## 2 Materials and Methods
### Laboratory Measurements
#### 2.2.2 GPR Measurements  
All GPR measurements were performed in the time-triggered mode, placing the antenna in the center of the upper block (Figure 4a). As shown in Figure 4a, the block above the thin layer was rotated 45\({}^{\circ}\) with respect to the lower blocks. This setup allows easier handling of the upper block, which had to be removed and replaced many times to change the fracture aperture. Prudentially, we performed a test to compare the data before and after rotation of the upper block without observing any difference. As a matter of fact, no artifacts are expected from this modification of the setup because the distance between the antenna and any edge of the first and second marble block is still equal or larger than 20 cm, thus ensuring that no other signals except the thin bed reflection can arrive within the first 3 ns. At the first step, GPR measurements were designed to calibrate the wave velocity in marble blocks in order to obtain an accurate estimation of the marble permittivity, which is a fundamental parameter to predict the thin bed behavior. In order to estimate the EM wave velocity in the blocks, the antenna was placed on the top block, and a metal shield was placed below it. The test was also performed with all the four blocks (Figure 4b). A sharp reflection of the shield was observed at the known depth (10 cm in the first record and 40 cm in the second record). The difference between the recorded two-way travel times is an accurate measurement of the time taken by the radar wave to travel forward and backward in 30 cm of marble material. In principle, this method is better than using only the single block data. The advantage of making two measurements rather than one is that with only one measurement, the result is affected by the accuracy of the time calibration,  
Figure 3: **(a)** The procedure to prepare resin sheets with the thickness of 1 mm in the laboratory: 1. Mixing resin components; 2. Preparing a flat surface covered by a plastic film and adding adhesive silicone side walls; 3. Pouring the volume of resin required to prepare a 40 \(\times\) 40 \(\times\) 0.1 cm layer, always keeping the surface horizontal; 4. Detaching the dried resin layer. **(b)** PVC material that was used instead of resin in the fractures (block contacts). which is always questionable. The background signal is different from the shield reflection and thus we should not use the difference between the background and the reflection for accurate velocity calculation. On the other hand, with two measurements on two different thickness values, the result is not affected by the time calibration. Therefore, we subtracted the time related to the reflection from the shield placed below one block from the time related to the reflection of the shield placed below all the four blocks. The result is thus the travel time of the wave along 60 cm of marble, which leads to calculating the wave velocity without any influence from the time calibration. Following this idea, the wave velocity was measured to be 10.2 cm/ns in the homogenous marble blocks used in this study, corresponding to a relative permittivity of 8.64. After estimating the velocity, GPR measurements were performed on air-filled and repaired fractures to test GPR response to thin layers. As mentioned earlier, due to economic problems and practical limitations, only two 1 mm-thick resin sheets were prepared. For these sheets, five measurements were performed with the following properties of the thin layer: 0 mm air, 1 mm air, 2 mm air, 1 mm resin, and 2 mm resin. Regarding using the PVC sheets, a more extended range of fracture thickness could be simulated. We performed GPR tests before and after fracture repair for fracture apertures as thin as 0.25 mm. The fracture aperture was gradually increased from 0.25 mm to 16 mm. Table 1 lists the 22 measurements that were performed on air-filled fractures with 22 different apertures, and then repeated after being filled with thin layers of PVC.