# Rapid Estimation of Earthquake Magnitude and Source Parameters Using Genetic Algorithms
## 3 Results
### GA Hyperparameter Tuning Experiments for Okada-GA Inversion Model
#### 3.1.2 Hyperparameter Tuning Results  
Based on the experimental results obtained from the hyperparameter tuning process, the GA performance in the Okada-GA inversion model was measured using the following parameters:  
1. The displacement error value, which was defined as the difference between GA displacement and Okada's displacement. This displacement error value was represented by using the RMSE of all the displacement values generated at each observation point. The error value was referred to as the \(error\_disp\) parameter;
2. The estimated magnitude \(Mw\), which was generated by the GA estimation compared with the reference magnitude value generated from the \(Mw\) calculation based on the length, width, and slip parameter values in the forward calculation of [PERSON]'s model. The best estimation result was the estimation with the minimal displacement error value and magnitude value error for all conducted experiments. Table 3 shows the best estimation result for each fault model tested in this stage of the experiment, compared with their original values as presented earlier in Table 1.  
Figure 5 compares GA displacement with [PERSON]'s displacement for each fault model tested. Blue vectors represent GA displacement and black vectors represent [PERSON]'s displacement. Coinciding vectors indicate that the estimation results are closer to the reference value. The red pentagram indicates the centroid of each fault model. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Hyperparameters** & **Description** & **List of Values** \\ \hline \(n\_gen\) & number of generations & [100, 200, 500] \\ \(n\_pop\) & size of the population & [20, 40] \\ \(n\_bits\) & number of chromosome bits & [16, 20, 24] \\ \(r\_cross\) & crossover rate & [0.8, 0.9] \\ \(r\_mut\) & mutation rate (\(\times 10^{-2}\)) & [1.563, 1.250, 1.042] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Hyperparameter values in the tuning process. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Model 1** & **Model 2** & **Model 3** & **Model 4** \\ \hline \multicolumn{5}{c}{Original Parameters Values to be Estimated by Okada-GA Inversion Model} \\ \hline length (km) & 250 & 625 & 186 & 194 \\ width (km) & 50 & 280 & 129 & 88 \\ rake (\({}^{\circ}\)) & 90 & 104 & 101 & 83 \\ slip (m) & 2 & 6 & 24.7 & 6.1 \\ \(Mw\) & 7.857 & 8.939 & 8.773 & 8.27 \\ \hline \multicolumn{5}{c}{Estimation Results from the Okada-GA Inversion Model} \\ \hline length (km) & 252 & 628 & 188 & 194 \\ width (km) & 48 & 280 & 137 & 86 \\ rake (\({}^{\circ}\)) & 91 & 104 & 101 & 83 \\ slip (m) & 2.125 & 5.971 & 22.920 & 6.239 \\ \(error\_disp\) (\(\times 10^{-3}\) m) & 3.572 & 4.339 & 3.614 & 3.609 \\ \(Mw\) & 7.865 & 8.939 & 8.772 & 8.270 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The best estimation results of the source parameters for each fault model tested. The hyperparameter combination settings shown in Table 3 that resulted in the best estimation performance were then selected to be used in the next stage of the experiment. The settings here included the number of generations, size of the population, number of chromosome bits, crossover rate, and mutation rate for each fault model. Table 4 shows the best configuration settings recommended by the tuning process for each fault model used. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Fault Model** & **Fitness Function** & **Generation** & \
\begin{tabular}{c} **Size of** \\ **Population** \\ \end{tabular} & **Number of Bits** & **Crossover Rate** &
\begin{tabular}{c} **Mutation Rate** \\ **(\(\times\)10\({}^{-2}\))** \\ \end{tabular} \\ \hline
1 & Equation (4) & 500 & 40 & 24 & 0.8 & 1.042 \\
2 & Equation (3) & 500 & 20 & 16 & 0.8 & 1.563 \\
3 & Equation (4) & 500 & 40 & 24 & 0.8 & 1.042 \\
4 & Equation (3) & 200 & 40 & 16 & 0.8 & 1.563 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The best configuration settings for each fault model.