## 5 Results  
The normalization errors of the elastic wave velocity distribution and arrival time are defined in Equations (17)-(19). The normalization error of the arrival time are used as convergence conditions of the analysis to visually discriminate between the damaged and  
Figure 4: Example of observation arrival time error distribution (\(E=0.15\)). Figure 5: Example of truncated normal distribution used to generate observation error (\(E=0.15\)). healthy areas and numerically judge the results from the normalization error of the elastic wave velocity distribution. \[L_{2\_A}=\frac{\left\|\Delta A_{j}^{c}\right\|_{2}}{\left\|\Delta A_{j}^{t} \right\|_{2}} \tag{17}\]  
where \(\left\|\Delta A_{j}^{I}\right\|_{2}\) is the sum of the \(L_{2}\) norm based on the observed arrival time from the initial elastic wave velocity distribution obtained for each event \(j\), and \(\left\|\Delta A_{j}^{c}\right\|_{2}\) is the sum of the \(L_{2}\) norm based on the observed arrival time from the identified elastic wave velocity distribution obtained for each event \(j\). The normalized observation error that is shown in Equation (18) is the ratio of L2 norm of the initial residual error of the arrival times and the residual error of the arrival times at the iteration. \[L_{2\_B}=\frac{\left\|\Delta B_{k}^{c}\right\|_{2}}{\left\|\Delta B_{k}^{I} \right\|_{2}} \tag{18}\]  
where \(\left\|\Delta B_{k}^{I}\right\|_{2}\) is the sum of the \(L_{2}\) norm of the true and initial elastic wave velocity distributions obtained for each event \(j\) at cell \(k\). The normalized error of slowness that is introduced in Equation (18) is the ratio of L2 norm of the difference between the initial slowness distribution and target slowness distribution and L2 norm of the difference between the initial slowness distribution and the slowness distribution at the iteration. Consequently, if the normalized error is smaller, the error is reduced to a greater degree. \(\Delta L_{2\_B}\) are the differences in normalized error of slowness between the unweighted and weighted result. \[\Delta L_{2\_B}=L_{2\_B}-L_{2\_B\_w} \tag{19}\]  
where \(L_{2\_B\_w}\) is the sum of the \(L_{2}\) norm of the weighted potential excitation times. We investigate the effectiveness of the proposed method that weights the potential excitation time via \(\Delta L_{2\_B}\). It should be noted that \(\Delta L_{2\_B}\) is larger if the proposed method gives better results than the conventional AET. In Figures 6-8, 100 instances of observation errors are generated for each observation error ratio via truncated normal distribution. The analysis results show that the normalization errors of the elastic wave velocity distribution increased in about 85%, 90%, and 95% of the cases for observation error ratios of 5%, 10%, and 15%. Figure 6: Frequency distribution table of the normalization error residuals of the identified elastic wave velocity distribution \(\Delta L_{2\_B}\) (\(E\) = 0.05). Table 4 shows the minimum, maximum, and average of \(\Delta L_{2\_B}\) for cases of each observation error ratio. In case of the higher observation error ratio, the maximum and average of \(\Delta L_{2\_B}\) largely increase in accordance with Table 4. This implies that the normalization error of the elastic wave velocity distribution decreases if the observation error ratio increases. However, the minimum of \(\Delta L_{2\_B}\) decreases, which means the accuracy of the identified elastic wave velocity distribution is worse with the proposed technique, in case of the higher observation error ratio. According to Figures 9-11, \(\Delta L_{2\_B}\) increases if \(L_{2\_B}\) increases. This reveals that the identified elastic wave velocity distribution is more improved in the presented method if