## 4 Materials and Methods  
### Processing Using the Genetic Algorithm in HVSRInv  
The estimation of the shear wave velocity of the HVSR sites was conducted in the software HVSRInv developed by [PERSON] and [PERSON] (2022) (2022) (2022). HVSRInv makes use of the equivalent linear approximation based on the viscoelastic Kelvin-Viogt model to calculate the site response of horizontally stratified soil layers. An elitist genetic algorithm (GA) is employed to perform multiple inversions in obtaining the shear wave velocity profile of the HVSR site. The GA has the feature of elitism, which ensures that the best-fit generation is chosen. The software requires the HVSR data, user-defined initial model parameters, and inversion parameters.  
The HVSR data from the previously extracted three-column ASCII files were converted into text files and loaded into the software. The user-defined initial model parameters are used to constrain the values of the resulting Vs profile. These values are typically lifted from the literature and in situ surveys characterizing the general subsurface where the HVSR survey was conducted. The initial model parameters, such as the number of layers and the minimum and maximum thickness and shear wave velocity of each layer, were derived from the Vs profile of a ReMi site, provided that the HVSR site is either centered on, very close to, or within the same geomorphologic unit of the ReMi array. A ReMi site whose site period is closer to the HVSR site period is preferred. Table 1 presents the model parameters used for a selected site located within the lower denudational slopes and hills geomorphologic unit in Leyte.  
The minimum and maximum density and damping ratios are automatically calculated by the software. The minimum and maximum frequency refers to the frequency range to be used for the inversions. The frequencies where the peak amplitude of the HVSR curve occurs (i.e., the predominant frequency) were selected (Table 2).  
The inversion parameters determine the number of generations and inversions, which, together with the computer specifications, affect the GA execution time. In this study, the inversion parameters utilized by [PERSON] and [PERSON] (2012) (2012) were adopted as presented in Table 3 The number of genes, populations, iterations, and inversions were set at 10, 100, 300, and 10, respectively. The computer specifications were 12 th Gen Intel Core i9-12900 CPU, 2.40 GHz, 32 GB RAM, 64-bit operating system, and took 55.87 s to execute per HVSR site.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Layer** & **Thickness (m)** & \begin{tabular}{c} **S-Wave Velocity** \\ **(ms\({}^{-1}\))** \\ \end{tabular} & \
\begin{tabular}{c} **Density** \\ **(gcm\({}^{-3}\))** \\ \end{tabular} &
\begin{tabular}{c} **Damping** \\ **Ratio** \\ \end{tabular} \\ \hline
1 & 1–6 & 180–360 & 1.7586–1.9378 & 0.02331–0.0463 \\
2 & 1–38 & 360–760 & 1.9378–2.1515 & 0.0110–0.0231 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Model parameters applied for the selected site.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Number of Layers** & **Minimum Frequency (Hz)** & **Maximum Frequency (Hz)** \\ \hline
3 & 0.6 & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Number of layers, Minimum Frequency (Hz), and Maximum Frequency (Hz) for the selected site.  
The inversion yields an estimated Vs profile (Figure 3, Table 4) along with a corresponding estimated HVSR curve. The estimated curves are accepted if their trends align with the observed HVSR curves. Additionally, the minimum and maximum standard deviations in the HVSR, as analyzed in Geopsy, serve as guides on whether the estimated curves qualify as matches (Figure 4). This ensures that the estimated site exhibits similar behavior to the initial model parameters from the reference ReMi site. Discrepancies between the curves may arise due to variations in site response, such as amplification, at certain frequencies in real-world conditions compared to theoretical models.