## 2 Improvement of Post-Processing and Localization
### Arrial Time Picking  
By an accurate determination of the arrival time, localization errors can be reduced significantly. Traditionally, the time of arrival (TOA) is defined by the first amplitude threshold crossing. However, this approach is sensitive to errors when this threshold is not set to an optimal value. In the presented experimental program, a first estimation of the TOA, \(t_{\text{first}}\), was used as a trigger to discretize different signals and store them, together with a pre-trigger part of the signal. A more exact estimation of the arrival time was subsequently determined using the Akaike Information Criterion or AIC picker as applied in the literature [27; 28]:  
\[\text{AIC}(t_{\text{w}})=t_{\text{w}}\cdot\log_{10}(\text{var}(R_{\text{w}}(1,t_{\text{w}})))+(T_{\text{w}}-t_{\text{w}}-1)\cdot\log_{10}(\text{var}(R_{ \text{w}}(t_{\text{w}}+1,T_{\text{w}}))), \tag{1}\]  
The signal \(R_{\text{w}}\) is divided into two sections at a point \(t_{\text{w}}\). Point \(t_{\text{w}}\) is varied from 1 to \(T_{\text{w}}\), with \(T_{\text{w}}\) the non-dimensional length of the time window. In this paper, the time at which the maximum amplitude of the signal was reached, was chosen as \(T_{\text{w}}\). The term \(\text{var}(R_{\text{w}}(1,t_{\text{w}}))\) is the variance function of all samples from 1 to \(t_{\text{w}}\) and \(\text{var}(R_{\text{w}}(t_{\text{w}}+1,T_{\text{w}}))\)  
Figure 1: Flowchart of the developed AE post-processing protocol. is the variance function of all samples from point \(t_{\text{w}}+1\) to \(T_{\text{w}}\). The absolute minimum of all values indicates the new onset time, \(t_{\text{AIC}}\):  
\[t_{\text{AIC}}=\underset{t_{\text{w}}}{\text{argmin}}\,\text{AIC}(t_{\text{w}}) \tag{2}\]  
Figure 2 exemplifies the difference between the AIC picker and a threshold-based arrival time picker. AIC is more reliable than a threshold-based TOA picking; however, errors may still occur [29]. Two criteria were applied to filter the most reliable AE signals for which the TOA could be picked accurately. The first criterion is based on the signal-to-noise ratio (SNR) and evaluates whether there is the potential that the TOA can be accurately picked. The second criterion evaluates whether the TOA was accurately picked by AIC based on the shape of the AIC value graph [30]. The SNR is defined as the ratio of the signal power \(S\) to the noise power \(N\) in which \(S\) is the maximum absolute amplitude value in mV of the entire signal, and \(N\) is the maximum absolute amplitude value in mV of the first couple of microseconds of the signal (Equation (3)). The SNR threshold was set to 10, which was determined based on careful analysis of the recorded AE signals. If the SNR was larger than 10, the difference between the actual signal and noise level was large enough and the signals were kept for further analysis. A similar approach based on the root mean square was previously presented by [PERSON] et al. [31]. \[SNR=20\cdot\log_{10}\left(\frac{S}{N}\right) \tag{3}\]  
The second criterion comprises the shape of the AIC value graph and has been presented by [PERSON] [30]. The criterion was adapted to the AE settings used in the current research. The actual TOA was estimated accurately if \(t_{\text{AIC}}\) coincided with the first low point (local minimum) of the AIC graph. If this was not the case, the time difference between this first low point and \(t_{\text{AIC}}\) was checked. It was found that if the time difference was less than 10 \(\mu\)s, the first local minimum was a better estimation of the arrival time than the global minimum. If the time difference was larger than 10 \(\mu\)s but the slope between the first low point and \(t_{\text{AIC}}\) was smaller than \(-25\)\(\frac{1}{\mu\text{s}}\), the estimation with the AIC picker was still found to be reasonably accurate. These limits were chosen based on a comparison with manually picked arrival times. Both criteria needed to be fulfilled, otherwise the signal was excluded from the analysis.