# Rapid Estimation of Earthquake Magnitude and Source Parameters Using Genetic Algorithms
## 3 Results
### GA Hyperparameter Tuning Experiments for Okada-GA Inversion Model
#### 3.1.1 Experimental Scenarios and Settings  
In simple terms, the task of the GA in the Okada-GA inversion model was to convert the earthquake displacement value into the estimated parameters (i.e., length, width, rake, and slip) based on [PERSON]'s inversion model. In this stage of the experiment, the displacement value used for the inversion was obtained from the forward calculation of [PERSON]'s model using a predetermined earthquake fault model. The displacement was referred to as [PERSON]'s displacement. As [PERSON]'s model involves observation points in its forward calculation, this stage of the experiment used 737 GPS stations related to the 2011 Tohoku Oki earthquake as the observation points. Hence, the fault model used in the experiment was also the fault model of the 2011 Tohoku Oki earthquake event. To obtain valid results for the GA performance when performing the inversion of [PERSON]'s model, more than one fault model was used for the experiment. The four predetermined earthquake fault models used in this stage of the experiment are shown in Table 1.  
The first model was based on prior knowledge about the 2011 Tohoku Oki earthquake, the second model referred to a study published formally by the Tectonics Observatory California Institute of Technology [37], and the third and fourth models were based on models published by the Geospatial Information Authority of Japan (GSI) [38]. Figure 4 shows the fault model and distribution of observation points in the experiment. To obtain a reliable estimation and represent the actual conditions of the data, some random error values were added to [PERSON]'s displacement; these values were about 2-5 mm for each displacement value in the horizontal component. Both the forward and the inversion calculations of [PERSON]'s model in this experiment involved the 737 GPS stations as observation points. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Model 1** & **Model 2** & **Model 3** & **Model 4** \\ \hline lat. (\({}^{\circ}\)) & 142.834 & 142.834 & 144.00 & 142.80 \\ long. (\({}^{\circ}\)) & 38.17 & 38.17 & 38.80 & 37.33 \\ depth (km) & 20 & 21 & 5.1 & 17 \\ strike (\({}^{\circ}\)) & 210 & 201 & 203 & 203 \\ dip (\({}^{\circ}\)) & 9 & 9 & 16 & 15 \\ 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 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Earthquake fault models used in the first stage of the experiment. As noted earlier, all parameters of each fault model presented in Table 1 were used as input for the forward calculation of [PERSON]'s model to generate Okada's displacement. In this stage of experiment, the Okada's displacement of each fault model was inversed using the GA to obtain four source parameters (i.e., the length, width, rake, and slip of the fault plane) by searching for the optimum solution that yielded the minimum fitness function. The range of search values for each estimated parameter and its data type were previously described in Section 2.2.1. From the estimated parameters obtained using the GA, the estimated displacement was calculated using [PERSON]'s model. In this study, the estimated displacement was referred to as GA displacement. GA performance strongly relies on the hyperparameter settings. Therefore, this study also included the tuning process in its experiments. In this stage, the hyperparameters of the GA were tuned to obtain the optimal estimation results. These hyperparameters included the number of generations (_n_gen_), size of the population (_n_pop_), number of chromosome bits (_n_bits_), crossover rate (_r_cross_), and mutation rate (_r_mut_). The previously mentioned tournament selection hyperparameter \(k\) was set as a fixed parameter in the experiment: \(k=4\). Each hyperparameter combination generated in the tuning process was tested on the four fault models using the two objective functions described previously.