## 6 Discussion  
### Using Time Window Sampling for VMD  
In this study, the data are decomposed using VMD with a rolling time window approach for single samples. The benefits of this approach are as follows:  
1. Capturing Individual Characteristics: Single-sample decomposition better captures the individual characteristics of each sample, avoiding information loss that may occur with overall decomposition. This is particularly important for magnitude prediction because earthquake events are highly localized and random. According to [PERSON] et al. [44], the independent decomposition of individual samples using VMD can effectively capture local features, thereby improving the model's prediction accuracy.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Time Window**} & \multicolumn{3}{c}{**6**} & \multicolumn{3}{c}{**12**} \\ \cline{2-7}  & **MSE** & **RMSE** & **MAE** & **MSE** & **RMSE** & **MAE** \\ \hline LSTM & 0.699 & 0.836 & 0.638 & 0.683 & 0.827 & 0.622 \\ BiLSTM & **0.666** & **0.816** & **0.623** & 0.717 & 0.847 & 0.650 \\ Att-LSTM & 0.718 & 0.846 & 0.645 & 0.710 & 0.842 & 0.639 \\ Att-BiLSTM & 0.708 & 0.841 & 0.666 & **0.678** & **0.824** & **0.635** \\ \hline \hline \multicolumn{7}{c}{**18**} & \multicolumn{3}{c}{**24**} \\ \cline{2-7}  & **MSE** & **RMSE** & **MAE** & **MSE** & **RMSE** & **MAE** \\ \hline LSTM & 0.685 & 0.828 & 0.622 & 0.711 & 0.843 & 0.625 \\ BiLSTM & **0.674** & **0.821** & **0.623** & 0.745 & 0.863 & 0.658 \\ Att-LSTM & 0.679 & 0.824 & 0.609 & **0.681** & **0.826** & **0.621** \\ Att-BiLSTM & 0.695 & 0.834 & 0.622 & 0.690 & 0.831 & 0.638 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Calculation results during VMD.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Time Window**} & \multicolumn{3}{c}{**6**} & \multicolumn{3}{c}{**12**} \\ \cline{2-7}  & **MSE** & **RMSE** & **MAE** & **MSE** & **RMSE** & **MAE** \\ \hline LSTM & 0.758 & 0.871 & 0.658 & 0.725 & 0.851 & 0.640 \\ BiLSTM & 0.782 & 0.884 & 0.670 & 0.706 & 0.840 & 0.655 \\ Att-LSTM & **0.707** & **0.841** & **0.632** & **0.705** & **0.840** & **0.625** \\ Att-BiLSTM & 0.738 & 0.859 & 0.652 & 0.724 & 0.851 & 0.641 \\ \hline \hline \multicolumn{7}{c}{**18**} & \multicolumn{3}{c}{**24**} \\ \cline{2-7}  & **MSE** & **RMSE** & **MAE** & **MSE** & **RMSE** & **MAE** \\ \hline LSTM & **0.724** & **0.850** & **0.644** & 0.755 & 0.869 & 0.657 \\ BiLSTM & 0.760 & 0.871 & 0.673 & 0.725 & 0.851 & 0.653 \\ Att-LSTM & 0.731 & 0.855 & 0.653 & 0.700 & 0.836 & 0.637 \\ Att-BiLSTM & 0.734 & 0.857 & 0.649 & **0.694** & **0.833** & **0.636** \\ \hline \hline \end{tabular}
\end{table}
Table 5: Calculation results without VMD.  
2. Enhancing Model Sensitivity: Since each sample is processed independently, single-sample decomposition enhances the model's sensitivity to anomalous samples and extreme events. [PERSON] et al. noted that for data with extreme variations, the single-sample decomposition strategy can significantly improve the model's ability to respond to abnormal changes [45].  
3. Reducing Information Leakage: Overall decomposition might lead to information leakage. The single-sample decomposition method effectively avoids the problem of information leakage that can occur with overall decomposition. Information leakage refers to the unintentional use of future sample information in the decomposition of current samples. Although this might lead to high accuracy in predictions, the lack of future data in actual applications could result in poor performance. Research by [PERSON] et al. [46] shows that single-sample decomposition can effectively avoid information leakage, thus improving the model's prediction reliability.