## 5 Results and Discussion
### Sensitive Analysis  
After determining the best prediction model, the sensitive analysis was carried out to calculate the parameter importance of the rock EM prediction. The average impact on model output magnitude (mean) is one of indices in the Shapley additive explanations (SHAP), which is used to represent the parameter importance, as shown in Figure 13. As can be seen in this graph, the porosity (Pn) has the larger importance value (30.52) than the other input variables in the EM prediction based on the PRO-RF model. After the Pn, the importance ranking of other three variables are the SHRN (3.8), Vp (4.09) and PLI (2.08). In addition, another SHAP index is the impact on the model output (SHAP value), which is used to describe the correlation between the input and output variables. As illustrated in  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multicolumn{6}{c}{**Statistical Indices**} \\ \cline{2-8}  & **Min** & **Max** & **Median** & **Mean** & **St. E** & **St. D** & **Sum** \\ \hline PRO-RF & 0.134 & 31.524 & 2.678 & 6.042 & 1.702 & 8.337 & 145.014 \\ GRNN & 0.328 & 35.992 & 3.477 & 8.267 & 2.135 & 10.458 & 198.417 \\ \hline \hline \end{tabular} Note: St. E—standard error value. St. D—standard deviation value.  
\end{table}
Table 6: Error analysis comparison between the PRO-RF model and the GRNN model.  
Figure 11: Intuitive comparison diagram of the measured EM and predicted EM by the proposed models: (**a**) PRO-RF model; (**b**) GRNN model.  
and the lower values of RMSE (13.1593) and MAE (8.2674). However, these four optimized RF models are superior to the GRNN model.
* The porosity (Pn) is the most important variable by means of the highest average impact value of 30.52 for predicting the rock EM. Meanwhile, the Pn is also the only variable negatively correlated with EM.  
This paper proposes four effective hybrid RF models to predict the rock EM. It shows a successful application of soft techniques for a rock parameter prediction. Nevertheless, more various rocks should be collected into the integrated database to increase the prediction model's accuracy. Furthermore, other rock properties such as the density, water content and UCS could be considered in the rock EM prediction.  
Conceptualization, C.L. and D.D.; methodology, C.L.; investigation, D.D.; writing--original draft preparation, C.L.; writing--review and editing, C.L. and D.D.; visualization, C.L.; funding acquisition, C.L. All authors have read and agreed to the published version of the manuscript.  
The first author was funded by the China Scholarship Council (Grant No. 202106370038).  
Not applicable.  
The data used in this study are from published research: [PERSON] et al. [3] ([[https://doi.org/10.1007/s12517-015-2057-3](https://doi.org/10.1007/s12517-015-2057-3)]([https://doi.org/10.1007/s12517-015-2057-3](https://doi.org/10.1007/s12517-015-2057-3))), [PERSON] et al. [21] ([[https://doi.org/10.1016/S1674-5264](https://doi.org/10.1016/S1674-5264)]([https://doi.org/10.1016/S1674-5264](https://doi.org/10.1016/S1674-5264))(09)60158-7) and [PERSON] and [PERSON] [52] ([[https://doi.org/10.1016/S0013-7952](https://doi.org/10.1016/S0013-7952)]([https://doi.org/10.1016/S0013-7952](https://doi.org/10.1016/S0013-7952))(98)00071-4).  
The authors declare that they have no known competing financial interest or personal relationships that could have appeared to influence the work reported in this paper.