## 3 Results
### GEP Method  
In this study, GenXproTools 5.0 software was utilized for the purpose of estimating the shear wave velocity through the GEP method. Furthermore, several tests with different ratios of the training data to the testing data were performed to assess the efficiency of the created GEP models. The relevant results have been shown in Table 6. As shown in this table, the best applied ratio is 60% training data to 40% testing data; in this case, the maximum values of \(R^{2}\) together with the minimum values of \(RMSE\) and \(MAE\) were acquired. Thus, the optimal GEP model was built using 60% training data and 40% testing data. Afterwards, the analysis was started using the \(V_{p}\) and \(PIGT\) logs. In fact, such a dataset was selected since the \(V_{p}\) and \(PIGT\) logs exhibited a high correlation coefficient with the \(V_{s}\) data (see Figure 4). Other parameters were added one by one to this input dataset. The obtained results are shown in Table 7. Based on this table, Dataset 3 delivered the \begin{table}
\begin{tabular}{c} _MAE_ \\ **(Train)** \\ \end{tabular} \\ \hline
90/10 & 0.961 & 0.886 & 0.000323 & 0.000317 & 0.000212 & 0.000235 \\
80/20 & 0.960 & 0.917 & 0.000342 & 0.000283 & 0.000231 & 0.000207 \\
70/30 & 0.956 & 0.947 & 0.000366 & 0.000218 & 0.000235 & 0.000198 \\
60/40 & 0.956 & 0.958 & 0.000371 & 0.000231 & 0.000205 & 0.000175 \\
50/50 & 0.944 & 0.960 & 0.000418 & 0.000277 & 0.000328 & 0.000201 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparing the efficiency of different GEP models in estimating the \(V_{s}\) with different ratios of training data to the testing data. Figure 7: The real \(V_{s}\) of the DSI logs versus the \(V_{s}\) estimated from the MLR algorithm. lowest values of \(RMSE\) and \(MAE\) values along with the highest values of \(R^{2}\) in comparison to other datasets; hence, the best statistical indicators (\(R^{2}\), \(RMSE\), and \(MAE\)) values were satisfied by this dataset. The performance and precision of the GEP model for Dataset 3 are shown in Figures 8 and 9. According to Figure 8, the correlation coefficients of the GEP model during the training and testing processes were calculated as 0.960 and 0.961, respectively. Those values imply that the accuracy of the \(V_{\mathrm{s}}\) estimation using the GEP model is suitably appropriate for the current study. Moreover, as shown in Figure 9, the relationship between the real and estimated \(V_{\mathrm{s}}\) values for training and testing steps are quite acceptable. Finally, using the generated GEP model for Dataset 3, the following nonlinear equation was acquired:  
\[V_{\mathrm{s}}=\frac{4.29489300174138}{\left[\left(\frac{7.70076553710087}{V_{p} }\right)+\left(PR\times CAL\right)\right]-\left[\frac{\left(\frac{0.580213914646 455}{CAL}\right)}{PIGT}\right]}\, \tag{11}\]  
where \(V_{p}\) (ft/\(\upmu\)s) and \(V_{\mathrm{s}}\) (ft/\(\upmu\)s) are compressional and shear wave velocities, respectively. Furthermore, \(PIGT\) is porosity, \(CAL\) (in) is caliper log, and \(PR\) is Poisson's ratio. Equation (11) was used to determine the \(V_{\mathrm{s}}\) in the wellbore A. The corresponding results have been shown in Figure 10 and Table 8.  
Figure 10: The real \(V_{s}\) data of the DSI logs versus the \(V_{s}\) values estimated by the GEP model. Figure 9: The performance of GEP method in estimating the \(V_{s}\) for different training and testing data. Figure 10 displays the \(V_{s}\) values estimated by the nonlinear equation extracted from the GEP method. The trend of this figure shows that such an equation is properly reliable for the Asmari reservoir. This matter is corroborated by the acceptable values of \(R^{2}\), \(RMSE\), and \(MAE\) mentioned in Table 8.  
Ultimately, the \(V_{s}\) values estimated by different methods were compared. Those comparative results are depicted in Figures 11 and 12. As shown in Figure 11, Equation (1), Pickett, MLR, and GEP models estimated \(V_{s}\) values close to the real \(V_{s}\) values.