## 4 Methods and Materials
For every 0.5 m of depth, D, the wavelength, \(\lambda_{R}\), was calculated using Equation (11):  
\[D=\ \frac{1}{3}\lambda_{R} \tag{11}\]  
As shown in Figure 11, the wavelength starting from 1.5-3 m belongs to 0.5-1 m layers of depth. Similarly, the wavelength starting from 3-4.5 m belongs to 1-1.5 m layers of depth, and 16.5-18 m of the wavelength belongs to 5.5-6 m of depth. Afterwards, all of the dispersion curves from the 50 SASW tests were combined and divided into these 12 layers  
Figure 7:0 Dataset preparation for ML algorithm. Figure 7:1 Implementation of ML in the SASW inversion method. at a 0.5 m interval. For training the datasets, the wavelength and the phase velocity were considered to be input corresponding to each layer. For instance, the wavelengths from 0-1.5 m were taken as input, as well as the shear wave velocities at 0-0.5 m depth. The theoretical dispersion curves, along with the soil profile from the database, were used to train the ML algorithms. The proportion of the training and testing datasets was 80% and 20%, respectively, in the ML algorithms. The contention was to generate the most extensive, theoretically possible input range. The number of observations obtained from the dispersion curve at different layers is shown in Figure 7:2 The deepest resolvable layer is related to the penetration depth of the surface wave. The penetration depth is controlled by the frequencies generated by the source on the surface and by the stiffness structure of the subsurface. The surface wave needs to propagate deeper with the right range of low frequencies in order to be able to capture the deep layer. Generally, hammer impact sources have a limitation in low-frequency generation in comparison to higher-frequency generation. Therefore, the data points obtained from the field decrease with deeper layers. To evaluate the \(V_{\text{S}}\) profile from the SASW measurements, dispersion curves must be determined. To measure the performance of the model, the coefficient of determination (R\({}^{2}\)) and RMSE were used. Equation (12) is employed to determine the RMSE in the ML algorithms:  
Figure 7:3  
where \(P_{i}\) is the predicted shear wave velocity, \(A_{i}\) is the shear wave velocity from conventional SASW inversion, and \(N\) is the sample size. The following parameters in Table 3 were used in ML for the algorithms. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Layer Number** & **Depth** & **No. of Observations** \\ \hline
1 & 0–0.5 & 756 \\
2 & 0.5–1 & 1242 \\
3 & 1–1.5 & 874 \\
4 & 1.5–2 & 532 \\
5 & 2–2.5 & 395 \\
6 & 2.5–3 & 340 \\
7 & 3–3.5 & 199 \\
8 & 3.5–4 & 118 \\
9 & 4–4.5 & 97 \\
10 & 4.5–5 & 92 \\
11 & 5–5.5 & 77 \\
12 & 5.5–6 & 60 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: No. of observations with the depth. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Parameter** & **Setting** \\ \hline \multirow{4}{*}{MLP} & Hidden layer sizes & 3 \\  & Maximum iteration & 2000 \\  & Activation & ReLU \\  & Validation threshold & 54 \\ \hline RF & N estimators & 50,000 \\  & Criterion & MSE \\  & Minimum sample splits & 67 \\  & Maximum features & Auto \\  & Verbose & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: ML algorithm parameter setting.