# Application of Machine Learning Models to Multi-Parameter Maximum Magnitude Prediction
## 5 Discussion
### Considering Different Parameters  
Parametric studies are performed by deleting one seismicity indicator at a time. The importance of each parameter and the differences in model performance in predicting earthquakes of different magnitudes are investigated by evaluating the effects of different seismic activity parameters on the prediction performance of the LSTM model. In this part of the study, we introduced the adjusted R score to comprehensively evaluate the prediction performance of the LSTM model [39; 40]. The R score ranges from \(-1\) to \(1\), where \(1\) indicates perfect predictions, and \(-1\) indicates no correct predictions. This scoring method comprehensively evaluates accurate predictions, false alarms, and missed alarms and can comprehensively reflect the model's predictive performance. The R score formula is as follows:  
\[R=POD-FAR \tag{24}\]  
where \(POD\) represents the proportion of correct predictions to the total number of actual occurrences, while \(FAR\) represents the proportion of false alarms to the total number of predictions. \[POD=\frac{N_{pc}}{N_{pc}+N_{ni}} \tag{25}\]  
\[FAR=\frac{N_{pi}}{N_{pc}+N_{pi}} \tag{26}\]  
where N\({}_{\text{pc}}\) indicates the number of times when the difference between the predicted magnitude and the actual magnitude is within \(\pm 0.5\), N\({}_{\text{ni}}\) indicates the number of times when the predicted magnitude is lower than the actual magnitude by \(0.5\) or more, and N\({}_{\text{pi}}\) indicates the number of times when the predicted magnitude is higher than the actual magnitude by \(0.5\) or more. In Region A (Table 8), for earthquakes with magnitudes of \(5<M_{\text{L}}\leq 6\), the R-value is \(0.85\) when all parameters are included, indicating the high predictive capability of the model. However, when the mean magnitude is removed, the R-value drops significantly to \(0.55\). This suggests that a higher mean magnitude, typically indicative of more frequent medium- to high-magnitude seismic activity and frequent crustal stress release, is crucial for accurate magnitude prediction in this region. Conversely, a lower mean magnitude, associated with more frequent low-magnitude earthquakes and weaker seismic activity, results in less accurate predictions. Interestingly, when the square root of total seismic energy or the mean longitude is removed, the R-value increases to \(0.96\), suggesting that these parameters may introduce noise or redundant information. The square root of total seismic energy reflects the overall energy release of seismic activity, but it may not be as critical as other factors for predictive accuracy in this region. Similarly, mean longitude, which represents the geographic distribution of earthquakes, appears to have a less stable or significant impact on the prediction model in this context. Further analysis reveals that removing the \(b\)-value results in R-values of \(0.82\) (calculated using the least squares method) and \(0.69\) (calculated using the maximum likelihood method). This reduction underscores the importance of the b-value in describing the relationship between earthquake frequency and magnitude, highlighting its critical role in earthquake prediction. For earthquakes with magnitudes greater than \(6\) (\(M_{\text{L}}>6\)), the R-value drops to \(0.37\) when all parameters are included, highlighting the increased complexity of predicting larger earthquakes. Notably, after removing the mean longitude, the R-value decreases to \(0\), indicating that the mean \begin{table}
\begin{tabular}{c c c} \hline \hline
**Metrics** & **5 \(<M_{\text{L}}\leq 6\)** & \(M_{\text{L}}>6\) \\ \hline Accuracy rate & 71\% & 62\% \\ False alarm rate & 29\% & 0 \\ Missed alarm rate & 0 & 38\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results of LSTM model for medium and strong earthquake prediction. longitude is essential for predicting large-magnitude earthquakes.