Estimating the permittivity of heterogeneous mixtures based on the permittivity of their components is of high importance with many applications in ground penetrating radar (GPR) and in electrodynamics-based sensing in general. Complex Refractive Index Model (CRIM) is the most mainstream approach for estimating the bulk permittivity of heterogeneous materials and has been widely 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 optimised 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-voids 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.

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 position subsurface targets, especially those located at shallow depths, at their true position in depth. As the transmitted and received signals from GPR antennas are affected by the presence of different materials with varying electromagnetic properties, adjusting the time zero appropriately is important, but often not straightforward to position accurately. This paper uses a realistic three‐dimensional 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 also needed around how the two‐way travel time of the reflected GPR wavelet is estimated. 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.

<p>The estimation of the bulk permittivity of heterogeneous mixtures is of great interest for many Ground Penetrating Radar (GPR) and electromagnetic sensing applications [1], [2]. The most used method for estimating the bulk permittivity is the Complex Refractive Index Model (CRIM). The simplicity of this method is one its advantages however, the accuracy of the permittivity estimation has not been tested. Here, the CRIM model’s shape factor is examined and optimised in order to achieve a more accurate concrete bulk permittivity estimation. The concrete components are aggregate particles, cement particles, air-voids and moisture content; and they are randomly distributed with different volume percentages to produce various combinations. These combinations are modelled using the Finite-Difference Time-Domain (FDTD) method as it is an accurate and computationally efficient method [3]. The numerical modelling is then used to predict the bulk permittivity allowing to fine-tune CRIM model’s shape factor. The models are modelled in 3D and a GSSI-like antenna structure is used as the transmitting source [4]. The permittivity estimation uses an accurate time-zero method, which increases the accuracy of the estimated bulk permittivity hence, the shape factor [5], [6]. The results have shown that the optimised CRIM model over-performs the original CRIM model shape factor therefore, a better and more accurate bulk permittivity estimation is achieved for concrete mixtures.</p><p> </p><p><strong>References </strong></p><p>[1] Daniels, D. J., (2004), Ground Penetrating Radar, 2nd ed. London, U.K., Institution of Engineering and Technology.</p><p>[2] Annan, A. P., (2005), Ground Penetrating Radar,  in Investigations in Geophysics, Society of Exploration Geophysicists, pp. 357-438.</p><p>[3] Taflove, A., Hagness, S. C., (2005), Computational electromagnetic: The Finite-Difference Time-Domain Method, Artech House, Norwood.</p><p>[4] Warren, C., & Giannopoulos, A., (2011), Creating Finite-Difference Time-Domain Models of Commercial Ground Penetrating Radar Antenna Using Taguchi’s Optimization Method, Geophysics, 76(2), G37-G47.</p><p>[5] Zadhoush, H., Giannopoulos, A., Giannakis, I., (2020), Optimising GPR time-zero adjustment and two-way travel time wavelet measurement using a realistic 3D numerical model, Near Surface Geophysics, Under review (Minor revisions).</p><p>[6] Zadhoush, H., (2020), Numerical Modelling of Ground Penetrating Radar for Optimization of the Time-zero Adjustment and Complex Refractive Index Model, PhD Thesis Submitted at The University of Edinburgh.</p>

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