# Rapid Estimation of Earthquake Magnitude and Source Parameters Using Genetic Algorithms
## 4 Discussion  
The estimation results of the first stage of the experiment in Table 3 showed that \(error\_disp\) was, on average, 3.784 \(\times\) 10\({}^{-3}\) m for all the models or 3.572 \(\times\) 10\({}^{-3}\) m for the first model as the minimum error and 4.339 \(\times\) 10\({}^{-3}\) m for the maximum error value. These values indicated that the Okada-GA inversion model generated estimated displacements close to the referenced displacements. The estimation results for each parameter in each model were also close to the reference values in all fault models tested. This meant that the Okada-GA inversion model proposed in this study could provide relatively accurate estimation results. Figure 5 also showed that the GA displacements almost coincided with [PERSON]'s displacements. However, the estimation results in the second stage of the experiment were not as accurate as the first stage results. The average of \(error\_disp\) in the second stage of the experiment (0.105 m) was larger than \(error\_disp\) generated in the first experiment (3.78 \(\times\) 10\({}^{-3}\) m). In the first stage, the referenced displacement values were [PERSON]'s displacements, which were fixed values generated from the forward calculation of [PERSON]'s model. Meanwhile, in the second stage, the reference values were the real permanent displacement values estimated from the permanent displacement formula [5], which presented significant errors compared with [PERSON]'s displacements. According to the calculations using all the observation points, the average of \(error\_disp\) in the RMSE between the real permanent displacements and [PERSON]'s displacements was 0.083 m for the N components and 0.148 m for the E components. For the vertical components, the RMSE of \(error\_disp\) in the Z components was 0.098 m.  
The Okada-GA inversion model proposed in this study used [PERSON]'s model as the main component of its objective function. Hence, the smaller the \(error\_disp\) was between the real permanent displacement and [PERSON]'s displacement, the smaller the RMSE was  
Figure 9: Comparison of GA displacement and referenced permanent displacement of the 2018 Lombok earthquake. between GA displacement and the reference value, which was [PERSON]'s displacement. Therefore, when the Okada-GA inversion model estimated the displacement values with real permanent displacement as its reference values, it was reasonable for the error difference to reach 0.105 m, but not when the Okada-GA inversion model estimated the displacement values using [PERSON]'s displacements as its reference values. However, the estimated result of each source parameter (length, width, rake, and slip) shown in Table 5 was reasonable according to the 2011 Tohoku Oki earthquake's source model described and analyzed in previous research [40; 41; 42]. Some fault plane models analyzed in previous research ranged from 600 to 812 km in length and from 109 to 240 km in width [41; 42], while the results estimated in this study used 668 km for the length parameter and 234 km for the width parameter in the third fault model tested. The range of estimated width parameter values that resulted from this study was between 153 to 234 km. The slip estimation value ranged between 25 and 60 m in most previous research [40; 41], while this study estimated slips in the range of 10 to 24.598 km. The _Mw_ estimation results in both the first and second stages of the experiment were also close to the reference values in each model, both in the 2011 Tohoku Oki and 2018 Lomb-bok earthquake events. Furthermore, Figure 8 showed that the proposed method provided a relatively stable estimation value from early observations (elapsed time \(t=173.81\) s)--that is, as soon as a permanent displacement was detected and estimated. In the testing experiment on the 2011 Tohoku Oki earthquake's data, the first _Mw_ estimations generated using each fault model in testing were 8.8, 8.823, 9.14, and 9.067 for fault model 1, 2, 3, and 4, respectively.