2022-09-24
Full Wave Modeling of Electromagnetic Scattering by an Object Buried Between Two Rough Surfaces: Application to GPR
By
Progress In Electromagnetics Research B, Vol. 96, 133-152, 2022
Abstract
In this paper, we present an efficient numerical method to calculate the frequency and time responses of the field scattered by an object buried between two random rough surfaces for a 2-D problem. This method is called Generalized PILE (GPILE) method because it extends the PILE method which considers only two surfaces or an object buried under a surface. The GPILE method solves the Maxwell equations rigourously by using a simple matrix formulation. The obtained results have a straightforward physical interpretation and allow us to investigate the influence of the object buried between the two rough surfaces. We distinguish the primary echo of the upper surface, the multiple echoes coming from the lower surface and those arising from the object. The GPILE method is applied to simulate the Ground Penetrating Radar (GPR) signal at nadir. The resulting time response helps the user to detect the presence of the object buried between the two random rough surfaces.
Citation
Marc Songolo, Nicolas Pinel, and Christophe Bourlier, "Full Wave Modeling of Electromagnetic Scattering by an Object Buried Between Two Rough Surfaces: Application to GPR," Progress In Electromagnetics Research B, Vol. 96, 133-152, 2022.
doi:10.2528/PIERB22020807
References

1. Jin, J., The Finite Element Method in Electromagnetics, John Wiley and Sons, 1993.

2. Volakis, J. L., A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics, IEEE Press, 1998.
doi:10.1109/9780470544655

3. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell equations in isotropic media," IEEE Trans. on Antennas and Propagation, Vol. 14, No. 3, 302-307, 1966.
doi:10.1109/TAP.1966.1138693        Google Scholar

4. Cole, J. B. and S. Banerjee, Computing the Flow of Light: Nonstandard FDTD Methodologies for Photonics Design, SPIE Press Book, 2017.
doi:10.1117/3.2250614

5. Harrington, F., Field Computation by Moment Methods, Macmillan, New York, 1968.

6. Bourlier, C., N. Pinel, and G. Kubické, Method of Moments for 2-D Scattering Problems. Basic Concepts and Applications, ser. Focus Series in Waves, Wiley, Hoboken, NJ, USA, 2013.
doi:10.1002/9781118648674

7. Kapp, D. A. and G. S. Brown, "A new numerical method for rough-surface scattering calculations," IEEE Trans. on Antennas and Propagation, Vol. 44, 711-722, 1996.
doi:10.1109/8.496258        Google Scholar

8. Holliday, D., L. L. DeRaad, Jr., and G. J. St-Cyr, "Forward-backward: A new method for computing low-grazing angle scattering," IEEE Trans. on Antennas and Propagation, Vol. 44, 1199-1206, 1995.
doi:10.1109/8.475091        Google Scholar

9. Iodice, A., "Forward-backward method for scattering from dielectric rough surfaces," IEEE Trans. on Antennas and Propagation, Vol. 50, 901-911, 2002.
doi:10.1109/TAP.2002.800700        Google Scholar

10. Chou, H. T. and J. T. Johnson, "A novel acceleration algorithm for the computation of scattering from rough surfaces with the forward-backward method," Radio Sci., Vol. 33, 1277-1287, 1998.
doi:10.1029/98RS01888        Google Scholar

11. Tsang, L., C. H. Chang, and H. Sangani, "A banded matrix iterative approach to Monte Carlo simulations of scattering of waves by large scale random rough surface problems: TM case," Electron. Lett., Vol. 29, 1666-1667, 1993.        Google Scholar

12. Tsang, L., C. H. Chang, H. Sangani, A. Ishimaru, and P. Phu, "A banded matrix iterative approach to Monte Carlo simulations of large scale random rough surface scattering: TE case," Journal of Electromagnetic Waves and Applications, Vol. 7, No. 9, 1185-1200, 2012.
doi:10.1163/156939393X00200        Google Scholar

13. Tsang, L., C. H. Chan, K. Pak, and H. Sangani, "Monte-Carlo simulations of large-scale problems of random rough surface scattering and applications to grazing incidence with the BMIA/canonical grid method," IEEE Trans. on Antennas and Propagation, Vol. 43, 851-859, 1995.
doi:10.1109/8.402205        Google Scholar

14. Kuo, C.-H. and M. Moghaddam, "Scattering from multilayer rough surfaces based on the extended boundary condition method and truncated singular value decomposition," IEEE Trans. on Antennas and Propagation, Vol. 54, No. 10, 2917-2929, 2006.
doi:10.1109/TAP.2006.882160        Google Scholar

15. Moss, C. D., T. M. Grzegorczyk, H. C. Han, and J. A. Kong, "Forward backward method with spectral acceleration for scattering from layered rough surfaces," IEEE Trans. on Antennas and Propagation, Vol. 54, No. 3, 1006-1016, 2006.
doi:10.1109/TAP.2006.869921        Google Scholar

16. El-Shenawee, M., "Polarimetric scattering from two-layered two-dimensional random rough surfaces with and without buried objects," IEEE Trans. Geoscience, and Remote Sensing, Vol. 42, No. 1, 67-76, 2004.
doi:10.1109/TGRS.2003.815675        Google Scholar

17. Déchamps, N., N. De Beaucoudrey, C. Bourlier, and S. Toutain, "Fast numerical method for electromagnetic scattering by rough layered interfaces: Propagation-inside-layer expansion method," J. Opt. Soc. Am. A, Vol. 23, No. 2, 359-369, 2006.
doi:10.1364/JOSAA.23.000359        Google Scholar

18. Déchamps, N. and C. Bourlier, "Electromagnetic scattering from a rough layer: Propagation-inside-layer expansion method combined to an updated BMIA/CAG approach," IEEE Trans. on Antennas and Propagation, Vol. 55, 2790-2802, 2007.
doi:10.1109/TAP.2007.905940        Google Scholar

19. Déchamps, N. and C. Bourlier, "Electromagnetic scattering from a rough layer: Propagation-inside-layer expansion method combined to the forward-backward novel spectral acceleration," IEEE Trans. on Antennas and Propagation, Vol. 55, 3576-3586, 2007.
doi:10.1109/TAP.2007.910360        Google Scholar

20. Bourlier, C., G. Kubické, and N. Déchamps, "A fast method to compute scattering by a buried object under a randomly rough surface: PILE combined to FB-SA," J. Opt. Soc. Am. A, Vol. 25, 891-902, 2008.
doi:10.1364/JOSAA.25.000891        Google Scholar

21. Kubické, G., C. Bourlier, and J. Saillard, "Scattering by an object above a randomly rough surface from a fast numerical method: Extended PILE method combined to FB-SA," IEEE Trans. on Antennas and Propagation, Vol. 18, No. 03, 495-519, 2008.        Google Scholar

22. Bourlier, C., C. Le Bastard, and V. Baltazart, "Generalization of PILE method to the EM scattering from stratified subsurface with rough interlayers: Application to the detection of debondings within pavement structure," IEEE Trans. Geoscience, and Remote Sensing, Vol. 53, No. 7, July 2015.        Google Scholar

23. Thorsos, E. I., "The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum," J. Acoust. Soc. Am., Vol. 83, 78-92, 1988.
doi:10.1121/1.396188        Google Scholar

24. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd Ed., Cambridge University Press, 1992.

25. Bourlier, C., C. Le Bastard, and N. Pinel, "Full wave PILE method for the electromagnetic scattering from random rough layer," Proc. GPR Int. Conf. Ground Penetrating Radar, 545-551, 2014.
doi:10.1109/ICGPR.2014.6970483        Google Scholar