RADIO SCIENCE, VOL. 37, NO. 3, 1033, 10.1029/2001RS002500, 2002 Trnsmitter-receiver-trnsmitter configurtions of ground-penetrting rdr Levent Gürel nd Uğur Oğuz Deprtment of Electricl nd Electronics Engineering, Bilkent University, Ankr, Turkey Received 29 My 2001; revised 8 Novemer 2001; ccepted 9 Novemer 2001; pulished 11 My 2002. [1] Three-dimensionl ground-penetrting rdr (GPR) geometries re simulted using the finite difference time domin (FDTD) method. The GPR is modeled with receiver nd two trnsmitters with ritrry polriztions in order to cncel the direct signls emitted y the two trnsmitters t the receiver. This GPR configurtion is used to simulte scenrios involving single or multiple trgets with ritrry sizes. The uried ojects re modeled s cylindricl disks. Perfectly mtched lyer soring oundry conditions re used to terminte the lyered FDTD computtionl domin. INDEX TERMS: 3210 Mthemticl Geophysics: Modeling; 3230 Mthemticl Geophysics: Numericl solutions; 6969 Rdio Science: Remote sensing; 0644 Electromgnetics: Numericl methods; 0933 Explortion Geophysics: Remote sensing; KEYWORDS: ground-penetrting rdr (GPR), finite difference time domin (FDTD) method, susurfce scttering, perfectly mtched lyer 1. Introduction [2] The need for simulting ground-penetrting rdr (GPR) systems [Dniels, 1996; Moghddm et l., 1991; Bourgeois nd Smith, 1996] hs incresed the populrity of the finite difference time domin (FDTD) method [Yee, 1966] mong other numericl modeling techniques. The FDTD method is powerful tool in solving prolems involving lyered medi nd complicted inhomogeneities [Moghddm et l., 1991; Gürel nd Oğuz, 2001]. In this pper, three-dimensionl GPR scenrios re simulted using the FDTD method nd the perfectly mtched lyer (PML) [Berenger, 1994; Chew nd Weedon, 1994] soring oundry conditions (ABC). [3] The geometry of GPR prolem consists of two hlf-spces, the ir modeled s vcuum nd the ground modeled s homogeneous dielectric medium, seprted y n interfce, s shown in Figure 1. The ground cn lso e modeled s lossy nd heterogeneous medium. The simultion results of such ground models re presented in other reports [Gürel nd Oğuz, 2001; Oğuz nd Gürel, 2002; L. Gürel nd U. Oğuz, Trnsmitter-receiver-trnsmitter-configured ground-penetrting rdrs over rndomly heterogeneous ground models, sumitted to Rdio Science, 2001] (hereinfter Copyright 2002 y the Americn Geophysicl Union. 0048-6604/02/2001RS002500$11.00 5-1 referred to s Gürel nd Oğuz, sumitted mnuscript, 2001). [4] Similr to the FDTD computtionl domin, the PML regions re lso designed s two lyers, mtching oth the ground nd ir regions nd the interfce etween them. Buried trgets cn e modeled with ritrry quntity, shpes, permittivities, nd conductivities. The rdr unit contins the trnsmitting nd receiving ntenns. These ntenns move over the ground-ir interfce t fixed elevtion, s depicted in Figure 1. [5] In this pper, uried trgets re modeled s single or multiple conducting disks. A relistic scenrio involving two nonidenticl disks is lso simulted. Other scenrios involving similr GPR configurtions ut different ground nd trget fetures, such s dielectric nd conducting trgets of rectngulr prism shpe nd ground models with higher permittivities, re reported y Gürel nd Oğuz [2000]. 2. Rdr Unit [6] Most of the GPR models found in the literture exhiit trnsmitter-receiver (TR) configurtion to illuminte the trget nd collect the scttered fields [Moghddm et l., 1991; Bourgeois nd Smith, 1996]. In tht configurtion the totl signl contins the sum of the desired scttered signl S, the direct signl D, nd the signl reflected from the ground G [Oğuz nd Gürel, 2001]. Usully, the totl collected signl is dominted y
