## 5 Experimental Results  
An experimental setup was organized at the Laboratory of Hydrogeophysics of the Institute of Methodologies for Environmental Analyses IMAA-CNR, in Marsico Nuovo (Potenza, Italy). In particular, a small tank of 70 \(\times\) 50 \(\times\) 45 cm was filled up, constituting a two-layered medium with a curved interface between the layers. The lower layer constituted wet sand, whereas the upper one constituted dry gravel. In Figure 11, a photograph of the tank during its filling is shown. Four metallic targets were inserted according to the scheme shown in Figure 12. In particular, the targets \"of interest\" for our purposes are A and B, whereas targets C and D are exploited for the direct evaluation of the propagation velocity. In fact, they are displaced in a flat zone of the interface between the two layers at a known depth. Consequently, the return time from their echoes will be exploited in order to evaluate the propagation velocity of the waves in the two layers. The GPR system exploited was a Ris Hi-mode equipped with an antenna at a nominal central frequency of 2 GHz. A single Bscan crossing all the metallic targets (which are essentially rods parallel to each other) was gathered. The measurement line was 63 cm long, the time bottom scale was 16 ns, the spatial step was 2 mm, and the time step was 0.0156 ns. In Figure 13, the preprocessed (not focused) data are shown. Pre-processing constituted zero timing, subtracting the average on 51 traces (i.e., shifting background removal performed on 51 traces), gain vs. depth, and 1D Butterworth filtering, plus a final  
Figure 10: Depth slices achieved from all the Bscans after joined migration but without combined time–depth conversion. time cut reducing the time bottom scale to 8 ns. In particular, in Figure 13, we indicate the vertexes of the diffraction curves of the four metallic targets with the same symbols used in Figure 12. In Figure 13, the interface between the two layers is clearly appreciated. In particular, the subtracted average has been adopted in order to avoid the production of spurious horizontal belts due to the background removal [37] on all the traces. Offline from this preprocessing, in order to ensure a more reliable evaluation of the propagation velocity in the second medium, in Figure 14, we show the result of another preprocessing performed on the same data, where the subtracted average has been replaced by background removal on all the traces. This has generated the spurious horizontal belt clearly visible in the figure. The imaging provided by Figure 14 is certainly worse than that provided by Figure 13; however, with regard to targets C and D, the horizontal belts make their time depth levels clearer. In Figure 14, we have also indicated target B, whereas target A disappears because it is covered by the strength of the horizontal belt generated by the diffraction curve of target D.  
As shown in Figure 12, the depth of target D is equal to 27 cm (bottom of the first layer) and the depth of target C is equal to 45 cm, which represents 18 cm in the deeper layer. Their time depth levels are instead (from Figure 14) 2.8 ns and 6.2 ns, respectively (which means 3.4 ns of time depth in the second layer). From these data, we retrieve a propagation velocity  
Figure 11: Tank filled up with sand gravel and metallic targets. Figure 12: Schematic of the ground truth. of 19.2 cm/ns for the upper layer (made up of dry gravel) and 10.6 cm/ns for the second layer (made up of wet sand). The diffraction hyperbola of target B in Figure 12 provides a propagation velocity of 20 cm/ns for the upper layer, which is in good agreement with the values retrieved from target D in Figure 14. Instead, from Figure 13, the diffraction curve of target A matches the propagation velocity of 13 cm/ns, with a meaningful discrepancy with respect to the evaluation provided by target C, as expected. In Figure 15, the result of joined migration is shown.