# Shear-Wave Velocity Model from Site Amplification Using Microtremors on Jeju Island
## 4 Results
### GOS Site  
Located on the western part of Jeju Island (Figure 1), the GOS site presented distinct characteristics in its HVSR curve analysis. Figure 4 illustrates both the observed and synthetic HVSR curves for the optimal Vs model at this site. The observed HVSR curve, represented by the red line, contrasts with the synthetic HVSR curve, indicated by the black dotted lines. These synthetic curves account for all inverted HVSR curves, excluding those deemed geologically implausible. The observed HVSR curve demonstrated two significant \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Layer**} & \multirow{2}{*}{\
\begin{tabular}{c} **Lower Limit Depth** \\ **of Each Stratum (m)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Shear Velocity** \\ **(m/s)** \\ \end{tabular} } & \multicolumn{2}{c}{**RC**} \\ \cline{3-5}  & & & **B (1–2)** & **B (2–3)** & **B (3–4)** \\ \hline
1 & 140–160 & 1900–2100 & \multirow{3}{*}{**0.02**} & \multirow{3}{*}{**0.04**} \\
2 & 340–360 & 2000–2200 & & \\
3 & 590–610 & 2200–2400 & & \\
4 & Bedrock & 2400–2600 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Depth, shear velocity (Vs), and RC of CJD sites. Figure 3: Estimated shear-wave velocity (Vs) profile from the inversion of CJD site; the thin lines indicate all the inversion results, and thick gray line indicates the optimal Vs profile. peaks at frequencies of 0.36 Hz and 1.46 Hz, with corresponding peak amplitudes of 4.33 and 3.39, as noted in Table 4.  
For the variance bounds ranging from 0.25 to 2.5, the misfit sizes obtained via inversion using the MC simulations were between 190.02 and 3.88, with the minimum misfit size observed at a variance of 2.5. The SA algorithm similarly revealed that the misfit sizes of the best-fit inversion model varied from 461.7091 to 4.292 over the same range of variance bounds. As observed at the CJD site, the misfit size decreased with increasing the variance bounds for both algorithms. Certain inverted-V models exhibited significant deviations from those used in previous studies, such as models with exceptionally thin layers (less than \(\sim\)10 m) or uniform Vs values that were either excessively high or low throughout the depth range. These models were subsequently excluded from further analysis. Despite variations in the inversion algorithms and the extensive range of permissible variances in the observed HVSR curves, the observed and synthetic HVSR curves for the optimal Vs model closely matched in amplitude and double peak frequencies, especially surrounding the first and second peaks. A prior study addressing the topology of HV curves indicated that when HV curves exhibit two peaks, the lower-frequency peak typically corresponds to the fundamental frequency [45]. The second peak, characterized by a higher frequency and smaller amplitude, may be influenced by valley formations or the corresponding surface topology. However, the study posited that aside from the fundamental resonance peak, smaller peaks might lack geological relevance unless demonstrated by multiple other studies. Field investigations confirmed the absence of unusual topographical features such as valley development around the GOS site. Consequently, further inquiries into the cause of the double-peak phenomenon using alternative methodologies are warranted [40]. Figure 5 depicts the Vs profiles, showcasing both all the inverted and the optimal Vs models. In determining the optimal shear velocity profile, we focused on the darker segments, representing the more frequently mapped areas. The Vs map alternates between these frequently mapped dark regions and the less frequently mapped lighter areas. The modal-Vs model, characterized by darker sections and thus given more weight, was selected to ascertain the optimal model. Figure 4: Observed and synthetic HVSRs of GOS site; the red line indicates the observed curve, and the black dotted line indicates the synthetic curve.