## 5 Conclusions  
The current research was conducted to compare the accuracy of different empirical and data-driven correlations for \(V_{s}\) prediction in limestone reservoirs. The study area was the Aboozar limestone reservoir located in the Persian Gulf. Different approaches including five existing empirical correlations as well as the LR, MLR, and GEP techniques were utilized for \(V_{s}\) prediction. The \(V_{s}\) values predicted by each method underwent validation and comparison with the actual \(V_{s}\) data obtained from the well logging data.  
Based on the conducted analysis, the Pickett empirical correlation showed more reliability than other available empirical correlations. Hence, to conduct an ordinary calculation of the \(V_{s}\) values, the Pickett equation can be utilized. Moreover, through the LR analysis, a simple empirical correlation (Equation (1)) was derived for \(V_{s}\) estimation in the oilfield. In that equation, the \(V_{s}\) was a function of only one parameter: the \(V_{p}\). On a positive note, the accuracy of Equation (1) was slightly better than the Pickett correlation.  
Regarding the AI techniques, the MLR demonstrated that \(V_{s}\) can be estimated with greater accuracy by incorporating additional parameters such as \(L\), \(PIGT\), \(PR\), \(RT\), \(GR\), and \(RHOB\) logs into the model. Moreover, the GEP model yielded the highest accuracy while utilizing a reduced set of input parameters, including \(V_{p}\), \(PIGT\), \(CAL\), and \(PR\). Thisresult demonstrated the success of the GEP method for \(V_{s}\) prediction in the study area, emphasizing its potential as a valuable tool for future geomechanical modeling. The values of statistical indices for Equation (11), which was extracted using the GEP algorithm, were \(R^{2}=0.972\), \(RMSE=0.000290\), and \(MAE=0.000208\).  
These findings have significant practical implications for the efficient management of limestone reservoirs, and the optimization of the hydrocarbon production operations. They can contribute to the development of more accurate geomechanical models, which ultimately lead to enhanced operational efficiency within the energy sector.  
For future works, it is recommended that the performance of the GEP method is compared with other nonlinear AI-based techniques such as genetic programing (GP) and genetic algorithms (GAs), etc. The extracted LR correlation of (Equation (1)) and data-driven correlations (Equations (10) and (11)) can be utilized for the Aboozar limestone reservoir and other global reservoirs where the geological characteristics are similar.  
Conceptualization, M.K.; methodology, M.K.; software, M.K.; validation, M.K. and D.K.; formal analysis, M.K. and D.K.; investigation, M.K.; resources, M.K.; data curation, M.K.; writing--original draft preparation, M.K. and D.K.; writing--review and editing, M.K. and D.K.; visualization, D.K.; supervision, D.K.; project administration, D.K.; funding acquisition, D.K. All authors have read and agreed to the published version of the manuscript.  
The project was supported by the AGH University of Krakow, Krakow, Poland, subsidy 16.16.190.779.  
No applicable.  
All used data are accessible in the context of the article.  
The authors would like to thank [PERSON], PhD student in AGH University of Krakow, and [PERSON], the exploration supervisor engineer in Iranian Offshore Oil Company (IOOC), for their support and collaboration during the conduction of this research.  
The authors declare no conflict of interest.