Numerical modelling of ground penetrating radar for optimization of the time-zero adjustment and complex refractive index model

Time-zero adjustment or the true ground surface for Ground Penetrating Radar (GPR) applications is a very important aspect and an essential factor in order to carry out accurate shallow depth measurements. As the transmitted and received signals from GPR antennas are affected by the presence of different materials with various dielectric constants and electromagnetic properties adjusting the time-zero appropriately is important. This study uses a realistic Three Dimensional (3D) numerical model of a GPR transducer in order to examine where is the best location for time-zero on a GPR trace. It is shown that in order to establish a robust and consistent time-zero position careful consideration is needed also of the way the two-way travel time of the reflected GPR wavelet is estimated as well. Starting with a simple homogeneous model with a set of different targets a better process of time-zero adjustment and time picking of the GPR wavelets is put forward that is verified using further more complex and realistic heterogeneous models. Further verification is obtained by using experimental data. Estimating the permittivity of heterogeneous mixtures based on the permittivity of their individual components is of high importance with many applications in GPR and in electrodynamics-based sensing in general. The Complex Refractive Index Model (CRIM) is the most mainstream approach for estimating the bulk permittivity of heterogeneous materials and has widely been applied for GPR applications. The popularity of CRIM is primarily based on its simplicity while its accuracy has never been rigorously tested. In the current study, an optimized shape factor is derived that is fine-tuned for modelling the dielectric properties of concrete. The bulk permittivity of concrete is expressed with respect to its components i.e, aggregate particles, cement particles, air-void and volumetric water fraction. Different combinations of the above materials are accurately modelled using the Finite-Difference Time-Domain (FDTD) method. The numerically estimated bulk permittivity is then used to fine-tune the shape factor of the CRIM model. Then, using laboratory measurements it is shown that the revised CRIM model over-performs the default shape factor and provides with more accurate estimations of the bulk permittivity of concrete. Numerical modelling of a heterogeneous concrete model and a bowtie antenna with a separate transmitter and receiver that are able to move independently are also presented in this study. Both models are used for the optimisation of the time-zero position and the CRIM model shape factor

Método das diferenças finitas no domínio do tempo aplicado à grade tridimensional formada por prismas hexagonais

Orientador : Prof. Dr. Sérgio ScheerTese (doutorado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Métodos Numéricos em Engenharia. Defesa: Curitiba, 02/06/2016Inclui referências : f. 211-215Resumo: O método das diferenças finitas no domínio do tempo, mais conhecido em inglês como Finite-Difference Time-Domain (FDTD), foi aplicado em uma grade tridimensional de prismas hexagonais, tendo como objetivo produzir menos anisotropia de velocidade de fase numérica que o método FDTD Yee (com células hexaédricas). Comparações de propagação de onda são feitas entre o método FDTD com grade de prismas hexagonais e o método FDTD Yee, com o objetivo de validar esse novo método FDTD. As análises teóricas da anisotropia, dispersão e condição de estabilidade numéricas são realizadas usando a análise de Fourier no método FDTD com grade de prismas hexagonais e comparadas com aquelas realizadas para o método FDTD Yee. Medidas de anisotropia numérica neste novo método FDTD são comparadas com os resultados da análise de Fourier. Uma formulação para camadas de absorção casadas perfeitamente, que emulam um espaço infinito, é desenvolvida para a grade de prismas hexagonais, e medidas de reflexão dessas camadas de absorção são comparadas com aquelas das camadas de absorção da grade Yee. Uma onda plana é aplicada na grade de prismas hexagonais usando a formulação de regiões de campos total e espalhado; e medidas de espalhamento de campo de placa retangular e esfera (ambas usando condutor elétrico perfeito) são realizadas na grade de prismas hexagonais, e comparadas com as medidas de espalhamento, para os mesmos objetos, na grade Yee e soluções analíticas. Um algoritmo de compensação de dispersão numérica é desenvolvido para o método FDTD com grade de prismas hexagonais, com a condição de que as dimensões da grade no plano x-y são muito maiores que a dimensão z (altura). Medidas de dispersão numérica na grade de prismas hexagonais e comparações com aquelas da grade Yee demonstram a eficácia do algoritmo proposto, que permite o uso de grade de prismas hexagonais com menor densidade de malha que a grade Yee, para uma certa precisão desejada. Os resultados obtidos são promissores para o uso do método FDTD com grade de prismas hexagonais em simulações de propagação de ondas eletromagnéticas irradiadas por redes Wireless em edificações, onde, normalmente, as dimensões no plano horizontal são muito maiores que a altura. Palavras-chave: FDTD. Dispersão numérica. Anisotropia numérica. Prisma hexagonal. Célula hexagonal. Propagação de onda. Redes sem fio.Abstract: The finite-difference time-domain (FDTD) method was applied at a grid of hexagonal prisms, with the objective to yield less numerical anisotropy of phase velocity than the Yee FDTD method (with hexahedral cells). Comparisons of wave propagation are made between the FDTD method with grid of hexagonal prisms and the Yee FDTD method, with the aim of checking the validity of this new FDTD method. The theoretical analyses of the numerical anisotropy, dispersion and stability condition are obtained using the Fourier analysis in the FDTD method with grid of hexagonal prisms, and they are compared with those accomplished for Yee FDTD method. Measurements of numerical anisotropy are accomplished in this new FDTD method, and then they are compared with the results of the Fourier analysis. A formulation for perfectly matched layer absorbing boundary conditions, which emulates an infinite space, is developed for a grid of hexagonal prisms, and reflection measurements of these perfectly matched layers (PMLs) are compared with those of the Yee grid PMLs. A plane wave is applied in the grid of hexagonal prisms using the total-field/scattered-field formulation, and scattered-field measurements of rectangular plate and sphere (both using perfect electric conductor) are made in the grid of hexagonal prisms, and the next ones are compared with the scattered-field measurements, for the same objects, in the Yee grid and theoretical solutions. An algorithm of numerical dispersion compensation is developed for the FDTD method with grid of hexagonal prisms, with the condition that the grid dimensions in the x-y plane are considerably larger than the z-dimension (height). Measurements of numerical dispersion in the grid of hexagonal prisms and comparisons with those of the Yee grid, it proves the effectiveness of the proposed algorithm, which allows using grid of hexagonal prisms with less density of mesh than the Yee grid, for a certain desirable accuracy. The obtained results are promising to use the FDTD method with grid of hexagonal prisms in simulations of electromagnetic wave propagation yielded for wireless networks in indoor buildings, where the dimensions in the horizontal plane are usually much larger than the height. Keywords: FDTD. Numerical dispersion. Numerical anisotropy. Hexagonal prisms. Hexagonal cells. Wave propagation, Wireless networks