Warning Performance of Singular Spectrum Approach

Because of the unique dynamic characteristics of the ultra-sensitive equipment, the far distant earthquakes have shown the ability to bring significant responses in Section 3.2. To set an early warning, the existence of long-period seismic waves and the potential of significant amplitude need to be addressed. It is interesting to note that, from the observation of the ground motion generated by the far distant earthquakes, the duration from the incoming P-waves to the following S-waves was over hundreds of seconds. Definitely, it is possible to issue a timely warning, turn off the wafer scanners, and avoid the impact before the arrival of the main shock. In the singular spectrum approach, the long-period seismic waves were decomposed by SSA and the significant amplitudes were examined through Arias intensity. Many far distant earthquakes from early 2008 to 2016 were sifted from the database of USGS, as listed in Table 4.1, to study the warning performance. In the 38 far distant earthquakes, the permanent broadband stations in the BATS network recorded all these seismic events; however, the RLNB station missed the 3 far distant earthquakes on May 30, 2015, April 13, 2016, and April 15, 2016. The rest of the seismic events with a total of 105 recorded seismic waveforms were investigated using the singular spectrum approach in Section 4.3.1. For the NCREE network, the permanent broadband stations recorded the 17 seismic events since early 2012. The NCREE network missed the 4 far distant earthquakes on (second) April 11, 2012, August 14, 2012, May 14, 2013, and October 15, 2013. The 17 seismic events with a total of 51 recorded seismic waveforms were then investigated in section 4.3.2. Subsequently, the same records were used to study the warning performance of the wavelet approach in Section 4.4.

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4.3.1 Result of BATS Network

SSA can be performed by embedding the seismic waveforms of the 35 far distant earthquakes into the trajectory matrices and conducting SVD on them. With a window length of 50 seconds and an appended data length of 20 seconds, moving window SSA was used to extract the primary components of the records collected from the RLNB station. The six figures, from Figure 4.18 to Figure 4.23, display the time-varying frequency identified by applying FFT and the peak picking technique to the primary components. It was observed that most of the seismic events contain the long-period seismic waves with the major frequency around 0.1 Hz. The results of the 4 far distant earthquakes on May 12, 2008, September 9, 2009, March 24, 2011, and April 20, 2013, were slighter higher; however, the major periods of these seismic waves were still convincingly long (up to 5 seconds). Admittedly, these long-period seismic waves were robust to the energy dissipation and can transmit over the long distances. The time-varying frequency of the seismic event on August 3, 2014, was dubious, as shown in Figure 4.22(f), since the identified frequency of 0.02 Hz came from the minimum resolution of FFT with the window length of 50 seconds (₅₀¹ = 0.02 Hz). Hence, in this case, the primary component may be a trend rather than seismic waves and the second component is expected for further analysis. So far, the results provided by moving window SSA already showed the existence of long-period seismic waves, and the recorded seismic waveforms were then examined through the slope index to identify the potential of significant amplitude during the far distant earthquakes.

To predict the significant amplitude in the main shock (on the S-waves arrival), the records were used to calculate the averaged slope of Arias intensity and nonlinearly mapped to the slope index through the pre-assigned parameter, 𝛼, which was 0.3 for the BATS network and the singular spectrum approach. With the same window length and the same appended data length, the slope index resulted from the 35 far distant earthquakes is shown in the following six figures, from Figure 4.24 to Figure 4.29. The cardinal directions (UD, NS, and EW directions) were all included because, from the conclusion drawn in Section 4.2, it is unsound to perform the analysis only on a particular direction. Obviously, all the seismic events on May 12, 2008, March 11, 2011, March 24, 2011, and (first) April 11, 2012, had a considerable value for the proposed index, meaning that these 4 far distant earthquakes generated the medium or severe impact on the ultra-sensitive equipment. The slope index of another 2 far distant earthquakes on April 20, 2013, and April 25, 2015, was larger than 0.2 and these far distant earthquakes brought the minor and medium impact, respectively. Although the losses during the far distant earthquake on February 26, 2010, were unclear, the result calculated from the recorded seismic waveforms showed a relatively small value, indicating that this seismic event should

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bring no impact on the wafer scanners. The result calculated from the far distant earthquake on (second) April 11, 2012, exceeded 0.2, too. The second seismic event on that day happened just two hours after the first one, and therefore it produced no impact because most of the wafer scanners in the high-tech fabs had not recovered from the first impact occurred at 8:38 PM. Moreover, the slope index calculated from the Samar (Philippine) earthquake (August 31, 2012) displayed a value smaller than 0.2 and hence there were no losses reported by the high-tech fabs.

4.3.2 Result of NCREE Network

To further verify the singular spectrum approach and compare the results between the BATS and NCREE networks, the seismic waveforms collected from the B550 station during the 17 far distant earthquakes were again analyzed by moving window SSA. The window length and the appended data length kept the same with those applied to the BATS network so that the results were comparable even the sampling rates of these two strong motion networks are different. The time-varying frequency identified from the primary components was shown in Figure 4.30, Figure 4.31, and Figure 4.32. The observation was similar to the one derived from the BATS network; almost all of the seismic events contain the long-period seismic waves with the major frequency around 0.1 Hz.

The time-varying frequency of the far distant earthquakes on April 20, 2013, was slighter higher but it was still considerably long (up to 6 seconds). It is confirmed that these long-period seismic waves traveled the long distances before they reach Taiwan because the energy of these waves lasted longer than the high frequency seismic waves. Moreover, in contrast to the dubious result came from the BATS network, the time-varying frequency of the seismic events on August 3, 2014, was clear and quite reasonable, as shown in Figure 4.31(c), indicating that the records collected from the BATS network do contain a trend. To sum up, the long-period seismic waves existed in all the 17 far distant earthquakes no matter these far distant earthquakes brought impact or not; therefore, the significant amplitudes were the next subject to be discussed.

To examine the potential of significant amplitude, the averaged slope of Arias intensity was first calculated from the recorded seismic waveforms with the same window length and the same appended data length. The records included all the cardinal directions (UD, NS, and EW directions) so that the number of the records was 51 in total. Then, it was nonlinearly mapped to the slope index with the pre-assigned parameter, 𝛼 , which was 0.2 for the NCREE network and the singular spectrum approach. The results of these 17 far distant earthquakes are shown in the following three figures, Figure 4.33, Figure 4.34, and Figure 4.35. Consequently, the far distant earthquake that brought the severe impact kept a quite large value for the slope index, as shown in Figure 4.33(a). This result was pretty similar to the one came from the BATS network, as shown in Figure 4.26(f). The slope index

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of the far distant earthquakes on April 25, 2015, and May 30, 2015, was clearly larger than 0.6, and these seismic events eventually induced the medium impact on the ultra-sensitive equipment. On the other hand, for the far distant earthquakes on April 20, 2013, the proposed index was smaller than 0.6 but slightly larger than 0.4 so this seismic event only produced the minor impact. Lastly, the result from the Samar (Philippine) earthquake (August 31, 2012) displayed a value slightly smaller than 0.2 and hence there were no losses reported by the high-tech fabs.