5-2 GÜREL AND OĞUZ: TRT CONFIGURATIONS OF GROUND-PENETRATING RADAR [8] Figure 1 displys four GPR models, referred to s GPR1, GPR2, GPR3, nd GPR4. The four TRT configurtions differ from ech other in the polriztion nd lignment of the three ntenns [Gürel nd Oğuz, 2000, 2002]. Ech trnsmitting ntenn is modeled y singlecell (D) volume current density. The time vrition of the current source is given y JðÞ¼ t 1 D 3 4 t 3 t 4 e t=t ; ð1þ t t Figure 1. Geometry of hlf-spce prolem with uried sctterer nd the GPR models used in this work: GPR1 is configured s three x-polrized ntenns ligned in the y direction. GPR2 consists of three y-polrized ntenns ligned in the x direction. GPR3 nd GPR4 represent three z-polrized ntenns ligned in the y nd x directions, respectively. the D signl, nd it is either hrd or impossile to detect the desired S signl in the totl received signl. Additionl hrdwre nd softwre components re developed in order to fcilitte the detection of the trget signl in the lrge ckground signl (U. Oğuz nd L. Gürel, Electromgnetic simultion of vrious techniques to fcilitte detection in ground-penetrting-rdr prolems, sumitted to Geophysics, 2001) or to reduce the mplitudes of the unwnted signls [Oğuz nd Gürel, 2001; Gürel nd Oğuz, 1999; Bourgeois nd Smith, 1998]. [7] In this work, rdr units consist of two trnsmitters (T 1 nd T 2 ) nd receiver (R), s shown in Figure 2. The two trnsmitters re fed with phse difference of 180. In this configurtion the two direct signls D 1 nd D 2 cncel ech other everywhere on symmetry plne tht is equidistnt to the two trnsmitters. The loction of the R ntenn is chosen to e exctly in the middle of two trnsmitters, coinciding with the symmetry plne [Luneu nd Delisle, 1996; Gürel nd Oğuz, 2000]. Similrly, the two reflected signls G 1 nd G 2 lso cncel out t the receiver, if the ground is homogeneous. Consequently, in the trnsmitter-receiver-trnsmitter (TRT) configurtion, the totl received signl is solely due to the uried oject (S 1 + S 2 ), which leds to the detection of the uried oject. The cses of inhomogeneous grounds re studied elsewhere (Gürel nd Oğuz, sumitted mnuscript, 2001). where t = 1/(4pf 0 ) nd f 0 is the center frequency of the pulse. The receiver is selected s single-cell dipole tht smples nd stores the vlues of the x, y, orz component of the electric field E n. The dt collected t single point for successive instnts of time n re clled n A scn. When the GPR unit moves on liner pth nd performs A-scn mesurements t discrete points, the collection of these A-scn mesurements is clled B scn. 3. Simultion Results [9] In this section, simultion results of the four GPR models introduced in section 2 re presented. A center frequency of f 0 = 1 GHz is used in ll of these simultions, nd D = 2.5 mm nd Dt = 4.5 ps re the smpling intervls in spce nd time, respectively. The trnsmitting nd receiving ntenns re seprted y two cells (2D). 3.1. Single Conducting Disk [10] The four GPR models re first tested on scenrio involving perfectly conducting disk with rdius of 10 Figure 2. Trnsmitter-receiver-trnsmitter (TRT) configurtion of the rdr unit nd the description of the direct (D), reflected (G), nd scttered (S) signls.
