## 6 Conclusions  
This study estimated shear wave velocity as one of the most important parameters in reservoir geophysical characterization via the Full-Self-Adaptive Harmony Search-GMDH neural network algorithm in a carbonate petroleum reservoir in the Persian Gulf. In doing so, a novel version of the Harmony Search (HS) algorithm was introduced and applied to optimize a GMDH-type neural network. In addition, only two of the parameters, including density (RHOB) and P-wave velocity (V\({}_{\mathrm{P}}\)), were utilized as inputs, as they have the highest correlation with the S-wave velocity, 0.71, and 0.86, respectively. The results proved that estimating S-wave data through our novel algorithm with \(\mathrm{R}^{2}\approx\) 0.97 is more accurate and cost-effective than similar studies. Previous studies used more than two inputs of data that led to spending more time and higher costs; however, their results were not as accurate as the results in this study. Nevertheless, from an optimization perspective, metaheuristic  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**[PERSON] et al. [8]** & **[PERSON] and [PERSON] [6]** & **[PERSON] et al. [8]** & **Equations (3)–(5)** & **Brocher [7]** & **FSHS-GMDH** \\
**Equation (1)** & **Equation (2)** & **Limestone** & **Dolomite** & **Shale** & **Equation (6)** & **FSHS-GMDH** \\ \hline
0.8130 & 0.8103 & 0.7962 & 0.8054 & 0.8051 & 0.4945 & **0.9688** \\ \hline \hline \end{tabular}
\end{table}
Table 2: Statistical analysis (\(\mathrm{R}^{2}\)) of shear wave velocity estimation calculated by experimental methods Equations (1)–(6).  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Train Data**} & \multicolumn{3}{c}{**Test Data**} & \multicolumn{3}{c}{**All Data**} \\ \hline
**Algorithm** & \(\mathrm{R}^{2}\) & **RMSE** & **MSE** & \(\mathrm{R}^{2}\) & **RMSE** & **MSE** & \(\mathrm{R}^{2}\) & **RMSE** & **MSE** \\ \hline
**MLP** & 0.8691 & 93.48 & 8738.92 & 0.8512 & 103.82 & 10778.8 & 0.8634 & 96.70 & 9351.77 \\
**GMDH** & 0.8935 & 83.64 & 6995.87 & 0.8647 & 101.49 & 10301.39 & 0.8834 & 89.38 & 7988.96 \\
**FSHS-GMDH** & **0.9728** & **43.36** & **1880.23** & **0.9514** & **55.82** & **3116.92** & **0.9688** & **46.12** & **2127.93** \\ \hline \hline \end{tabular}
\end{table}
Table 3: Statistical analysis of shear wave velocity estimation calculated by ML methods.  
algorithms concentrate on providing a comprehensive search to find a global optimum and it may lead to the model become over-fit. In order to overcome this problem, it is crucial to conduct a deep study to enhance the generalizations in the future work.  
Conceptualization, methodology, software, validation, and data curation: A.T.; conceptualization, validation, and investigation: Z.W.G. and K.R.; writing--review and editing: A.T., E.M., N.S.M., H.J., T.-H.K., Z.W.G. and K.R.; supervision, Z.W.G. and K.R.; funding acquisition: Z.W.G. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Energy Cloud R&D Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT (2019M3F2A1073164).  
Not applicable.  
The authors want to express special thanks to the National Iranian South Oil Company (NIOC) for providing well-log data to prepare this research manuscript.  
The authors declare no conflict of interest.