyperbole in B-scans, C-scan as shown in figure 3 [14][17].
(a)
(b)
(a)
(b)
(c)
Fig.3. Mode scan by RADAN 7 (a) B-scan (b) A-scan (c) C-scan. Fig.2. (a) Plane wave incident on a disperser; (b) Defining positions and vectors sources.
𝑀 = 𝑗𝑤𝜇0 (𝜇𝑟 − 1)𝐻 𝑗 = 𝑗𝑤𝜀0 (𝜀𝑟 − 1)𝐸 𝐸 = 𝐸𝑖 + 𝐸 𝑠
𝑎𝑛𝑑
𝐻 = 𝐻𝑖 + 𝐻 𝑠
(4) (5) (6) (a)
Copyright © 2010 Praise Worthy Prize S.r.l. - All rights reserved Int. Journal on Communications Antenna and Propagation, Vol. x, N. x
G.Alsharahi, A.Faize, A. Mint Mohamed Mostapha , A.Driouach
(b) Fig 4. (a) A simple reflection model for GPR (b) The antenna position x and the echo delay time t approximately satisfy a hyperbolic equation.
Hyperboles are a form of source reflection point, caused by B-scan, and they are due to the fact that the GPR energy is emitted in a cone as shown in figure 4, which radiates outward with depth. The energy is reflected by objects that are not directly below the antenna; reflection, however, is recorded as directed by the antenna receiving, and to a greater depth, because of the oblique wave transmission. Only the top hyperbole indicates the actual position of the source point.
model of bar circular conductor used for the simulation of the reflected radar signals. The obtained results are summarized and represented by the software Radargram as in figures 5(c, d) and Figures 5 (f, g). The simulated rectangular bar is shown in figures 5l, z, h, t; in these figures it can be noted the presence of the diffraction hyperbolas that indicates the presence of the rectangular and circular bars, of around 0.4 m; this is exactly the depth at which these bars are supposed to bury. (a)
(c)
(b)
(d)
(f)
(g)
(k)
(m)
III. Results and discussion The various materials used in this research are described in Table I. TABLE I: PHYSICAL PROPERTIES OF MATERIALS Material Relative Conductivity Velocity permittivity (S/m) (m/ns) Wood
3
0.003
0.17
Iron
1.45
9.99*106
0.24
Air
1
0
0.3
Dry sand
3
0.0001
0.17
Water
81
0.0005
0.03
Sea water
81
0.5- 4
0.03
Plastic
4
0.0004
0.15
Concrete wet
9
0.08
0.1
Concrete
6
0.005
0.12
Rock
10
0.1
0.09
Brick
4
0.001
0.15
Clay wet
20
0.1
0.067
3.1 Medium homogeneous (dry sand) a) Detection bars rectangular and circular conductor In the simulation, done by Reflexw and GprMax2d/3d, the soil, in which the bar rectangular is buried, is simulated by dry sand whose dielectric and conductivity properties are shown in table 1. The bar iron is buried at a depth of 0.5 m. The frequency simulation is set at 800 MHz. The emission and reflection of the simulated signal are recorded on a time window of 20 ns with a spatial increment of 7 cm. Figures 5a and b show a geometric
(l)
(h)
(m)
(z)
(t)
Fig.5. Radargram detect bar circle conductor (Radius=0.05) f=800MHz, 400 MHz (a) modeling by GprMax2d; (b) modeling by Reflexw; (c) Radargram of model detect metal circle bar by Reflexw at 800MHz; (d) Radargram of model detect metal circle bar by Reflexw at 400MHz; (f) Radargram of model detect metal circle bar by GprMax2d at 800MHz; (g) Radargram of model detect metal circle bar by GprMax2d at 400MHz ; (k) Response signal of GPR trace from metal circle bar in dry sand at 800 MHz and iteration 90; (m) Response signal of GPR trace from metal circle bar in dry sand at 400 MHz and iteration 90 (l) Rectangular metal bar by GprMax2d at 800MHz;
(z) Rectangular metal bar by GprMax2d at 400MHz (h) Rectangular metal bar by Reflexw at 800MHz; (t)
Rectangular metal bar by Reflexw at 400MHz.
