## 2 Survey and Data Analysis
The depth, z, of the targets is estimated by converting the _round-trip travel time_, \(t\), according to the following relation:  
\[z=\frac{c\cdot t}{2\sqrt{\varepsilon}} \tag{1}\]  
wherein \(c=3\times 10^{8}\) m/s represents the light propagation velocity, and \(\varepsilon\) is the average relative dielectric permittivity of the investigated medium, e.g., [41]. We collected four LDGPR profiles at Ischia Is., three parallel-trending N-S profiles approximately 1300 m long (namely ISH1, ISH2, ISH4), spaced about 600 m from each other and orthogonal to the expected direction of the fault. The fourth profile (ISH3) trends NW-SE and is about 1 km long (Figure 1). Table 1 reports the acquisition parameters adopted for each profile in terms of length, spatial step, working frequency, and maximum depth of the investigation. Figure 3 shows the row data obtained along our four profiles for frequencies of 15, 25, and 100 MHz. We employed different antennas with frequencies for our profiles for two reasons. The first reasoning is logistical. As the 15 MHz antenna array has a length of approximately 13 m (including the Tx and Rx offset), its use is mostly not feasible for the steep and narrow roads on the slopes of Mt. Epomeo, except for the ISH1 profile located on wider roads. For profiles ISH2, 3, and 4, we could instead easily use the 25 MHz frequency, given that the overall length of the array is 7 m. The second reasoning for using antenna with different frequencies is our need to have radargrams with different resolutions at variable depths. As the ISH2 profile crosses over the 2017 earthquake co-seismic ruptures [3], and we reported signs of breakages already in the first meters below the surface, we used a 100 MHz frequency antenna there as well, to focus on the shallowest 20-30 m. As regards the polarization mode of the radar, we note the 100 MHz antenna has a co-polarized polarization and an orthogonal configuration of Tx and Rx, whereas the 25 MHz antenna has a co-polarized polarization with a parallel configuration of Tx and Rx. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**ID Data**} & **Length** & **Spatial** & **Frequency** & **Dielectric** & **Max.** & **Estimate** & **Satur** & **Satur** & **Satur** \\  & **(m)** & **Step (m)** & **(MHz)** & **Average** & **Depth of** & **(UTM—m)** & **(UTM—m)** & **(UTM—m)** & **(UTM—m)** \\ \hline \hline  & 862 & 0.9 & 15 & 6 & 125 & 406,698 & 4,510,675 & 407,103 & 4,511,304 \\ \hline  & 1330 & 1.5 & 100, 25 & 13, 5 & 190 & 407,324 & 4,510,451 & 407,273 & 4,511,211 \\ \hline  & 509 & 0.9 & 25 & 5 & 95 & 407,177 & 4,510,726 & 406,757 & 4,510,879 \\ \hline  & 814 & 0.8 & 25 & 5 & 180 & 406,015 & 4,510,572 & 406,182 & 4,511,279 \\ \hline \hline  & & & & & & & & & \\ \end{tabular}
\end{table} 
Table 1: Acquisition parameters of the LDGPR survey at Ischia Island. In our study, the max observation time window is 2044 ns, discretized by 512 time samples. To improve the interpretability of the considered LDGPR data, we performed the following data corrections: (i) a band-pass filter, which allows for removing noise from the radargram and improving the results of later procedures; (ii) zero timing, which defines the actual starting time, t_0, of the observation time window. In this survey, we set t_0 = 1.5 ns; (iii) time gating, which selects the portion of the observation time window where the target response occurs and allows for eliminating the direct antenna coupling, t_TG, as well as the clutter signal. In this survey, we set t_TG = 10 ns; (iv) topographic correction, to insert the real altitude of each acquired A-scan and georeference in the radargrams; (v) two-way time-depth conversion by means of Equation (1) by assuming an average relative dielectric permittivity \(\varepsilon\) = 5-6. This permittivity was inferred based on the analysis of stratigraphic information of boreholes we drilled in the area.