## 3 Methodology
### Training and Testing Dataset  
The data used in this study were provided by Graz University of Technology [35] (Graz, Austria). The complete dataset consists of 1339 cone penetration tests (CPT, CPTu, SCPT, and SCPTu) conducted in Austria and Germany by Premataller Geotechnik ZT GmbH [35] (Hallein, Austria). For this study, we utilized only the SCPT (46 tests in total) and SCPTu (50 tests in total) datasets. The SCPT and SCPTu can measure Vs at various intervals (e.g., at every 1 m) along the penetration depth, in addition to cone penetration data (i.e., cone tip resistance, qc and sleeve friction, fs). Before training the ML algorithm, the dataset underwent preprocessing. Raw data are rarely error-free or perfectly structured for ML training. Data often arrive in raw, messy, or incomplete forms, rendering them unsuitable for direct use in ML models. Initially, the dataset was filtered to include only SCPT and SCPTu tests. Unnecessary columns, and non-relevant measurements, were removed. Rows with zero or negative values for critical parameters were excluded. The differences in sampling intervals between CPT and Vs measurements were reconciled as per procedures described in [36]. This involved computing interval-based statistics (mean and coefficient of variation, cv) for relevant input features within the depth intervals where Vs data were recorded. Initial input features considered include mean cone tip resistance (qc_mean) and its coefficient of variation (qc_cv); mean sleeve friction (fs_mean) and its coefficient of variation (fs_cv); mean friction ratio (Rf_mean) and its coefficient of variation (Rf_cv); mean of soil behavior type index (Ic_mean); total overburden stress (\(\sigma\),\(v\)); and depth of soil while Vs served as the target variable. Outliers in Vs were identified and removed using the interquartile range (IQR) method, with a threshold of 2.5 times the IQR above the third quartile. The cleaned and processed dataset was then saved for further modeling and analysis. Table 1 presents a statistical summary of the dataset after preprocessing, while Figure 2 displays a pair plot of the input features and the target variable, Vs. The diagonal of the matrix contains histograms that illustrate the distribution of each individual feature. The off-diagonal scatter plots depict the pairwise relationships between features. Additionally, the upper triangle includes linear correlation coefficients, highlighting the strength and direction of these relationships.  
Figure 1: Flow diagram illustrating the methodology for developing and evaluating XGBoost and Bayesian GLMs.  
the optimization was to maximize the coefficient of determination (\(R^{2}\)). The optimized model was used to conduct partial dependence analysis to examine the influence of each feature on Vs. Features with negligible importance were excluded, and the model was retrained using the updated feature set. For the Bayesian GLM, only features exhibiting a linear or nearly linear relationship with Vs were selected. The performance of the final XGBoost model was assessed using multiple statistical metrics. Additionally, the predictive performance of both the Bayesian GLM and XGBoost models was validated on a separate validation dataset.