b) Detection bar : a perfect Triangular conductor
Copyright © 2010 Praise Worthy Prize S.r.l. - All rights reserved Int. Journal on Communications Antenna and Propagation, Vol. x, N. x
G.Alsharahi, A.Faize, A. Mint Mohamed Mostapha , A.Driouach
Radar GPR is issued by this same buried under 0.4 m with dry sand triangular bar and signals are simulated using software GprMax2d. The transmission and reflection signals are recorded over a period of time of 18 ns. A simple calculation shows that the spatial increment equals to 0.007 m. The geometry of this model is shown in figure 6a ; the figure 9b shows the synthetic Radargram generated by the simulator, it shows the presence of a hyperboles revealing the presence of the bars triangular conductor and dielectric. The radargrams illustrated in Figures 6b and 6d, are horizontal lines resulting from reflections on planar surfaces, the Triangular conductor, ending in hyperbolae caused by wave reflections on the edges of the planar surface. The tails of the hyperbolae indicate the position of the edge with respect to the movement of the transmitter and receiver; that is, the right hyperbola tails indicate that the transmitter and receiver are moving away from the edge, while the left hyperbola tails indicate that the transmitter and receiver approach the edge.
(d)
(e) Fig.6. Radargramdetect triangular form at f=800MHz. (a) modeling by GprMax2d; (b) Radargram of model detect metal triangular bar by GprMax2d at 800MHz; (f) Radargram of model detect wooden triangular bar by GprMax2d at 800MHz; (c) Simulation GPR trace from metal triangular bar in dry sand at 800 MHz and iteration 90; (d) Response signal of GPR trace from wooden triangular bar in dry sand at 800MHz and iteration 90; (e) Simulation GPR trace from dielectric triangular bar in dry sand at 800 MHz and iteration 90.
(a) 3-2 Medium inhomogeneous
(b)
Model 1: Different layers During the simulation by GprMax2d/3d, medium inhomogeneous is examined, in which the bar rectangular conductor is buried at a depth of 0.3 m and 0.5 m in medium inhomogeneous whose dielectric properties and conductivity are shown in table1. The emission and reflection of the simulated signal are recorded for period of time of 18 ns using an excitation source of Ricker type for a central frequency of 0.8 GHz Dry sand
Clay
(c)
(a)
Copyright © 2010 Praise Worthy Prize S.r.l. - All rights reserved Int. Journal on Communications Antenna and Propagation, Vol. x, N. x
G.Alsharahi, A.Faize, A. Mint Mohamed Mostapha , A.Driouach
(a) Modeling byGprMax2d; (b) Radargram of model detect medium inhomogeneous by GprMax2d at 800MHz.
3-3 different targets buried in medium homogeneous Model 1: Different targets in the same medium It is considered the homogeneous medium consisting of dry sand buried at the same depth of 0.5m. The Figure (9a) shows the model of buried objects used for simulation of radar signals reflected by a simulator GprMax2d. The simulation results of this model are shown in figures 9b and c, here the hyperboles of the objects, supposed to be buried (water, plastic, iron and water sea) can be noted, attached to the depth (0.5 m).The radargram of the synthetic model is simulated with an excitation signal with 800 MHz of central frequency. In these figures it is clear that the hyperboles associated with each object are different. For example, if considered the example of water, in this figure it can be seen the presence of several hyperboles that match several consecutive reflections, but at different times for the used frequency (800 MHz). Indeed, the water has a high permittivity which decreases the rate of propagation of electromagnetic waves.
(b)
(c) Fig.7. Radargram detect medium inhomogeneous f=800MHz. (a) Modeling byGprMax2d; (b) Radargramof model detect medium inhomogeneous by GprMax2d at 800MHz; (c) Response signal of GPR trace medium inhomogeneous at 800 MHz and iteration 90.
The Figures 7a and 8a show a geometric model of two bars rectangular conductor used for simulation of radar signals reflected by a simulator (GprMax2d/3d). The total simulated length is 2.0 m x 1.0 m. The signal (Figures 7b and 8b) from the model allows the differentiation among almost all the single scattered, but the identification of the soil/clay interface is still difficult.
Water
plastic Iron
Air
sea wate r
(a)
Dry sand
Clay
(b) (a)
(c) (b) Fig.8. Radargram detect medium inhomogeneous f=800MHz.
