Proposing New Methods to Enhance the Low-Resolution Simulated GPR Responses in the Frequency and Wavelet Domains

Document Type : Research Paper


1 Mining Engineering Department, Arak University of Technology, Arak, Iran; School of Mining, College of Engineering, University of Tehran, Tehran, Iran

2 Mining Engineering Department, Isfahan University of Technology, Isfahan, Iran

3 School of Mining, College of Engineering, University of Tehran, Tehran, Iran


To date, a number of numerical methods, including the popular Finite-Difference Time Domain (FDTD) technique, have been proposed to simulate Ground-Penetrating Radar (GPR) responses. Despite having a number of advantages, the finite-difference method also has pitfalls such as being very time consuming in simulating the most common case of media with high dielectric permittivity, causing the forward modelling process to be very long lasting, even with modern high-speed computers. In the present study the well-known hyperbolic pattern response of horizontal cylinders, usually found in GPR B-Scan images, is used as a basic model to examine the possibility of reducing the forward modelling execution time. In general, the simulated GPR traces of common reflected objects are time shifted, as with the Normal Moveout (NMO) traces encountered in seismic reflection responses. This suggests the application of Fourier transform to the GPR traces, employing the time-shifting property of the transformation to interpolate the traces between the adjusted traces in the frequency domain (FD). Therefore, in the present study two post-processing algorithms have been adopted to increase the speed of forward modelling while maintaining the required precision. The first approach is based on linear interpolation in the Fourier domain, resulting in increasing lateral trace-to-trace interval of appropriate sampling frequency of the signal, preventing any aliasing. In the second approach, a super-resolution algorithm based on 2D-wavelet transform is developed to increase both vertical and horizontal resolution of the GPR B-Scan images through preserving scale and shape of hidden hyperbola features. Through comparing outputs from both methods with the corresponding actual high-resolution forward response, it is shown that both approaches can perform satisfactorily, although the wavelet-based approach outperforms the frequency-domain approach noticeably, both in amplitude and shape of the outputted hyperbola response.


[1] Goodman, D., (1994). Ground-Penetrating Radar simulation in engineering and archaeology. Geophys. v. 59, pp. 224-232.
[2] Karpat, E., Akır, M.C., Sevgi, L., (2009). Subsurface imaging, FDTD-based simulations and alternative scan/processing approaches. Microw. Opt. Techn. Let. v. 51, no. 4, pp. 1070-1075.
[3] Irving, J., Knight, R., (2006). Numerical modelling of ground penetrating radar in 2-D using MATLAB. Comput. & Geosci. v. 32, pp. 1247–1258.
[4] Giannopoulos, A., (2005). Modeling ground penetrating radar by GprMax. Constr. Build. Mater. v. 19, pp. 775-762.
[5] Cassidy, N.J., (2001). The application of mathematical modelling in the interpretation of Ground Penetrating Radar data. Ph.D. Thesis, Keele University.
[6] Chen, H.W., Huang, T.M., (1998). Finite- difference time- domain simulation of GPR data. J. Appl. Geophys. v. 40, pp. 139–163.
[7] Teixeria, F.L., Chew, W.C., Straka, M., Oristaglio, M.L., Wang, T., (1998). Finite- difference time- domain simulation of Ground Penetrating Radar on dispersive, inhomogeneous and conductive soils. IEEE. T. Geosci. Remote. v. 36, no. 6, pp. 1928–1937.
[8] Bergmann, T., Robertsson, J.O.A., Holliger, K., (1998). Finite- difference modelling of electromagnetic wave propagation in dispersive and attenuating media. Geophys. v. 63, no. 3, pp. 856–867.
[9] Yee, K.S., Chen, J.S., (1997). The finite- difference time- domain (FDTD) and the finite- volume time- domain (FVTD) methods in solving Maxwell’s equations. IEEE. T. Antenn. Propag. v. 45, no. 3, pp. 354–363.
[10] Roberts, R.L., Daniels, J.J., (1997). Modelling near-field GPR in three dimensions using the FDTD method. Geophys. v. 62, no. 4, pp. 1114–1126.
[11] Bourgeois, J.M., Smith, G.S., (1996). A fully three- dimensional simulation of a ground penetrating radar: FDTD theory compared with experiment. IEEE. T. Geosci. Remote. v. 34, pp. 36–44.
[12] Weedon, W.H., Rappaport, C.M., (1997). A general method for FDTD modelling of wave propagation in arbitrary frequency-dispersive media. IEEE. T. Antenn. Propag. v. 45, no. 3, pp. 401–409.
[13] Jol, H.M., (2009). Ground-Penetrating Radar theory and applications. First edition, Elsevier Science. 543 Pages.
[14] Delbò, S., Gamba, P., Roccato, D., (2000). A fuzzy shell clustering approach to recognize hyperbolic signatures in subsurface radar images. IEEE. T. Geosci. Remote. v. 38, no. 3, pp. 1447–1451.
[15] Strange, A., Chandran, V., Ralston, J., (2002). Signal processing to improve target detection using ground penetrating radar, Fourth Australasian Workshop on Signal Processing and Applications (WOSPA), Brisbane, Australia.
[16] Rossini, M., (2003). Detecting objects hidden in the subsoil by a mathematical method. Comput. Math. Appl. v. 45, no. 1, pp. 299–307.
[17] Lian Fei-yu, Li Qing, (2011). Recognition method based on SVM for underground pipe diameter size in GPR map. Inform. Elect. Eng. v. 9, no. 4, pp. 403-408.
[18] GPR2. htm
[19] Annan, A.P., (2001). Ground-penetrating radar workshop notes, Sensors and Software Inc. Mississauga, ON, Canada, 192 pages.
[20] Bergmann, T., Robertsson, J.O.A., Holliger, K. (1996). Numerical properties of staggered finite-difference solutions of Maxwell's equations for ground-penetrating radar modeling. Geophys. Res. Let. v. 23, no. 1, pp. 45-48.
[21] Georgakopoulos, S.V., Birtcher, C.R., Balanis, C.A., Renaut, R.A., (2002). Higher-order finite-difference schemes for electromagnetic radiation, scattering, and penetration, Part 1: theory. IEEE. Antenn. Propag. M., v. 44, pp. 134–142.
[22] Grossman, A., Morlet, J., (1984). Decomposition of Hardy functions into square integrable wavelets of constant shape. SIAM. J. Math. Anal. v. 15, no. 4, pp. 723-736.
[23] Walker, J.S., (2008). A primer on wavelets and their scientific applications, second edition, Chapman & Hall/CRC, Taylor & Francis Group.
[24] Gilbert, S., (1989). Wavelets and dilation equations: a brief introduction. SIAM Review, Published by: Soc. Ind. Appl. Math. v. 31, no. 4, pp. 614-627.
[25] Naik, S., Patel, N., (2013). Single image super resolution in spatial and wavelet domain. Int. J. Multi. Appl. (IJMA), v. 5, no. 4, pp. 23-32.
[26] Temizel, A., Vlachos, T., (2005). Image resolution up scaling in the wavelet domain using directional cycle spinning. J. Electron. Let. v. 41, pp. 119–121.
[27] Misiti, M., Misiti, Y., Oppenheim, G., Poggi, J.-M. (eds) (2007). Frontmatter, in wavelets and their applications, ISTE, London, UK. doi:10.1002/9780470612491.fmatter
[28] Jensen, A., Courharbo,, (2001). Rip Math: The Discrete Wavelet Transform, springer.