GÜREL AND OĞUZ: TRT CONFIGURATIONS OF GROUND-PENETRATING RADAR 5-3 c d Figure 3. Simultion results of perfectly conducting disk uried 5 cells under the ground. The simultions re crried out using () GPR1, () GPR2, (c) GPR3, nd (d) GPR4. cells uried 5 cells under the ground-ir interfce. The reltive permittivity of the ground is selected s e r =2. The rdr unit trvels on stright line 10 cells wy from the center of the disk, which corresponds to pth pssing through the edge of the conducting disk. Figures 3 3d present the B-scn results s function of the rdr position (verticl xis) nd time (horizontl xis). For ech GPR model the mximum vlue otined in the B scn is given t the top of the corresponding plot. The lrgest of these four E mx vlues is used to normlize ll four B-scn plots. Figures 3 3d show tht the responses of the four GPR models re different even for the sme scenrio. GPR1 collects electric fields with the highest mgnitudes. However, GPR1 produces visile responses only when the rdr unit is very close to the trget, while GPR2 responds even when the rdr unit is fr from the trget. [11] In order to further illustrte the differences in their responses the four GPR models re moved on twodimensionl grid, where n A-scn mesurement is
5-4 GÜREL AND OĞUZ: TRT CONFIGURATIONS OF GROUND-PENETRATING RADAR Figure 4. Energy digrms mesured y () x-polrized nd () z-polrized TRT rdr units moving on two-dimensionl grid. A perfectly conducting disk is uried 5 cells under the ground. performed in ech discrete position. The energy vlues of these A-scn signls re computed s ENERGY ¼ X n je n j 2 ð2þ wveforms otined y GPR1 nd GPR2, respectively. Similrly, Figure 4 cn e otined y either GPR3 units moving in the x direction or GPR4 units moving in the y direction. [12] Figures 4 nd 4 demonstrte tht GPR1 nd GPR2 collect 2 times lrger scttered energy thn GPR3 nd GPR4. A constnt-y trce in Figure 4, which corresponds to GPR1 B scn, contins single pek, locted close to the center of mss of the trget. However, constnt-x trce, which is B scn performed y GPR2, displys two peks, locted ove the edges of the disk. A similr comprison cn e mde upon the investigtion of the constnt-y nd constnt-x trces of Figure 4, which re the B-scn results otined with GPR3 nd GPR4, respectively. Therefore it is possile to conclude tht GPR2 nd GPR4 detect the edges of the disk, wheres GPR1 nd GPR3 respond to the whole mss of the uried trget. [13] Figure 4 further demonstrtes tht GPR2 receives detectle mount of energy while the rdr unit moves wy from the sctterer, if the pth itself is close to the uried trget. If the pth is not close to the sctterer, the energy collected y GPR2 is ignorle everywhere on the pth. In contrst, GPR1 responds only when it is close to the uried trget, ut these responses re detectle even if the pth itself is wy from the trget. 3.2. Multiple Conducting Disks [14] The detection of two closely uried disks (Figure 5) is investigted next, fter hving demonstrted the sensitivities of GPR2 nd GPR4 to distnt trgets nd GPR1 nd GPR3 to nery trgets in section 3.1. Figure 6 presents the simultion results of two conducting disks, ech with 10-cell rdius nd 16-cell height, uried 5 cells under the ground nd seprted y 20 cells. The nd given in Figure 4. Figures 4 nd 4 re otined y rdr units consisting of x- nd z-polrized dipoles, respectively. Since the rdr units move in two directions, results otined y the x-polrized configurtion, displyed in Figure 4, contin oth GPR1 nd GPR2 results. Similrly, the energy plot of the z-polrized configurtion given in Figure 4 encompsses oth GPR3 nd GPR4 models. Constnt-y nd constnt-x trces tken from the two-dimensionl grid of Figure 4 correspond to the energy plots of the Figure 5. Simultion geometry tht contins two identicl perfectly conducting disks. Both disks hve dimeters of 5 cm. The rdr unit trvels long liner pth tht is tngentil to oth disks.
