## 4 GPR Imaging Results  
A representative GPR section after the initial processing steps over a study line at the center of the grid is depicted in Figure 3a. By applying constant-velocity migration using all of the velocity values as depicted in the horizontal axis of Figure 4a, namely, from 0.04 to 0.24 m/ns, with a 0.005 m/ns step, the std of the local slopes of the migrated sections were calculated (Figure 4a). After linear detrending, the normalized inverse std values of the local slope distribution of each constant-velocity migrated section are shown in Figure 4b, using Equation (2). By assigning the specific weights of Figure 4b to each one of the constant-velocity migrated sections before stacking them, the stacking procedure for a range of velocities from 0.04 to 0.155 m/ns (Equation (3)) resulted in well-focused diffractions (comparison of Figure 3a,b), while on the contrary, blurriness from both the migration and the stacking procedure is evident. This can be circumvented by time-varying spectral whitening (Figure 5). The spectral whitening algorithm balances the amplitude spectrum in time gates of 1.5 times the duration of each trace in such away to achieve a dominant frequency up to 1.5 times its initial dominant frequency [23]. Figure 3: A representative GPR section after initial processing (**a**). The data of this section after multipath summation and depth conversion with V = 0.095 m/ns (**b**). Each GPR section of the grid underwent the aforementioned procedure and the result of the proposed methodology is highlighted by selected envelope depth slices. Consid  
Figure 4: The local slopes’ std values for each constant velocity migrated section (**a**) and the corresponding weights, evaluated using equation (2) after linear detrend, with which these sections contribute to the final stack of Figure 3b (**b**). Figure 5: The multipath summation depth section depicted in Figure 3b after time-varying spectral whitening. ering a mean velocity of 0.95 m/ns, we imaged depth slices at a depth of approximately 1.6 m (Figure 6) and 1.8 m (Figure 7). The depth slice at a depth of 1.6 m, shows the focused energy of the diffractions, indicating the linear response of fractures at this depth (Figure 6a). The blurriness that was introduced by the migration and the stacking procedure was avoided by time-varying spectral whitening, which increased the resolution of the multipath summation depth slice, delineating, in this way, limestone fractures in more detail (Figure 6b). A similar response was imaged at a depth of 1.8m by the proposed methodology (Figure 7a), with time-varying spectral whitening increasing the resolution in a similar and sufficient way. Figure 8 depicts the details of Figure 7. Time-varying spectral whitening, by increasing the temporal resolution, focused the signal's strength in terms of time and depth, which resulted in the suppression of the relatively lower dominant frequency contribution, increasing, in this way, the linearity of the events of interest. Figure 6: Horizontal depth slices depicting the envelope at a depth of 1.6 m after multipath summation (**a**) and after time-varying spectral whitening (**b**). Figure 7: Horizontal depth slices depicting the envelope at a depth of 1.8 m after multipath summation (**a**) and after time-varying spectral whitening (**b**). Color scale is the same as in Figure 6.  
Even if the results of this methodology did not correspond to a specific velocity value, the desired diffraction focusing was implemented for almost all of the section. Moreover, this method avoids the drawback of the accidental involvement of diffraction multiples by the user, as it does not estimate migration velocities, but instead examines the degree of focusing. We avoided a 3D migration approach because of the large computational time needed and the aliasing that may arise due to insufficient interval of the study lines. Thus, our 2D migration approach does not deal with out-of-plane diffraction energy.