## 3 Acoustic Emission Tomography with Potential Excitation Time Weight  
When the sensor and excitation points are close to each other and the propagation distance of the elastic wave is short, the first travel time will be small, and the effect of the error on the observed values would be relatively large. Therefore, the identification accuracy of elastic wave velocity distribution is generally improved by removing elastic wave events in which the excitation point is close to the sensor. However, these processes are based on actual measurements and not theoretically validated. Furthermore, the number of excluded equations would increase, resulting in the final number of equations falling short of the number needed to properly identify the elastic wave velocity distribution. In this study, we multiplied the weights via linear interpolation from the potential excitation time distribution and the distances between the candidate points and sensors instead of removing observation equations that may contain large observed arrival time errors. Considering the weighting of the potential excitation time, the potential excitation time and the distance between the sensor and candidate point in an event are classified into the  
Figure 1: Example of elastic wave velocity distribution identification via AET. following three ranges. The ranges that are specified in Equations (9) to Equation (11) are named range 1, range 2 and range 3, respectively. \[l_{ij}<\beta,\ \ P_{ij}>\overline{P}_{j} \tag{9}\]  
\[l_{ij}>\beta,\ \ P_{ij}>\overline{P}_{j} \tag{10}\]  
\[l_{ij}>\beta,\ \ P_{ij}<\overline{P}_{j} \tag{11}\]  
where \(l_{ij}\) is the distance between the sensor \(i\) and candidate point \(j\), and \(\beta\) is the threshold of the distance between the candidate point and sensor for computing the weight. Figure 1(a),b show the relation of \(l_{ij}\) and \(P_{ij}\) without and with weighting. For determining \(\beta\), firstly the line of \(P_{ij}\) is equal to \(\overline{P}_{j}\), and it is drawn in Figure 1(a). Secondly, areas in which the points that represent the pair of \(P_{ij}\) and \(l_{ij}\) at the candidate points exists are clipped and the boundaries of the clipped areas are computed. Finally, the intersections of the line and the boundaries are calculated, and then minimum distance between the vertical axis and the intersection is adopted as \(\beta\). All ranges are divided by these thresholds and are based on elastic wave velocity in the soundness condition and damages condition. In Equation (3), if the ray-path passes through the damage area, \(A_{i}\) is larger than the arrival time of the case in which the ray-path passes through the soundness area because the ray-path diffracts or the travel time is larger. Hence, in accordance with Equation (3), if the location of the candidate point \(j\) is identical to the actual source location and the actual ray-path from sensor \(i\) to candidate point \(j\) passes through the damage area, \(P_{ij}\) would be over \(\overline{P}_{j}\). Thus, if \(P_{ij}\) is over \(\overline{P}_{j}\), it should not be weighted since it involves the information of the damaged area. On the other hand, the potential excitation times of other candidate points that are likely to be affected by errors are weighted so that their absolute values are close to \(\overline{P}_{j}\) for clearly identifying damage areas. The potential excitation times in range 3 were processed with weights. \(w_{ij}\) is the potential excitation weight from the source candidate \(j\) to the sensor \(i\), and it is shown in Equation (12). \[w_{ij}=\frac{l_{ij}-l_{max}}{\beta-l_{max}} \tag{12}\]  
Figure 2: Example of potential excitation time and distance between the sensor and candidate point of event E1 (\(E=0.15\)): (**a**) non-weight and (**b**) weight. where \(l_{\max}\) is the maximum length of the ray-path from the source candidate point \(j\) to the sensor \(i\). \(Pw_{ij}\) is the potential excitation time of AE with the weight and is shown in Equation (13).