GPR Polarization Simulation with 3D HO FDTD

Transcription

1 Progress In Electromagnetics Research Symposium Proceedings, Xi an, China, March 6, GPR Polarization Simulation with 3D HO FDTD Jing Li, Zhao-Fa Zeng,, Ling Huang, and Fengshan Liu College of Geoexploration Science and Technology, Jilin University Changchun 3006, China Applied Mathematics Research Center, Delaware State University, DE 990, USA Abstract Polarization signal is important in designing GPR data measurement. Its scattering characteristics can be used to discriminate the targets. For the target with different medium properties or orientation, the GPR signal response has a significant difference in different polarization mode. The targets such as metallic, low impedance object and PVC, high impedance objects have different polarization signals while are difficult to discriminate in the conventional GPR acquiring methods. The polarimetric measurement has the potentials to improve the discrimination, reduce the clutter interference and get the better prospecting effect. Meanwhile, the simulation is one of key research issues to understand the radar polarization theoretical. In order to improve simulation accuracy, we use 3D high-order finite difference time domain (HO-FDTD) method to simulate the polarization. It obtains a good application effect. Through the simulation study of GPR polarization measurement, we can provide more accurate and richer theoretical for the practical work. provide more accurate and richer theoretical for the practical work.. INTRODUCTION Ground Penetrating Radar (GPR) is a geophysical technique which use of high frequency electromagnetic wave ( Hz) to detect electrical distribution for investigating the shallow subsurface medium []. The polarization characteristic signal is an important information such as amplitude, phase and Doppler frequency of radar for data interpretation. The signal from the receive antenna is a function of the polarization of the transmit antenna and properties of subsurface targets []. The dipole antenna of GPR radiate linearly polarized wave with the predominant polarization direction parallel to the long axis of the antenna. Receive antennas are very sensitive to the electric field component parallel to the long axis. In practical, the complexity geological environment, the distribution of underground target without regularity, and complex medium properties make the results shown obvious difference in the same condition. The polarization of electromagnetic wave is a fundamental property of propagation that provides the GPR with a unique opportunity for producing improved images of object in the subsurface. Many researches have done the studies and got some important improvement. Yong and Caldecot [3] designed the GPR system which used to locate underground pipe lines. Two orthogonal dipole antennas are used in the system. Roberts, Daniels and Radzevicius [4, 5] have done research on the polarization characteristics of GPR. They pointed out that there are significant difference between TE and TM polarization scattering. P. Capizzi and P. L. Cosentino [6] study the GPR multi-component data analysis, and so on. In this paper, we use 3D high-order FDTD method [7] to simulate the GPR polarization measurement. Our study mainly focus on the polarization characteristic in different antenna geometric modes when the targets have different dielectric properties, shape and orientation. The results show that choosing appropriate polarization not only effectively improve the SNR and resolution but also can discriminate the medium properties, shape and orientation of targets. It could provide more effective geological information.. PRINCIPLE OF HIGH-ORDER FDTD FDTD is a direct time-domain method to solve Maxwell equation which is simple, visual, flexible, and has a large dynamic range in calculation that apply in the GPR polarization simulation. However, one of the major limitations of the FDTD approach for the numerical solution of Maxwell s equations is its calculation accuracy. High-order FDTD method is one of ways to improve simulation accuracy. It uses Taylor expansion to expand the time-domain difference equation and to set a new difference equation. The time integration is implemented using second-order central finite difference and the space integration is implemented by using M-order central finite difference.

2 000 PIERS Proceedings, Xi an, China, March 6, 00 It can be obtained the discrete Maxwell s equations. M Ex n+ ( = ( ε0ε r t + ) a(l) Hn+ z i, j+l+, k) σe y l= M Hn+ y ( i, j, k+l+ z ) +( ε0 ε r t σ e ) E n x () where, x, y, z as the along x, y, z direction s grid size, i, j, k is the grid number. the along x, y, z direction, a(l) gives as: a(l) = ( )l ( l + ) [(M )!!] (M l)!! (M + l)!! () Numerical stability condition: M ( ) ( ) ( ) t v max a(l) + + x y z l=0 (3) For the absorbing boundary condition, we use the uniaxial anisotropy perfectly matched boundary (UPML) which proposed by Sacks [9] and Gedeny [8]. It does not need split the electromagnetic field. The algorithm is very concise and easy to understand. It is a non-physical absorbing medium and wave impedance which is not dependent on outward-wave angle and frequency. 3. ELECTROMAGNETIC WAVE POLARIZATION The EM wave field strength changes with direction of EM wave. Such phenomenon can be observed: when the metal wire parallel to the electric field, electromotive force which electric field induced in the wire is strongest; when the metallic wire vertical to the electric field, electromotive force is zero. It shows that the direction of electromagnetic field in space is a very important issue. The polarization of plane wave can characterize the features that fixed electric field vector in space change with time. The conventional GPR antennas use two linear dipole antennae with identical properties which is vertical to the propagation direction of electromagnetic. The polarization modes are less to be used in which antenna parallel to the direction of electromagnetic wave propagation and cross-cutting along the direction. The GPR multi-polarization (Fig. ) provides more information of underground target. The geometries shown as Fig. is four components of acquired electromagnetic field: parallel broadside with y-directed antenna (Y Y ), parallel broadside with x-directed antenna (XX), perpendicular antennas with y-directed source and x-directed receiver (Y X) and perpendicular antennas with x-directed source and y-directed receiver orientation (XY ). The electric field traveling in the z direction can be described by two orthogonal components as given in Balanis 989: E x (z, t) = E x0 e αz cos(ωt βz φ x ), E y (z, t) = E y0 e αz cos(ωt βz φ y ) where α represents the attenuation coefficient, β represents the phase constant, ω the angular frequency, φ the phase, and E x0 and E y0 are the maximum amplitudes of the E x and components respectively E y. Figure : The polarization mode of GPR antenna.

