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[1] Pajewski, L., Benedetto, A., Derobert, X., Giannopoulos, A., Loizos, A., Manacorda, G., et al., Applications of Ground Penetrating Radar in Civil Engineering – COST Action TU1208, 2013.
[2] Warren, C., Chiwaridzo, N. & Giannopoulos, A., Radiation characteristics of a highfrequency antenna in different dielectric environments. 15th International Conference on Ground Penetrating Radar – GPR, Brussels, Belgium, pp. 796–801, 2014.
[3] Gürel, L. & Oguz, U., Three-dimensional FDTD modeling of a ground-penetrating radar. IEEE Transaction on Geoscience and Remote Sensing, 38(4), 2000.
[4] Cassidy, N.J. & Millington, T.M., The application of finite-difference time-domain modelling for the assessment of gpr in magnetically lossy materials. Journal of Applied Geophysics, 67(4), pp. 296–308, 2009. [Crossref]
[5] Shangguan, P. & Al-Qadi, I.L., Calibration of FDTD simulation of GPR signal for asphalt pavement compaction monitoring. Geoscience and Remote Sensing, IEEE Transactions on, 53(3), pp. 1538–1548, 2015.
[6] Poljak, D. & Roje, V., Time domain calculation of the parameters of thin wire antennas and scatterers in a half-space configuration. IEE Proceeding Microwaves Antennas and Propagation, 145(1), pp. 57–63, 1998. [Crossref]
[7] Poljak, D., Tham, C.Y., McCowen, A. & Roje, V., Transient analysis of two coupled horizontal wires over a real ground. IEE Proceding Microwave, Antnnas and Propagation, 147, pp. 87–94, 2000.
[8] Poljak, D., Advanced Modeling in Computational Electromagnetic Compatibility, John Wiley and Sons: New York, 2007. [Crossref]
[9] Poljak, D., Sesnic, S., Paric, D. & El Khamlichi Drissi, K., Direct time domain modeling of the transient field transmitted in a dielectric half-space for GPR applications. In Electromagnetics in Advanced Applications (ICEAA), 2015 International Conference on, pp. 345–348, 2015. [Crossref]
[10] Warren, C., Pajewski, L., Poljak, D., Ventura, A., Giannopoulos, A. & Sesnic, S., A comparison of finite-difference, finite-integration, and integral-equation methods in the time-domain for modelling ground penetrating radar antennas, GPR 2016.
[11] Lallechere, S., Antonijevic, S., El Khamlichi Drissi, K. & Poljak, D., Optimized numerical models of thin wire above an imperfect and lossy ground for GPR statistics. In Electromagnetics in Advanced Applications (ICEAA), 2015 International Conference on, pp. 907–910, 2015. [Crossref]
[12] Dodig, H., Lallechere, S., Bonnet, P., Poljak, D. & El Khamlichi Drissi, K., Stochastic sensitivity of the electromagnetic distributions inside a human eye modeled with a 3D hybrid BEM/FEM edge element method. Engineering Analysis with Boundary Elements, 49, pp. 48–62, 2014. [Crossref]
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Open Access
Research article

Stochastic Post-Processing of the Deterministic Boundary Element Modelling of the Transient Electric Field from Gpr Dipole Antenna Propagating Through Lower Half-Space

d. poljak1,
s. sesnic1,
s. lallechere2,
k. el khamlichi drissi2
1
University of Split, Split, Croatia
2
Blaise Pascal University, Clermont-Ferrand, France
International Journal of Computational Methods and Experimental Measurements
|
Volume 5, Issue 5, 2017
|
Pages 678-685
Received: N/A,
Revised: N/A,
Accepted: N/A,
Available online: N/A
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Abstract:

The paper deals with time domain-deterministic stochastic assessment of a transient electric field generated by a ground penetrating radar (GPR) dipole antenna and transmitted into a lower half-space. The deterministic time domain formulation is based on the space-time Hallen integral equation for half-space problems. The Hallen equation is solved via the Galerkin–Bubnov variant of the Indirect Boundary Element Method (GB-IBEM) and the space-time current distribution along the dipole antenna is obtained, thus providing the field calculation. The field transmitted into the lower medium is obtained by solving the corresponding field integrals.

As GPR systems are subjected to a rather complex environment, some input parameters, for example the antenna height over ground or earth properties, are partly or entirely unknown and, therefore, a simple stochastic collocation (SC) method is used to properly access relevant statistics about GPR time responses. The SC approach also aids in the assessment of corresponding confidence intervals from the set of obtained numerical results. The expansion of statistical output in terms of mean and variance over a polynomial basis, via the SC method, is shown to be a robust and efficient approach providing a satisfactory convergence rate.