Fig.9. Radargram detects medium contain targets in different physical properties at f=800 MHz(a) Modelling byGprMax2d; (b) Radargram of model detect medium contain targets in different physical properties by GprMax2d at 800MHz; (c) Response signal of GPR trace medium
Copyright © 2010 Praise Worthy Prize S.r.l. - All rights reserved Int. Journal on Communications Antenna and Propagation, Vol. x, N. x
G.Alsharahi, A.Faize, A. Mint Mohamed Mostapha , A.Driouach
contain targets in different physical properties at 800 MHz and iteration 90. Dry sand
Model 2: More targets ((position vertical) The data processing, with more targets or more objects, results in a 2D image as shown in Figure 10.a. In this model much low overlap among the reflected signals from the rooftops are obtained because they buried targets not located at same depth and direction. (a)
Dry sand
(a) (b)
(b)
(b) (c)
(c) Fig.11. Radargram detect medium f=800MHz. (a) Modeling byGprMax2d; (b) Radargram of model detect medium inhomogeneous by GprMax2d at 800MHz; (c) Response signal of GPR trace medium at 800 MHz and iteration 90.
IV. (c) Fig.10. Radargram detect more targets at f=800MHz. (a) Modeling byGprMax2d; (b) Radargram of model detect more targets by GprMax2d at 800MHz; (c) Response signal of GPR trace medium at 800 MHz and iteration 90.
In this model got a lot of low overlap between the reflected signals from the rooftops because they buried targets not located at same a depth and direction. Model 3: More targets (position horizontal) Fig.11a shows the simulation GPR response having an antenna set-up at 800 MHz frequency. The radargram (fig.11b) reveals the capability of 800 MHz antenna to detect the target related by the reflections In this model there are lot of strong overlap among the reflected signals from the rooftops because they buried targets located at same depth and direction.
Conclusion
The simulation of the radar GPR signals, used to study the objects buried in the homogenous and inhomogeneous mediums, using appropriate softwares, shows the influence of the constitution of the medium on the signals detected by the GPR. The obtained radargrams for the homogeneous mediums (e.g. fig.5) are clearer and more conclusive than those obtained in the case of those obtained for the objects detected in inhomogeneous mediums (e.g. fig.7 and fig.8 ).
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Copyright © 2010 Praise Worthy Prize S.r.l. - All rights reserved Int. Journal on Communications Antenna and Propagation, Vol. x, N. x
G.Alsharahi, A.Faize, A. Mint Mohamed Mostapha , A.Driouach
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GamilAlsharahi, was born in Amran City, Yemen in 1979. He received the B.S in Mathematics and Physic. and Master degrees in Telecommunication and elect- onics from the AbdelmalekEssaadi University, Faculty of Sciences, Tetouan. Currently he is working toward the Ph.D degree in University Abdelmalek Essaadi, Faculty of Sciences "Communication Systems".(
[email protected])
Abdellah Driouach, was born in Al Hoceima City (Morocco) in 1954. He got his license, in electronic physics, at the University of Rabat (Morocco) in 1979, his doctorate (of third cycle ) in "spectronomiehertzienne" , at the University of Bordeaux 1 (France) in 1983 and his doctor title (as sciences) at the University of Grenade (Spain). Professor and researcher at the Faculty of Science, AbdelmallekEssaadi University since 1983. He has participated in several scientific research, including the dispersion of electromagnetic waves on obstacles to arbitrary structures. Currently he is a member of the research team "Communication Systems". Ahmed Faize, was born Morocco in 1985.Currently he is Professor and researcher at Mohammed 1stUniversity, Faculty Polydisiplinarly Nador.
Aye Mint Mohamed Mostapha, was born in Magtalahjar City, Mauritania in 1991. She received a professional license in applied physics option Electronic-Electrotechnical-Automatic. And Master specialized in Telecommunication Systems Engineering from the AbdelmalekEssaadi University, Faculty of Sciences, Tetouan. She is currently working toward the Ph.D degree in University AbdelmalekEssaadi, Faculty of Sciences "Communication Systems" (
[email protected]).
Authors’ information 1
Department of Physic, Abdelmalek Essaâdi University, Faculty of Sciences,Tetouan 93000, Morocco 2 Department of Physic, Mohammed 1st University, Faculty Polydisiplinarly, Nador 62000, Morocco
Copyright © 2010 Praise Worthy Prize S.r.l. - All rights reserved Int. Journal on Communications Antenna and Propagation, Vol. x, N. x
