## 3 Analysis of Geophysical Data
### Gravity and H/V Correlation  
In this section, the residual gravity anomaly is compared to the H/V predominant period in each site to define possible correlations. As a first approximation, the geology of the soils is incorporated using the seismic classification presented in Table 1. A more detailed analysis of the geology, including the basement rocks, is presented in the discussion Section 4. Figure 7 shows this comparison in the city of Vina del Mar. This city presents the ideal conditions in terms of geology, where a relatively homogeneous medium density soil \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Category**} & \multicolumn{2}{c}{**First Criterion:**} & \multirow{2}{*}{**Second Criterion: T\({}_{0}\) (s)**} & \multirow{2}{*}{**Site Type**} \\  & \(V_{s,30}\) or \(V_{s}<900\) (m/s) & & \\ \hline A & \(\geq\)900 & \(<\)0.15 or flat HVSR & Rock, cemented soil \\ \hline B & \(\geq\)500 & \(<\)0.30 or flat HVSR & Soft or fractured rock, very dense/firm ground \\ \hline C & \(\geq\)350 & \(<\)0.40 or flat HVSR & Dense/firm soil \\ \hline D & \(\geq\)180 & \(<\)1 or flat HVSR & Moderately dense/firm soil \\ \hline E & \(<\)180 & & Medium compactness/consistency soil \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Seismic classification (modified from [PERSON] et al. [56]). layer overlies the rock. Therefore, the results in this city are used as a reference to evaluate the correlations in the other cities. The upper panel of Figure 7 shows the sites classified according to the seismic classification of Table 1 in colored squares, while the red continuous line represents the linear trend between the gravity residual and the predominant period. The lower panel shows the same comparison but only considering the soft soils with a seismic classification of D or E. The results in both panels show a very clear tendency between both properties, where larger negative gravity residuals occurred in zones with higher predominant periods. In the upper panel, only two sites are far from the tendency, both classified as dense to very dense sites (B and C classification). This generates a lower R\({}^{2}\) in the tendency, which increases up to 0.82 when only the soft sites are considered. Furthermore, the slope of the trend increases when only soft sites are considered. A less satisfactory case in terms of correlation between both parameters is Iquique city. Figure 8 shows the same comparison in this city, which presents a totally different geology background compared to Vina del Mar. Here, the geology is very heterogeneous. The rock is very shallow in a great portion of the city, e.g., [14], and outcrops in different zones of the basin. Additionally, the soils presented in the city are dense with a lower impedance contrast with the basement, and stiffer seismic classifications. In Figure 8 it is possible to see that most of the soils are A, B or C, and only five sites are classified as D. In  
Figure 7: Correlation between gravity residuals and H/V predominant periods in Vina del Mar. Upper panel shows the results for all the type of sites presented in the area according to the seismic classification in Table 1. The lower panel shows the same results only for soft sites with classification of D and E.  
this case, there is not a clear tendency between the properties, with an R\({}^{2}\) almost equal to zero. The analysis with soft sites is not reasonable here because there are only five sites in this condition. On the other hand, Santiago appears as the more complete case study because of the high number of measurements and the presence of different types of infilling sediments in a complex geology background. The results of the comparison between gravity residual and H/V predominant period are shown in Figure 9, following the same properties of Figures 7 and 8. The upper panel shows all the soil categories, while the lower panel shows only sites type D and E. The red line represents the linear trend in this case.