## 4 Numerical Results
It can be seen that a small distortion is introduced with regard to pipe P\({}_{2}\), whose image is no longer \"roundish\" and is influenced by the shape of the interface between the two layers. It can be also seen that P\({}_{2}\) now appears smaller than pipe P\({}_{3}\): this, however, is natural because it is related to the smaller wavelength in the second layer, which drives a better resolution. The same processing applied to the Bscan in Figure 8 was then applied to all of the Bscans, identifying the interface in the time domain between the two media each time. Of course, the shape of this interface changes for the Bscans directed along the short side of the observation grid with respect to those directed along the long side and generally changes from Bscan to Bscan. This processing produced 26 Bscans (11 along the long side and 15 directed along the short side) all properly focused and time-depth-converted, and from them, we retrieved depth slices. Let us specify that since the Bscans have undergone a combined time-depth conversion, they are vertically calibrated directly in meters, and so the slices achieved from them are determined directly in the spatial domain, unlike the customary slices that are determined in the time domain. Notwithstanding, the slicing in the spatial domain does not require the implementation of an algorithm. In particular, the slices can be produced with any commercial code accepting ASCII files as input: in this way, we only have to input the spatial bottom scale in meters to the code. Then, the code will \"understand\" the bottom scale as a number expressed in nanoseconds, but this is not relevant. A sequence of depth slices achieved from Bscans processed with a joined migration and combined time-depth-converted Bscan is shown in Figure 9. From the slices at subsequently deeper levels, we note a sort of belt directed along the short side of the slice, shifting from the left-hand side to the right-hand side progressively vs. the depth. This echo is the reflection provided by the interface between the two media at the considered depth level. Due to the shape of the interface, descending from the left- to the right-hand side of each (long) Bscan, this belt shifts toward the right-hand side at progressively deeper levels. Figure 7: Sixth processed Bscan on the long side. Joined migration is performed and applied but not combined time–depth conversion. Beyond this reflection, pipe P\({}_{1}\) is well identified between the depth levels of 40 and 50 cm, whereas pipes P\({}_{2}\) and P\({}_{3}\) are imaged between the depth levels of 90 and 100 cm, and correctly, they are at the same depth level. Pipe P\({}_{3}\) provides a stronger echo because it is displaced in the upper layer and there is no further interface beyond the air-soil one between the antennas and the pipe. On the other hand, it appears broken in the middle because of the overflying pipe P\({}_{1}\). This breaking effect is instead not evident with regard to pipe P\({}_{2}\) because the further interface between the upper and lower layer introduces more complicated scattering phenomena. Figure 3:0 Sixth processed Bscan on the long side. Both joined migration and combined time–depth conversion are applied. Figure 3:1 Depth slices achieved from all the Bscans after joined migration and combined time–depth conversion. For comparison, in Figure 10, we also propose the imaging achieved from Bscans focused through joined migration but not processed with a combined time-depth conversion. The depth levels are evaluated according to the propagation velocity in the upper layer. From Figure 10, we can see that while pipe P\({}_{3}\) is still correctly imaged, pipe P\({}_{2}\) is imaged more intensely between 140 and 150 cm. Moreover, the non-compensated apparent bending of pipe P\({}_{1}\) on the left-hand side generates an artifact resembling a target different from the pipe itself and extending along a depth of up to 60 cm or more, which makes it tricky to determine the correct interpretation of the data.