# Rapid Estimation of Earthquake Magnitude and Source Parameters Using Genetic Algorithms
## 3 Results
### Testing the Okada-GA Inversion Model Using the Observation Data
#### 3.2.1 The 2011 Tohoku Oki Earthquake Event  
The time series data used for the testing were 1 Hz real-time kinematic-GPS data recorded at 737 observation points during this major earthquake. Here, the displacement of the 2011 Tohoku Oki earthquake was first calculated using the permanent displacement detection and estimation formula [5] described earlier. The displacement result from the formula using the real GPS time series data is referred to, in the next section, as the referenced permanent displacement. From the permanent displacement detection and calculation process, information about the permanent displacement detection and estimation time needed by each GPS station was obtained. Figure 6 shows the number of GPS stations involved in the calculation of the permanent displacement completed at a certain elapsed time \(t\). The estimated permanent displacement was then inversed using the GA to obtain the estimated source parameters. Figure 6: Number of GPS stations with completed permanent displacement as input for the Okada–GA inversion at a certain elapsed time \(t\). The permanent displacement results were used as input for the Okada-GA inversion model. The fault centroid, depth, strike, and dip parameters used for the inversion were the same parameters of the fault models used in the previous stage of the experiment. Comparison between the GA displacements and the referenced permanent displacement can be seen in Figure 7. The blue vectors are GA displacements, and the black vectors are the referenced permanent displacements of the 2011 Tohoku Oki earthquake event. The red pentagram indicates the centroid of each fault model. The estimation results for the 2011 Tohoku Oki earthquake's source parameters of each fault model are shown in Table 5. Table 5 also presents the \(error\_disp\) between the GA displacement and referenced permanent displacement obtained from the permanent displacement formula [5] using the real time series data of 2011 Tohoku Oki earthquake event. The \(error\_disp\) is illustrated earlier in Figure 7.  
Figure 7: Comparison of GA displacement and referenced permanent displacement of the 2011 Tohoku Oki earthquake: (a) fault model 1; (b) fault model 2; (c) fault model 3; (d) fault model 4. From the estimated results of the length, width, rake, and slip of the parameters, the _Mw_ value was estimated using Equations (7) and (8). Tables 3 and 5 show the estimated results of _Mw_ for the first and second stages of the experiment, respectively. In this stage of the experiment, in addition to the displacement results to be used as input into the GA, information about the elapsed time required by each GPS station was also retrieved to complete the permanent displacement formula as shown in Figure 6. Here, \(t_{pd}\) is the elapsed time required to complete the calculation of the estimated permanent displacement, and \(t_{GA}\) is the GA computational time required to obtain the parameter estimation results and _Mw_, calculated from the time of the permanent displacement is input into the GA. Hence, the total elapsed time required by the Okada-GA inversion model proposed in this study to complete the source parameters and magnitude _Mw_ estimation (\(t_{est}\)) was as follows:  
\[t_{est}=t_{pd}+t_{GA}. \tag{14}\]  
Table 6 shows the GA computational time required (\(t_{GA}\)) to obtain the estimated source parameters and the estimated _Mw_ of the 2011 Tohoku Oki earthquake for each fault model tested in the experiment using the previously mentioned hardware specification. According to the data shown in Figure 6, Equation (14), and the \(t_{GA}\) data presented in Table 6, the progress of the _Mw_ estimation could be observed per elapsed time, as shown in Figure 8. The figure presents an update of the estimated value _Mw_ per unit of elapsed time for each fault model employed in the testing, starting from the elapsed time \(t\) = 173.81 to \(t\) = 713.13 s. The first estimation is obtained at the elapsed time \(t\) = 173.81 s, which yields an _Mw_ value of 9.067 using fault model 4.