## 4 Discussion
The SNR improved from non-stacked data to off-line stacked data in both 2D radargrams and depth-slices. Compared with traditional in-line stacking, off-line stacking shows a substantial advantage. This result allows for better interpretation of multichannel GPR data, which generally involves both radargrams and time-slices visualizations. In this work, we mainly compared the off-line stacking to in-line stacking since these two processing steps share the same philosophical approach. However, we do not see any stacking approach as an alternative to other, more sophisticated, filtering approaches that are commonly used in challenging environments (e.g., \(f\)-k filtering [14; 24] or wavelet denoising [25; 26]). Indeed, further filtering can still be applied to the stacked traces in order to exploit the potentiality of these last processing approaches to increase the data quality. As mentioned before, the resolution reduction due to (any type of) stacking was assessed to be not an important problem in the test site, where the survey targets were relatively big features such as buried walls. Indeed, it has been already discussed in the literature [18] that generally a denser GPR profile spacing can guarantee that all target features will fall within the radar's footprint. In this respect, multichannel GPR systems usually easily allow a significantly denser spacing than standard GPR single-channel systems. But the question is how dense is dense enough? Normally, the spacing of GPR profiles is suggested to be no larger than the anticipated feature size of the targets or the distance between adjacent features [27]. If the target features are large enough, not all the acquired channels are strictly necessary and can be stacked, as performed in this study. When feature size and feature spacing are both unknown, the radar's wavelength is the only factor to be taken into account, based on the principle of radar footprint, to establish the lateral separation among traces. Usually, the profile spacing is suggested to be a quarter of the wavelength [17; 28]. Indeed, for the Stream C system adopted in this study, the VV channel separation of 4 cm strictly derives from this consideration: at the nominal frequency of 600 MHz, with an assumed standard radar velocity of 10 cm/ns, the resulting wavelength is of about 16 cm, and its quarter about 4 cm, as the adopted antenna separation. However, this antenna separation can be valuable only for the imaging of very tiny structures but not generally necessary. Indeed, even acquisition grids of an eighth of the wavelength have shown to guarantee a proper sampling of the high-frequency content of the GPR signal spectrum, and resulting in optimum image quality, but mainly for fracture imaging purposes [22]. Moreover, the quarter wavelength value may vary depending on the effective central frequency of the signal (at the test site, we observed a shift to lower frequencies in the 300 Hz range) and on the effective radar velocity of the tested material (generally lower than 10 cm/ns in natural clayey soils). Therefore, most of the sampled information with the multichannel system adopted in this work on a real subsoil in a real archaeological site can result well below the quarter wavelength criterion, and, consequently, the proposed off-line stacking approach can be seen also as a necessary step to restore the real lateral resolution of the data and not as an artificial processing strategy. Indeed, for the studied case history, considering an approximate radar velocity of 7 cm/ns, dependent on the clay content [29], and the observed peak frequency of about 300 MHz would result in a quarter wavelength value of about the same order as the one obtained with the off-line stacking of five adjacent traces, as performed in the analyses reported in this paper. The general message is to not remain stuck by manufacturer specification but be flexible depending on the required resolution of the surveys and on survey specifications.