volume | PIER Journals

Abstract

In this paper, a new theoretical approach for the classification of multiple reflections in time-domain e.m.~inverse scattering of multi-layered media is presented. The existence of multiples limits the capabilities of inversion algorithms, thus suitable identification and suppression techniques should be applied to reduce this undesired effect. Assuming a scenario composed of loss-less and non-dispersive media, and providing an accurate time delay estimation (TDE) of backscattered signals, the proposed method allows not only to evaluate the presence of multiples and discriminate them from primary reflections, but also to determine their propagation paths. Preliminary tests performed on FDTD simulated data have shown its potentialities to effectively handle multiple reflections and therefore to enhance the e.m. signals backscattered by primary reflectors.

1. Essenreiter, R., M. Karrenbach, and S. Treitel, "Multiple reflection attenuation in seismic data using backpropagation," IEEE Transactions on Signal Processing, Vol. 46, No. 7, 2001-Jul. 2011, 1998.
doi:10.1109/78.700971

2. Backus, M. and J. Simmons, "Multiple reflections as an additive noise limitation in seismic reflection work," Proceedings of the IEEE, Vol. 72, No. 10, 1370-1384, Oct. 1984.
doi:10.1109/PROC.1984.13024

3. Zhou, B. and S. Greenhalgh, "Multiple suppression by a waveequation extrapolation method," Explor. Geophys., Vol. 22, No. 2, 481-484, 1991.
doi:10.1071/EG991481

4. Essenreiter, R., M. Karrenbach, and S. Treitel, "Identification and classification of multiple reflections with self-organizing maps," Geophysical Prospecting, Vol. 49, No. 3, 341-352, 2001.
doi:10.1046/j.1365-2478.2001.00261.x

5. Lahouar, S. and I. L. Al-Qadi, "Automatic detection of multiple pavement layers from GPR data," NDT & E International, Vol. 41, No. 2, 69-81, 2008.
doi:10.1016/j.ndteint.2007.09.001

6. Lee, J. S., C. Nguyen, and T. Scullion, "A novel, compact, low-cost, impulse ground-penetrating radar for nondestructive evaluation of pavements," IEEE Transactions on Instrumentation and Measurement, Vol. 53, No. 6, 1502-1509, Dec. 2004.
doi:10.1109/TIM.2004.827308

7. Verma, P. K., A. N. Gaikwad, D. Singh, and M. J. Nigam, "Analysis of clutter reduction techniques for through wall imaging in UWB range," Progress In Electromagnetics Research B, Vol. 17, 29-48, 2009.
doi:10.2528/PIERB09060903

8. Moutinho, L., J. L. Porsani, and M. J. Porsani, "Deconvolução preditiva de dados GPR adquiridos sobre lâmina d'Água: Exemplo do rio taquari, pantanal matogrossense," Revista Brasileira de Geofísica, Vol. 23, 61-74, Mar. 2005.

9. Nakashima, Y., H. Zhou, and M. Sato, "Estimation of groundwater level by GPR in an area with multiple ambiguous reflections," Journal of Applied Geophysics, Vol. 47, No. 3--4, 241-249, 2000.

10. Zhao, Y., J. Wu, X. Xie, J. Chen, and S. Ge, "Multiple suppression in GPR image for testing back-filled grouting within shield tunnel," 2010 13th International Conference on Ground Penetrating Radar (GPR), Jun. 1--6, 2010.

11. Mordell, L., Diophantine Equations, Academic Press, 1969.

12. Rosen, K. H. and J. G. Michaels, Handbook of Discrete and Combinatorial Mathematics, CRC Press, 2000.

13. Wilf, H. S., Generatingfunctionology, A. K. Peters, Ltd., 2006.

14. Sertöz, S., "On the number of solutions of a diophantine equation of frobenius," Discrete Mathematics and Applications, Vol. 8, 153-162, 1998.
doi:10.1515/dma.1998.8.2.153

15. Komatsu, T., "On the number of solutions of the diophantine equation of frobenius --- General case," Mathematical Communications, Vol. 8, 195-206, Dec. 2003.

16. Aardal, K., C. A. J. Hurkens, and A. K. Lenstra, "Solving a system of linear diophantine equations with lower and upper bounds on the variables," Math. Oper. Res., Vol. 25, 427-442, Aug. 2000.
doi:10.1287/moor.25.3.427.12219

17. Lenstra, A., H. Lenstra, and L. Lovász, "Factoring polynomials with rational coefficients," Math. Ann., Vol. 261, 515-534, 1982.
doi:10.1007/BF01457454

18. Bryant, R. E., "Graph-based algorithms for boolean function manipulation," IEEE Transactions on Computers, Vol. 35, 677-691, 1986.
doi:10.1109/TC.1986.1676819

19. Giannopoulos, A., "Modelling ground penetrating radar by GprMax," Construction Building Mater., Vol. 19, No. 10, 755-762, Dec. 2005.
doi:10.1016/j.conbuildmat.2005.06.007

20. Courant, R., K. Friedrichs, and H. Lewy, "On the partial difference equations of mathematical physics," IBM J. Res. Dev., Vol. 11, 215-234, Mar. 1967.
doi:10.1147/rd.112.0215

21. Protiva, P., J. Mrkvica, and J. Macháč, "Time delay estimation of UWB radar signals backscattered from a wall," Microwave and Optical Technology Letters, Vol. 53, No. 6, 1444-1450, 2011.
doi:10.1002/mop.25985

22. Caorsi, S. and M. Stasolla, "Electromagnetic infrastructure monitoring: the exploitation of GPR data and neural networks for multi-layered geometries," Proc. of IGARSS'10, Honolulu, Hawaii, USA, Jul. 25--30, 2010.

23. Saarenketo, T. and T. Scullion, "Road evaluation with ground penetrating radar," Journal of Applied Geophysics, Vol. 43, No. 2--4, 119-138, 2000.
doi:10.1016/S0926-9851(99)00052-X

Dr. Salvatore Caorsi

Dr. Mattia Stasolla