## 3 Methodology
### Feature Extraction  
Accompanying this is a host of geophysical features extractable from the HVSR spectrum, with important insight each into the seismic behavior of the site [36]. In particular, these include the following:  
* The amplitude spectra are obtained via Fast Fourier Transform (FFT): \[A_{x}(f)=|\text{FFT}(x(t))|\quad\text{for }x=e,n,z\]
* \(A_{n}(f)\) is the amplitude spectrum of the North-South component;
- \(A_{e}(f)\) is the amplitude spectrum of the East-West component;
- \(A_{z}(f)\) is the amplitude spectrum of the vertical component. Then, this ratio is smoothed using a moving average with a kernel of size 10: \[\text{hvsr\_smooth}(f)=\frac{1}{10}\sum_{i=-5}^{5}\text{hvsr\_ratio}(f_{i})\]
* Mean and Standard Deviation of HVSR: Shapes and variability in the overall HVSR curve provide critical information on resonance and amplification phenomena of the site. The mean of the smoothed HVSR ratio is expressed as follows: \[\text{hvsr\_mean}=\frac{1}{N}\sum_{i=1}^{N}\text{hvsr\_smooth}(f_{i})\] where \(N\) is the total number of frequency points. The standard deviation of the smoothed HVSR is expressed as follows: \[\text{hvsr\_std}=\sqrt{\frac{1}{N}\sum_{i=1}^{N}(\text{hvsr\_smooth}(f_{i})- \text{hvsr\_mean})^{2}}\]Alpha and gamma are parameters derived as the logarithmic and direct ratio, respectively, between the amplification factor and the fundamental frequency of the site; these are important in interpreting the dynamic resonance characteristics of the site. \[Alpha=\frac{\log_{10}(A_{f})}{\log_{10}(f_{0})}\quad\text{if }f_{0}>0\]  
\[Gamma=\frac{A_{f}}{f_{0}}\quad\text{if }f_{0}>0\]  
* Z represents the energy distribution between horizontal and vertical components of microseismic waves to provide an integrated view of wave characteristics. \[Z=\frac{\sum_{i}A_{h}(f_{i})}{\sum_{i}A_{z}(f_{i})}\]  
where  
\[A_{h}(f_{i})=\sqrt{(A_{n}(f_{i}))^{2}+(A_{e}(f_{i}))^{2}}\]  
* The vulnerability index (\(K_{g}\)) is derived from the amplitude factor (\(A_{f}\)) and the resonant frequency (\(f_{0}\)), which provides more detail for the determination of spectral properties of the site. \[K_{g}=\frac{A_{f}^{2}}{f_{0}}\quad\text{if }f_{0}>0\]  
Features are extracted with the raw and filtered East, North, and Vertical components in the structured feature data. This process structures the features in a form that retains other critical information in a format known as a 'rich feature' set ready for deeper analysis, maintaining station identifiers, as well as the day of recording, fundamental frequency (f0), amplification factor (Af), and HVSR metrics. Consequently, Figure 1 extracts key features from microtremor data. The essential core horizontal-to-vertical spectral ratio is calculated for six related processes, each contributing to the extraction and cleaning of seismic features. First, the pipeline takes in raw seismic data from seismic stations, recording three basic components of motion, namely East, North, and Vertical, denoted as E, N, and Z, respectively. These are the minimum recorded measurements for data filtering. The raw data are filtered through a bandpass filter to isolate frequency ranges between 0.1 and 20 Hz where relevant seismic signals exist. The successive steps involve Fourier transformation applied to the filtered data for all three components. It is a process in which a time-domain signal is decomposed into the frequency domain and presents the power of seismic data. The spectral representation then gives the variable frequency characteristics of the signal. Later, the HVSR juxtaposes horizontal motion, combining the East and North components with vertical motion. It also carries a significant amount of information about resonance and amplification at the site and reflects some subsurface properties of the seismic site. Savitzky-Golay Smoothing [37; 38]: Smoothing of the HVSR curve improves its interpretability by removing high-frequency noise using a moving-average filter; this stabilizes the HVSR and makes it more reliable.