3 Progress In Electromagnetics Research Symposium Proceedings, Xi an, China, March 6, GPR POLARIMETRIC SIMULATION The steel and other metallic with low impedance, or PVC and other dielectric with high impedance are the common detecting target in the GPR detection. The result is often difficult to interpretation due to the dielectric properties of object as well as the clutter interference of the surrounding medium. The high-frequency electromagnetic waves which emissions by GPR have different polarization signal responses. 3D high-order FDTD method used to simulate the polarization characteristics of two object models: the PVC ε r = 3, σ = S/m. We can clearly see that there are significantly differences for the two models (Fig. 3 and Fig. 4). For the PEC cylinder models, the signal from Y Y polarization mode could clearly discriminate the location of targets and has very small diffraction interference error. the steel cylinders in Y Y polarization mode and we can clearly discriminate the lower steel cylinders. The signal amplitude is stronger than other modes. But the other polarization can not achieve prospecting effect. For the PVC pipes model, the XX polarization signal response is stronger than other modes (Fig. 5). The clutter interference is also low. The signal is best imaged. The position relation of survey direction and target orientation is an important factor to improve the GPR polarization effect. So, we design the model respectively vertical and parallel to the survey direction (Fig. 6). From the profile we can conclude that, for the metallic which parallel to the survey direction and the dielectric which vertical to the survey direction, the XX polarization has stronger signal response. For the metallic which vertical to survey direction and the dielectric which parallel to survey direction, the Y Y polarization signal response is stronger than the signal from other modes (Fig. 7). The above analysis based on the target trend along a certain direction. It may be effect by the trend of target and the survey direction. Whether have the same conclusion for the equiaxed target such as sphere and cube. In order to verify this problem, we select the sphere and cube model with different dielectric properties. The map is the single-trace reflection signal in the same location of XX and Y Y polarization mode after removing the direct wave. From the single-trace signal, the metallic models have stronger signal amplitude in Y Y mode, the XX mode make the dielectric have stronger signal amplitude. It is well to prove that different dielectric properties target suitable for different polarization mode (Fig. 8 and Fig. 9). Summing up all the simulation and analysis, we can get that for the equiaxed target, the metallic and low impedance dielectric objects, are best imaged with the long axis of the dipole antennas Figure : PEC cylinder or PVC pipe model. Figure 3: The GPR slice of double PEC cylinder model with different polarization.

4 00 PIERS Proceedings, Xi an, China, March 6, 00 Figure 4: The GPR slice of double PVC model. Figure 5: The GPR signal response of double PVC. Figure 6: Cylinder model in different trend. Figure 7: The GPR slices of different model in different polarization. Figure 8: The single-trace signal of metallic cube and sphere model (left map is cube, right is sphere).

5 Progress In Electromagnetics Research Symposium Proceedings, Xi an, China, March 6, Figure 9: The single-trace signal of dielectric cube and sphere model (left map is cube, right is sphere). oriented parallel to the long axis (Y Y mode). The dielectric, and high impedance dielectric objects, are best imaged with the long axis of the dipoles oriented orthogonal to the long axis (XX mode); If the object have a certain extension direction, the metallic object which is parallel to the survey direction and the dielectric which is vertical to the survey direction are best imaged with the XX polarization mode; the metallic which is vertical to the survey direction and the dielectric which parallel to the survey direction are best with the Y Y polarization mode. For the XY and Y X polarization modes can not have a good prospecting effect in any case. 5. CONCLUSIONS Through the study of GPR polarization measurement simulation with high-order FDTD method, we have an overall understanding to the GPR signal response for the target with different dielectric properties and shape in different polarization modes. By choosing appropriate GPR polarization mode, we can significantly improve the SNR, the recognition ability and the resolution. Moreover, the GPR polarization measurement also plays a prominent role in detecting 3D complex target. In the case of complex targets, the effect of polarization is even more critical to ultimately obtaining a good 3D view of individual objects within a group of complex features. ACKNOWLEDGMENT The research work was supported by NSFC ( ) of China, and a DoD DEPSCoR W9NF of USA. REFERENCES. Annan, A. P., Radio interferometry depth sounding: Part. Theoretical discussion, Geophysics, Vol. 38, No. 3, , Radzevicius, S. J. and J. J. Daniels, Ground penetrating radar polarization and scattering from cylinders, Journal of Applied Geophysics, Vol. 45, 5, Yong, J. and T. R. Caldecot, A portable detector for plastic pipe and other underground objects, Final Report 404X-, Columbus, The Ohio State University Electro Science Laboratory, Daniels, D. J., D. J. Gunton, and T. H. F. Scot, Introduction to subsurface radar, IEE Proceedings, Vol. 33, No. 4, 78 36, Roberts, R. L. and J. J. Daniels, Analysis of GPR polarization phenomena, Journal of Environmental and Engineering Geophysics, Vol., No., 39 57, Capizzi, P. and P. L. Cosentino, GPR multi-component data analysis, Near Surface Geophysics, 87 95, Georgakopoulos, S. V., C. R. Birtcher, et al., Higher-order finite difference schemes for electromagnetic radiation scattering and penetration, IEEE Antenna s and Propagation Magazine, Vol. 44, 34 4, Gedney, S. D., An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices, IEEE Trans. Antennas Propagat., Vol. 44, No., , Sacks, Z. S., D. M. Kingsland, and J. F. Lee, A perfectly matched anisotropic absorber for use as an absorbing boundary condition, IEEE Trans. Antennas Propagat., Vol. 43, No., , 995.