GÜREL AND OĞUZ: TRT CONFIGURATIONS OF GROUND-PENETRATING RADAR 5-5 c d Figure 6. Simultion results of two identicl perfectly conducting disks uried 5 cells under the ground nd seprted y 20 cells. Both disks hve dimeter nd height of 5 cm nd 4 cm, respectively. The ground hs reltive permittivity of e r = 2. The simultions re crried out using () GPR1, () GPR2, (c) GPR3, nd (d) GPR4. rdr unit trvels long stright line ove the ground. The projection of this pth is tngent to oth of the disks uried under the ground, s displyed in Figure 5. The reltive permittivity of the ground is selected s e r = 2. The energies of the A-scn signls re evluted ccording to eqution (2) nd presented in ddition to the B-scn results in Figures 6 6d. Figures 6 nd 6c demonstrte tht oth ojects cn e detected y GPR1 nd GPR3. However, the signls produced y GPR2 nd GPR4 re not esy to interpret. Figures 6 nd 6d contin two nulls, due to the minim encountered ove the centers of mss of the two disks, s they pss ner the two trgets. However, third null exists, which corresponds to the symmetry plne tht is locted exctly in the middle of the two ojects. For this reson, Figures 6 nd 6d do not clerly indicte the two trgets under the ground. [15] In Figure 5 the prolem geometry is perfectly symmetric with respect to the plne in the middle of the two disks. Therefore ll the results presented in Figures 6 6d re symmetric round the middle plne. In order to investigte more generl sitution where such symmetry does not exist, nother simultion, involving two disks with different rdii, is considered. The first conducting disk hs rdius of 2.5 cm, while the other disk s rdius is 4 cm. Both disks re 4 cm high nd uried 5 cm under the ground. The four GPR models trvel long pth whose projection is tngentil to oth disks, s shown in Figure 7. Figures 8, 8, 8c, nd 8d disply the signls recorded y GPR1, GPR2, GPR3, nd GPR4, respectively. Similr to Figure 6, next to ech B-scn result in Figure 8, the energies oserved in the A-scn mesurements re lso presented. Figures 8 8d demonstrte the effects of the geometricl differences of this prolem, compred to the results in Figure 6. Figure 8 displys two peks of energy with similr mplitudes, ut different widths, received y GPR1.
5-6 GÜREL AND OĞUZ: TRT CONFIGURATIONS OF GROUND-PENETRATING RADAR Figure 7. Simultion geometry tht contins two nonidenticl perfectly conducting disks, with 5 cm nd 8 cm dimeters. The rdr unit trvels long liner pth tht is tngentil to oth disks. GPR3 produces similr results, s demonstrted in Figure 8c. However, in Figure 8c, the mximum energy oserved ove the lrge disk is smller compred to the energy oserved ove the smll disk. In Figure 8 the B-scn mesurements of GPR2 re shown. Although there is no symmetry plne etween the two disks in this prolem, GPR2 still encounters three minim. However, in Figure 8, the minimum in the middle is not n exct null, in contrst to Figure 6. The effects of the difference of the two disks re oserved extensively in Figure 8d, where the results otined y GPR4 re displyed. Similr to the GPR2 results in Figure 8, Figure 8d displys three minim in the B-scn mesurements. Figures 8 nd 8d demonstrte tht it is not esy to detect the two closely plced disks with GPR2 or GPR4. 4. Conclusion [16] Three-dimensionl GPR scenrios re simulted using the FDTD method comined with the PML ABCs. The rdr unit is modeled s TRT configurtion with c d Figure 8. Simultion results of two nonidenticl perfectly conducting disks uried 5 cells under the ground nd seprted y 20 cells. The heights of the disks re oth 4 cm. The dimeters of the two disks re 5 cm nd 8 cm. The ground hs reltive permittivity of e r = 2. The simultions re crried out using () GPR1, () GPR2, (c) GPR3, nd (d) GPR4.
