## 3 Results and Discussion  
The laboratory data were processed by using the ReflexW software, but the amplitude picking was performed manually. To prevent the influence of any DC or very low frequency components on the amplitude values, we decided to analyze the peak-to-peak amplitudes (sum of positive and negative peaks) of the reflected waves. We did not make any amplitude compensation for possible variations of the power radiated by the TX antenna during the measurements since the antenna was properly warmed up before the measurements, and the time needed to collect all the data, before and after filling the fracture, was short enough to assume that the radiated power could not be affected by drift phenomena induced by battery discharge. GPR findings before and after filling the thin layer with resin are shown in Table 2. A 33% amplitude difference between the air-filled and the resin-filled fracture was predicted based on the thin bed analytical model (Figure 7). An amplitude decrease is confirmed by the real data, but the intensity of the amplitude variation is less remarkable, although high enough to be observed on the real data. These findings indicate that GPR can detect the change in the filling material at these thickness values, i.e., it can be used to perform a quality check of the resin injection. However, the accuracy is not high enough to use the amplitude variations to estimate the permittivity of the filling material, i.e., to identify the filling material. Since the amplitude decrease observed in the results of laboratory measurements is lower than the prediction, \begin{table}
\begin{tabular}{c c} \hline
**Fracture Thickness (mm)** & **Difference in the Peak-to-Peak Amplitude (\%)** \\ \hline
1 & 20.0 \\
2 & 12.1 \\ \hline \end{tabular}
\end{table} 
Table 2: Variations in the peak-to-peak amplitudes of the air-filled and resin-filled layers between marble blocks. Figure 8: Comparing the predicted amplitudes for the air-filled fractures versus the PVC-filled fractures with a 3 GHz antenna. Circles: air data, stars: PVC data. the permittivity of the filling material would be underestimated. Nevertheless, the quantitative interpretation of the amplitude variations is beyond the objectives of this work. Our assumption is that we know the injected material and what we need to control with a nondestructive method is only its diffusion within the injected fractures. The results of the laboratory tests where PVC was used as a substitute of the resin are shown in Figure 9. The plots compare the expected theoretical trend with the observed amplitude trend for the air-filled fractures (left) and the PVC-filled fractures (right). The graphs of the real amplitudes have been properly rescaled before plotting to fit the theoretical values of the reflection coefficient calculated at the thickness of 16 mm. We observe an encouraging similarity between the theoretical and the experimental trends. It is also encouraging to observe that it was possible to pick the amplitudes of the thin bed reflections even when the fracture thickness is very small (0.25 mm). Figure 10 illustrates the quantitative comparison of the percentual amplitude variations as predicted from the thin bed theory and as observed experimentally. For most thicknesses, the observed values are very similar to the values predicted by the thin bed theory. More specifically, we can notice that the final trend of the theoretical plot that is progressively increasing, arriving at 35% for 16 mm, is not perfectly matched by the real data that start to deviate from this trend when the thickness overcomes 13 mm. However, this is consistent with the theory, because according to the resolution limit determined by [PERSON]'s criterion mentioned in Section 2.3, the maximum thickness that we can consider as a thin bed after filling the layer is about 14 mm. Thus, the theoretical predictions become questionable for thickness values larger than 14 mm.