## 3 Results
### MLR Method  
In well logging, each well log shows a series of the reservoir characteristics. If several well logs are used to determine the properties of a reservoir rock, it leads to more reliable results. Considering those characteristics, in this research, several well logs were deployed to estimate the values of \(V_{s}\). At the beginning of the analysis, two logs including the \(V_{p}\) and \(PIGT\), which showed strong correlations with the \(V_{s}\) data, were selected. Then, other logs were added one after another. In Table 4, the \(R^{2}\), \(RMSE\), and \(MAE\) values corresponding to seven datasets imported to the MLR models have been tabulated. Figure 6: Comparison between the real \(V_{s}\) data (DSI logs) and the \(V_{s}\) estimated by five existing empirical correlations [14; 15; 18; 23; 27]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & \(\mathbf{R^{2}}\) & \(RMSE\) & \(MAE\) \\ \hline [PERSON] et al., 1998 [18] & 0.49 & 1.02261 & 1.02161 \\ [PERSON], 1969 [15] & 0.68 & 0.02358 & 0.02343 \\ [PERSON] et al., 2010 [27] & 0.67 & 0.01642 & 0.01627 \\ [PERSON], 1963 [14] & 0.95 & 0.00042 & 0.00032 \\ [PERSON] and [PERSON], 1993 [23] & 0.35 & 0.00825 & 0.00816 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The calculated values of \(R^{2}\), \(RMSE\), and \(MAE\) for different empirical correlations. Comparing the results obtained from the different MLR models, it can be expressed that the correlation coefficients for all datasets were nearly equal to 0.96; however, Dataset 6 gave the lowest \(RMSE\) and \(MAE\) value. Therefore, this dataset is more appropriate than other datasets to derive an accurate estimation of the shear wave velocity from the MLR method. Ultimately, using Dataset 6, the following equation was extracted:  
\[ \begin{array}{l}V_{s}=-0.1180+0.456290\ V_{p}-0.000726\ PIGT+0.000141\ CAL-\\ 0.003617\ PR+0.000001\ RT-0.000005\ GR+0.119900\ RHOB,\end{array}  \tag{10}\]  
where \(V_{p}\) (ft/ us) and \(V_{s}\) (ft/ us) are compressional and shear wave velocities, respectively. Furthermore, \(PIGT\) is porosity, \(CAL\) (in) is the caliper log, \(PR\) is the Poisson's ratio, \(RHOB\) (g/cm\({}^{3}\)) is density, \(GR\) (GAPI) is gamma ray, and \(RT\) (\(\Omega\cdot\)m) is the resistivity. In Equation (10), it is evident that the coefficients for \(RT\) and \(GR\) parameters are notably smaller compared to the other parameters. This suggests a potential limited impact of these two parameters on the predicted \(V_{s}\). To offer a more detailed understanding, Table 5 provides the coefficients and the respective ranges for each independent parameter incorporated in Equation (10). These coefficients reflect the sensitivity of the model to changes in each parameter. As observed, \(RT\) and \(GR\), having smaller coefficients, indicate a relatively lower influence on the predicted \(V_{s}\). Moreover, the wide ranges of these two parameters demonstrate the variability of them across the dataset, contributing to their limited impact on the overall model. This nuanced understanding enhances the interpretability of Equation (10) and emphasizes the dominant role of other parameters in predicting \(V_{s}\) within the studied geological context. Equation (10) was utilized to estimate the values of \(V_{s}\) in the geological profiles of the wellbore studied in this research. Such results have been shown in Figure 7. In accordance with the information shown in this figure, the accuracy of \(V_{s}\) predicted by the MLR method (Equation (10)) is quite noticeable.