GÜREL AND OĞUZ: TRT CONFIGURATIONS OF GROUND-PENETRATING RADAR 5-7 ritrry polriztions of trnsmitting nd receiving ntenns. The trgets re modeled s perfectly conducting cylindricl disks. [17] The dvntges of the TRT configurtion re demonstrted using the simultion results. It is shown tht the cncelltions of the direct signls (due to the direct coupling from the trnsmitters to the receiver) nd the reflected signls (from the ground-ir interfce) yield totl received signl tht is only due to the sctterer, which fcilittes the detection of the uried trget. The specific dvntges nd disdvntges of vrious polriztions of the ntenns in TRT configurtions re demonstrted. The responses of the presented GPR models re different in chrcter, which suggests tht polriztion-enriched GPR systems will chieve etter detection performnces. [18] Acknowledgments. This work ws supported y Bilkent University under Reserch Fund EE-01-01. References Berenger, J. P., A perfectly mtched lyer for the sorption of electromgnetic wves, J. Comput. Phys., 114, 185 200, 1994. Bourgeois, J. M., nd G. S. Smith, A fully three-dimensionl simultion of ground-penetrting rdr: FDTD theory compred with experiment, IEEE Trns. Geosci. Remote Sens., 34(1), 36 44, 1996. Bourgeois, J. M., nd G. S. Smith, A complete electromgnetic simultion of the seprted-perture sensor for detecting uried lnd mines, IEEE Trns. Antenns Propg., 46(10), 1419 1426, 1998. Chew, W. C., nd W. H. Weedon, A 3D perfectly mtched medium from modified Mxwell s equtions with stretched coordintes, Microwve Opt. Technol. Lett., 7(13), 599 604, 1994. Dniels, D. J., Surfce-Penetrting Rdr, IEE, London, 1996. Gürel, L., nd U. Oğuz, Employing PML sorers in the design nd simultion of ground penetrting rdrs, pper presented t 1999 IEEE AP-S Interntionl Symposium nd USNC/URSI Ntionl Rdio Science Meeting, Inst. of Electr. nd Electron. Eng., Orlndo, Fl., July 1999. Gürel, L., nd U. Oğuz, Three-dimensionl FDTD modeling of ground-penetrting rdr, IEEE Trns. Geosci. Remote Sens., 38(4), 1513 1521, 2000. Gürel, L., nd U. Oğuz, Simultions of ground-penetrting rdrs over lossy nd heterogeneous grounds, IEEE Trns. Geosci. Remote Sens., 39(6), 1190 1197, 2001. Gürel, L., nd U. Oğuz, Optimiztion of the trnsmitter-receiver seprtion in the ground-penetrting rdr, IEEE Trns. Antenns Propg., in press, 2002. Luneu, P., nd G. Y. Delisle, Underground trget proing using FDTD, pper presented t 1996 IEEE AP-S Interntionl Symposium nd URSI Rdio Science Meeting, Inst. of Electr. nd Electron. Eng., Bltimore, Md., July 1996. Moghddm, M., E. J. Ynnkkis, W. C. Chew, nd C. Rndll, Modeling of the susurfce interfce rdr, J. Electromgn. Wves Appl., 5(1), 17 39, 1991. Oğuz, U., nd L. Gürel, Modeling of ground-penetrting-rdr ntenns with shields nd simulted sorers, IEEE Trns. Antenns Propg., 49(1), 1560 1567, 2001. Oğuz, U., nd L. Gürel, Frequency responses of ground-penetrting rdrs operting over highly lossy grounds, IEEE Trns. Geosci. Remote Sens., in press, 2002. Yee, K. S., Numericl solution of initil oundry vlue prolems involving Mxwell s equtions in isotropic medi, IEEE Trns. Antenns Propg., 14(4), 302 307, 1966. L. Gürel nd U. Oğuz, Deprtment of Electricl nd Electronics Engineering, Bilkent University, TR-06533, Bilkent, Ankr, Turkey. (lgurel@ee.ilkent.edu.tr; uoguz@ee.ilkent. edu.tr)