## 3 Results
### Factors  
Inspecting the HVSR data and characteristics reveals some areas that may have been unaddressed in previous studies, which may help in this investigation. These include the use of an arithmetic or geometric mean for the station-specific HVSR, minimum frequencies, and conditional peaks. An interesting point is the type of mean used in calculating the station-specific HVSR. All response spectra-based HVSR studies use a mean of logarithms, suggesting the HVSR distribution per frequency is logarithmic. On top of relative simplicity, a point of justifica  
Figure 4: (**a**) Resultant \(f_{\rm p}\) and \(V_{\rm S30}\) for acceleration and velocity datasets. Regressed line for acceleration data is shown in bold with dashed lines being \(\pm 1\) standard deviation; (**b**) Residuals between the logarithm of measured data and the logarithm of estimates from acceleration and velocity-based data regression models. tion would be that HVSRs cannot be negative. Figure 5 displays examples of the differences between the different means. Figure 5a shows station YSUK again, displaying minor differences between the different mean types and range of uncertainties and results in the same \(f_{\rm P}\). Figure 5b shows the different means for station GCN. It shows the arithmetic mean being higher than the logarithmic mean for \(f<3\) Hz. This would result in significantly different \(f_{\rm P}\) and \(A_{\rm P}\). In addition to an influence on selecting HVSR characteristics, the arithmetic mean has standard deviations that put the range of possible manifestations in the negative range due to the presence of outliers on the positive side. Therefore, applying a logarithmic mean is more reasonable. The restriction of using frequencies above a certain threshold has been previously justified, saying lower peak frequencies are more characteristic of deep sediments, where \(V_{\rm S30}\) is not a good representative for amplification, and HVSR characteristics at lower peak frequencies do not follow the same HVSR behavior as those with \(f_{\rm P}>1\) Hz. In the current dataset, only three stations exhibited an absolute maximum below 1 Hz from surface recordings, with two of the three satisfying the aforementioned \(A_{\rm P}\) conditions. Figure 3b shows station HCH, where the absolute maximum occurs at \(f=0.4\) Hz for both acceleration and velocity HVSR. Station JUC also shows similar characteristics. A review of Figure 5b shows station GCN has a peak at 0.1 Hz and may suggest a higher peak at \(f<0.1\) Hz, bringing into issues with data resolution. Figure 6 replots the HVSR data when minimum frequencies are removed. Acceleration HVSR for station GCN and velocity HVSR for station HCH did not satisfy amplitude conditions and are displayed in gray. The figure also shows the regression for data with \(f_{\rm P}>1\) Hz, which, when using a power law fit,  
\[\log V_{\rm S30}=0.52\log f_{p}+2.32 \tag{6}\]  
with a standard deviation, \(\sigma_{\rm log}=0.10\). The decrease in uncertainty is primarily due to the removal of moderate outlier station HCH. The regression for velocity is not different from Equation (5). Overall, it appears that imposing a minimum frequency makes sense with respect to peak values and does not significantly affect any regressions when only considering the main body of data above the threshold frequency. Figure 5: Examples of different acceleration HVSRs derived using an arithmetic mean in blue or a mean of logarithms shown in red. The gray lines represent the HVSRs derived from individual earthquake events. Dashed lines represent the mean \(\pm 1\) standard deviation: (**a**) Station YSUK, where the means do not differ by much; (**b**) Station GCN, where the means differ significantly for \(f<3\) Hz. The more interesting factor of conditional amplitude peaks may have more of an impact on regression. Figure 3c,d show the conundrums peak amplitude conditions may have on datasets.