# Two-Dimensional Linear Inversion of GPR Data with a Shifting Zoom along the Observation Line
## 5 Experimental Results
In the lower image, a time cut has also been done, in order to focus on the depth range of interest. Figure 10 depicts the result when the shifting zoom procedure is applied. It can be seen that the stitching lines disappeared and some artifacts (especially for the investigation domain of the second target) were mitigated. The effect would be stronger still if the targets were not centered with respect to their relative investigation domains. We simulated such a situation by shifting the starting point of the inverted data 35 cm beyond the initial point of Figures 9 and 10. Then, in order to keep the comprehensive length of the B-scan equal to 240 cm, we fictitiously added identically null data on the right-hand side of the gathered data. In this way, it is as if the targets were pulled 35 cm towards the left-hand side (we could not do this experiment by physically gathering a new B-scan, shifted 35 cm with respect to the previous one, due to the comprehensive size of the sand pool). Then, we inverted the data along three adjacent investigation domains in the same way as adopted for Figure 10. The results are shown in Figure 11. Now, the three targets have become peripheral to the relative investigation domains, and the consequence is some meaningful deformation (particularly evident with respect to the central target and to the right-hand side target, which cross the boundary between two adjacent investigation domains). It can be also appreciated that in Figure 11, the deformations and the artefacts tend to be quite asymmetrical, because the view angles under which the three targets are seen now, are meaningfully asymmetrical. Finally, we applied the shifting zoom to the inversion of the shifted data. The result is shown in Figure 12, and, as shown, the targets are shifted with respect to Figures 9 and 10, but no substantial deformation can be found on the targets, with respect to Figures 9 and 10. Figure 10: Reconstruction achieved with a shifting zoom. The shifting step is 1 cm, equal to the spatial step of the data, and to the horizontal size of the pixels, for the representation of the reconstruction. Figure 9: Reconstruction achieved with three adjacent investigation-observation domains (0.8 m long). Finally, in Figure 13, the result of a migration performed on the same data of Figures 9 and 10 is reported. Specifically, a Kirchhoff migration was performed on 41 traces, making use of the same relative permittivity (2.37) exploited for the inverse scattering results. The migration was performed by importing the synthetic time data into Reflexw (the previous elaborations were performed by means of homemade MATLAB routines). After migration, the data were re-imported into MATLAB and a time-depth conversion was performed for the representation. It can be seen that the effects of the ringing of the antennas and the effects of the background removal are more visible. Figure 11: Reconstruction achieved with three adjacent investigation-observation domains, under a data shift of 35 cm. Figure 12: Reconstruction achieved with the shifting zoom, under a data shift of 35 cm. Figure 13: Result of a Kirchhoff migraton performed on the same data as in Figure 8.0