Keywords: deterministic boundary element modelling, ground penetrating radar, hallen integral equation, stochastic collocation method, time domain, transmitted field
Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

References
[1] Pajewski, L., Benedetto, A., Derobert, X., Giannopoulos, A., Loizos, A., Manacorda, G., et al., Applications of Ground Penetrating Radar in Civil Engineering – COST Action TU1208, 2013.
[2] Warren, C., Chiwaridzo, N. & Giannopoulos, A., Radiation characteristics of a highfrequency antenna in different dielectric environments. 15th International Conference on Ground Penetrating Radar – GPR, Brussels, Belgium, pp. 796–801, 2014.
[3] Gürel, L. & Oguz, U., Three-dimensional FDTD modeling of a ground-penetrating radar. IEEE Transaction on Geoscience and Remote Sensing, 38(4), 2000.
[4] Cassidy, N.J. & Millington, T.M., The application of finite-difference time-domain modelling for the assessment of gpr in magnetically lossy materials. Journal of Applied Geophysics, 67(4), pp. 296–308, 2009. [Crossref]
[5] Shangguan, P. & Al-Qadi, I.L., Calibration of FDTD simulation of GPR signal for asphalt pavement compaction monitoring. Geoscience and Remote Sensing, IEEE Transactions on, 53(3), pp. 1538–1548, 2015.
[6] Poljak, D. & Roje, V., Time domain calculation of the parameters of thin wire antennas and scatterers in a half-space configuration. IEE Proceeding Microwaves Antennas and Propagation, 145(1), pp. 57–63, 1998. [Crossref]
[7] Poljak, D., Tham, C.Y., McCowen, A. & Roje, V., Transient analysis of two coupled horizontal wires over a real ground. IEE Proceding Microwave, Antnnas and Propagation, 147, pp. 87–94, 2000.
[8] Poljak, D., Advanced Modeling in Computational Electromagnetic Compatibility, John Wiley and Sons: New York, 2007. [Crossref]
[9] Poljak, D., Sesnic, S., Paric, D. & El Khamlichi Drissi, K., Direct time domain modeling of the transient field transmitted in a dielectric half-space for GPR applications. In Electromagnetics in Advanced Applications (ICEAA), 2015 International Conference on, pp. 345–348, 2015. [Crossref]
[10] Warren, C., Pajewski, L., Poljak, D., Ventura, A., Giannopoulos, A. & Sesnic, S., A comparison of finite-difference, finite-integration, and integral-equation methods in the time-domain for modelling ground penetrating radar antennas, GPR 2016.
[11] Lallechere, S., Antonijevic, S., El Khamlichi Drissi, K. & Poljak, D., Optimized numerical models of thin wire above an imperfect and lossy ground for GPR statistics. In Electromagnetics in Advanced Applications (ICEAA), 2015 International Conference on, pp. 907–910, 2015. [Crossref]
[12] Dodig, H., Lallechere, S., Bonnet, P., Poljak, D. & El Khamlichi Drissi, K., Stochastic sensitivity of the electromagnetic distributions inside a human eye modeled with a 3D hybrid BEM/FEM edge element method. Engineering Analysis with Boundary Elements, 49, pp. 48–62, 2014. [Crossref]
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Poljak, D., Sesnic, S., Lallechere, S., & Drissi, K. E. K. (2017). Stochastic Post-Processing of the Deterministic Boundary Element Modelling of the Transient Electric Field from Gpr Dipole Antenna Propagating Through Lower Half-Space. Int. J. Comput. Methods Exp. Meas., 5(5), 678-685. https://doi.org/10.2495/CMEM-V5-N5-678-685
D. Poljak, S. Sesnic, S. Lallechere, and K. E. K. Drissi, "Stochastic Post-Processing of the Deterministic Boundary Element Modelling of the Transient Electric Field from Gpr Dipole Antenna Propagating Through Lower Half-Space," Int. J. Comput. Methods Exp. Meas., vol. 5, no. 5, pp. 678-685, 2017. https://doi.org/10.2495/CMEM-V5-N5-678-685
@research-article{Poljak2017StochasticPO,
title={Stochastic Post-Processing of the Deterministic Boundary Element Modelling of the Transient Electric Field from Gpr Dipole Antenna Propagating Through Lower Half-Space},
author={D. Poljak and S. Sesnic and S. Lallechere and K. El Khamlichi Drissi},
journal={International Journal of Computational Methods and Experimental Measurements},
year={2017},
page={678-685},
doi={https://doi.org/10.2495/CMEM-V5-N5-678-685}
}
D. Poljak, et al. "Stochastic Post-Processing of the Deterministic Boundary Element Modelling of the Transient Electric Field from Gpr Dipole Antenna Propagating Through Lower Half-Space." International Journal of Computational Methods and Experimental Measurements, v 5, pp 678-685. doi: https://doi.org/10.2495/CMEM-V5-N5-678-685
D. Poljak, S. Sesnic, S. Lallechere and K. El Khamlichi Drissi. "Stochastic Post-Processing of the Deterministic Boundary Element Modelling of the Transient Electric Field from Gpr Dipole Antenna Propagating Through Lower Half-Space." International Journal of Computational Methods and Experimental Measurements, 5, (2017): 678-685. doi: https://doi.org/10.2495/CMEM-V5-N5-678-685
POLJAK D， SESNIC S， LALLECHERE S， et al. Stochastic Post-Processing of the Deterministic Boundary Element Modelling of the Transient Electric Field from Gpr Dipole Antenna Propagating Through Lower Half-Space[J]. International Journal of Computational Methods and Experimental Measurements， 2017， 5(5)： 678-685. https://doi.org/10.2495/CMEM-V5-N5-678-685