# Shear-Wave Velocity Model from Site Amplification Using Microtremors on Jeju Island
## 3 Methods
[43], a seven-layer model was selected as the initial model. This decision was informed by examining the tendency of misfit value sizes after numerous inversion trials with five-, six-, seven-, and eight-layer velocity models, along with local geological data. The six- and eight-layer velocity models often resulted in outcomes that were physically inconsistent with the existing geological and geophysical studies. Therefore, in this study, inversions were conducted on a Vs profile comprising seven layers, including the basement, as the initial model. Table 4 presents the initial seven-layer model for the Jeju region, established prior to the aforementioned random search stage. For each inversion algorithm, an initial population of 100 individuals was utilized to randomly search for Vs and layer thickness, based on a given input HVSR curve. To ascertain the global optimal solution, iterations were terminated when no further notable reduction in the misfit was observed for each inversion algorithm. At each site, greater emphasis was placed on the modal value of the most frequently mapped velocity models, indicated by darker colors, rather than on the less frequently mapped sections of layers, to determine the optimal velocity model. In cases where the modal value was not distinctly \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Layer** & **Thickness (m)** & **Vs (m/s)** & **Density (kg/cm\({}^{3}\))** \\ \hline
1 & 50–150 & 1600–1800 & 1600–1800 \\
2 & 50–150 & 1800–2000 & 1600–1900 \\
3 & 50–250 & 1800–2500 & 1800–2100 \\
4 & 50–250 & 1800–2500 & 1900–2200 \\
5 & 50–250 & 1800–2500 & 1900–2200 \\
6 & 50–250 & 2000–3000 & 2000–2200 \\
7 & Basement & 2000–3000 & 2000–2200 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Range of initial inversion parameters for inversion. observable, the optimal velocity model was determined based on the average value of the corresponding section. The inversion process was conducted employing 10 variance bounds to examine the HVSR for each algorithm. In this study, where the MC and SA algorithms were used, typically 20 inversion outcomes were generated per session. If the velocity model failed to converge satisfactorily after a single inversion session, the process utilizing the two algorithms was repeated one or two additional times. This repetition was carried out until the modal models were sufficiently delineated, evident by their darker mapping, utilizing the results of from 40 to 60 inversions. Moreover, the reflection coefficients (RCs) of the Vs profile were calculated using the elastic impedance, defined as the product of Vs (in m/s) and density (in kg/cm\({}^{3}\)). This metric signifies the degree of contrast in the velocity and density between adjacent layers. The magnitude and corresponding depth of the RC values derived from the inversion were also considered to ascertain an optimal velocity model. RC serves as a crucial indicator of discontinuity and contrast within a medium, based on the elastic impedance of the medium. Given that seven layers were set as the initial values for the inversion process in this study, only the relatively large values among the six potential RC values were considered for the Vs profile. Consequently, the final velocity model was determined by comprehensively considering not only the modal models that were most frequently mapped, as indicated by a relatively darker color, but also the RC values.