## 2 Acoustic Emission Tomography  
AET is a method developed by combining AE testing and elastic wave tomography, which only uses the AE arrival time at the sensor to locate the excitation source and identify the elastic wave velocity distribution. Generally, the observation equation of AET can be considered as follows. \[A=f(V,L,O) \tag{1}\]  
where \(A\) is the arrival time of the observed elastic wave, \(V\) is the elastic wave velocity distribution, \(L\) is the position of the AE excitation point, and \(O\) is the onset time of the AE. However, practically, AET firstly identifies \(O\) and \(L\) by assuming \(V\) and then identifies \(V\) using \(O\) and \(L\) by combining the source location technique of AE testing and elastic wave velocity tomography [13]. Because AET is constructed on the basis of elastic wave velocity tomography, the first travel time is computed using ray-trace technique in the computational procedure. On the ray-trace technique, the theoretical first travel time \(T_{ij}\) is between the source candidate \(j\) and the sensor \(i\), and the elastic wave velocity distribution is shown in Equation (2). \[T_{ij}=\sum_{k}S_{k}l_{ijk} \tag{2}\]  
where \(S_{k}\) is slowness, the reciprocal of the elastic wave velocity, in cell \(k\); \(l_{ijk}\) is the length of the ray-path from the source candidate \(j\) to the sensor \(i\) in cell \(k\). Figure 1 shows an overview of the identification of elastic wave velocity distribution via AET. The velocity within each cell in the model is constant. In AET, the elastic wave velocity is updated only on the cells in which the ray-paths pass through. Further, in the least-squares method, the number of ray-paths is the number of equations, and the number of cells is the number of the variables. The number of elastic wave events is a crucial parameter in identifying the elastic wave velocity distribution. Moreover, since the source location is assigned at the nodal and relay points, which are called \"candidate points\" altogether, in the cell, the number of relay points evidently contributes to the analysis accuracy because it shows the resolution of the source location [22]. On the other hand, the potential excitation time \(P_{ij}\) calculated from the arrival time of sensor \(i\) at candidate point \(j\) is shown in Equation (3). \[P_{ij}=A_{i}-T_{ij} \tag{3}\]  
where \(A_{i}\) is the observed arrival time at sensor \(i\). It should be noted that the ray-path is approximated as a straight path by assuming the local damage is not severe and the effect of diffraction and refraction is limited in this study. Then, as shown in Figure 1, the elastic wave oscillates in AET; the elastic wave travels in a straight line from the excitation source to the sensor, and the arrival time is used to update the velocity distribution. \(\overline{P}_{j}\) is the average of the potential excitation times at candidate point \(j\) and it is obtained as shown in Equation (4). \[\overline{P}_{j}=\frac{1}{n}{\sum_{i=0}^{n}}\ P_{ij} \tag{4}\]  
\(v_{j}\) is the variance of the potential excitation times at candidate \(j\), which is shown in Equation (5). \[v_{j}=\frac{1}{n}{\sum_{i=0}^{n}}\Big{(}P_{ij}-\overline{P}_{j})^{2} \tag{5}\]  
where \(n\) is the number of sensor points. Although the elastic wave velocity distribution and ray-paths are completely reproduced, the potential excitation times are equal to each other at the source location. However, this is not generally achieved since the reproduction is insufficient due to the limitations of the resolution of modeling. Therefore, the point with the smallest variance of the potential excitation times is selected as the source location and \(\overline{P}_{j}\) at the selected point is adopted as the excitation time of the event. After locating the source location, the first travel time can be determined by using \(\overline{P}_{j}\).