## 5 Results and Discussion  
### Greater Metro Manila Area Results  
Understanding the reliability of HVSR inversion for estimating shear wave velocity is crucial for its application in seismic hazard assessments. For the GMMA dataset, a comparison of Vs profiles obtained from HVSR inversion and those derived from ReMi surveys at sample sites (Figure 5) shows strong agreement, with consistent layer depths and velocities.  
As for the calculated Vs30 values, HVSR inversion via GA generally yielded results comparable to those obtained from ReMi surveys (Figure 6), with percent differences mainly ranging from 10% to 30%. While no consistent trend was observed, the Vs30 values were underestimated in most cases--specifically in 18 out of 25 sites--compared to the ReMi-derived values. This tendency may suggest that HVSR inversion may systematically produce slightly lower estimates under certain site conditions.  
Table 6 shows the values of statistical parameters, namely the coefficient of regression (R2), coefficient of correlation (r), and root mean square error (RMSE) for the measured ReMi Vs30 values and the estimated Vs30 values. A visual is provided in Figure 7, showing that though some profile types have limited data, the estimated Vs30 values generally align with the measured ReMi values, with most data points plotting near the 1:1 line.  
Figure 5: Vs profile comparison in sample sites between ReMi (in blue) and HVSR inversion (in orange) in sample GMMA sites.  
Additionally, the majority of sites exhibit matching soil profile types. In cases where the assigned profile type differs, the Vs30 values remain close, with discrepancies primarily occurring near classification boundaries (e.g., around 360 m/s or 760 m/s, where soil profile types transition).  
Based on these statistical parameters, the overall results demonstrate that the inversion process provides reasonably accurate estimates of Vs30, although with some variability in performance across different soil profile types. Class \(S_{E}\), based on the match rate, exhibits the highest accuracy, with an R\({}^{2}\) of 0.920 and the lowest RMSE of 8.402. Class \(S_{D}\) sites, composed of stiff soils, also perform well with high R\({}^{2}\) and r values, although the RMSE increases. In contrast, class \(S_{C}\) sites, which include a mix of dense soil and soft rock, show the weakest correlation and the highest RMSE. The variability in subsurface conditions for  
Figure 6: Comparison between ReMi-derived Vs30 (in blue) and GA-derived Vs30 (in orange) in GMMA sites.  
Figure 7: Comparison of measured Vs30 from ReMi and estimated Vs30 for GMMA data.  
this class may be contributing to these larger errors, as the HVSR method may struggle to accurately capture wave propagation behavior in more complex subsurface settings (Figure 7).  
Overall, the estimated values have a 76% match rate with high R\({}^{2}\) and r values of 0.885 and 0.941, respectively. This indicates a strong positive correlation between the ReMi- and estimated values and showcases that the inversion effectively captures the overall trend of the ReMi data. The RMSE further supports that the algorithm can effectively estimate the Vs30 values.  
A power regression analysis revealed a strong inverse correlation between the site period and Vs30 (R\({}^{2}\) = 0.772), as shown in Figure 8. This indicates a strong correlation between the variables, aligning with the expectation that the relationship between site period and Vs30 is typically inverse. As Vs30 decreases, which indicates softer and less rigid soil, the site period increases, meaning the natural period of vibration of the soil profile is longer. Conversely, higher Vs30 values, which indicate stiffer and more rigid soil or rock, correspond to shorter site periods [36].