## 3 Analysis of Geophysical Data
### Seismic and Gravimetric Basement Depth Inversion  
The mechanical basement derived from seismic H/V measurements and the geological basement derived from gravity modeling are not necessarily the same. One of the goals of this research is to clarify the precise meaning of each basement definition, and how this understanding impacts the geological conditions in which the relation between predominant period and gravity residual is valid. Therefore, in this section we discuss the comparison between the depth-to-basement derived only from H/V measurements and the one derived from the 1-D gravity residual inversion in some sites of interest, considering  
Figure 9: Correlation between gravity residuals and H/V predominant periods in Santiago. Red line corresponds to the calculated linear regression. The black lines correspond to the trend calculated for Vña del Mar. The continuous line is the original trend, while the dashed lines is displaced in \(-3.5\) mGal. 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.  
different geological settings. Even though these inversions can be made in a more regional way considering data distributed in space (2D or 3D inversions), we perform only local 1D inversions to simplify the comparison of results. The seismic basement derived from H/V is obtained through an inversion using the ellipticity of the Rayleigh waves [17]. The ellipticity corresponds to the ratio between the horizontal and the vertical particle motions and gives valuable information of the whole sedimentary layer [19]. [PERSON] et al. [18] gives a detailed description of the methods to obtain this parameter. In this work, the ellipticity is obtained using the H/V TFA tool available in the software Geopsy(r) [57]. However, the ellipticity curve cannot be used alone in the inversion because different soil structures can produce the same curve [19]. As a result, the inversions were complemented using dispersion curves from active seismic arrays available in the corresponding projects for each city. [PERSON] et al. [19] gives recommendations about the portions of the curve to be included in the inversion through the analysis of synthetic and real data; according to their work, the right flank of the ellipticity peak contains the most important information, although the left flank can be used to constrain the peak frequency, if necessary. These recommendations were used in  
Figure 10: Correlation between gravity residuals and H/V predominant periods in the five cities studied in this research. Red line corresponds to the calculated linear regression. 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 work, although, some portions of the curve are unconstrained during the inversion. The focus of these inversions is to estimate the depth to the basement and not its shear wave velocity. This result is compared with the sediment thickness (H) obtained from the 1-D relation shown in Equation (1), that correlates H with the predominant period (T\({}_{0}\)) and the harmonic mean shear-wave velocity (\(V_{s}\)). This relation can lead to wrong interpretations under 2-D environments, however, in this work it is only used as a way of comparison between independent results. On the other hand, the gravimetric basement is calculated assuming a 1-D model consisting only in one soil layer overlying the rock. Assuming a unique density contrast between soil and bedrock, it is possible to obtain the thickness of the soil column through Equation (2) [1] for a semi-infinite horizontal slab.