## 6 Characterization of the Pulse-Like Seismic Motion for Chi-Chi Event
No clear trend was found for the relationship between the number of pulses and the closest distance-to-fault. In Table 2, the mother wavelets chosen for each station were different from each other. Of the frequencies, 79.31% were located within 0.1-0.2 Hz. In Table 3, all records (except for TCU068) used different types of mother wavelets to represent the profile of the pulse waveform in the seismic signals. The average frequency for \(f_{1}\) was 0.128 Hz. The average frequency for \(f_{2}\) was 0.176 Hz, 37.5% higher than that of \(f_{1}\). In Table 4, the average frequencies for \(f_{1}\), \(f_{2}\), and \(f_{3}\) were 0.158 Hz, 0.164 Hz, and 0.227 Hz, respectively. In Table 3, the wavelet coefficient for the component \(p_{1}\) was always larger than that for the component \(p_{2}\), indicating that the extracted component \(p_{1}\) was always the one containing larger pulse energy than component \(p_{2}\). A similar pattern was also found in Table 4. Thus, the individual pulse components extracted using the author's method were sorted by the pulse energy from high to low. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline
**No.** & **Station** & **Wn\({}_{1}\)** & **Coef\({}_{1}\)** & **f\({}_{1}\)/Hz** & **Time\({}_{1}\)/s** & **No.** & **Station** & **Wn\({}_{1}\)** & **Coef\({}_{1}\)** & **f\({}_{1}\)/Hz** & **Time\({}_{1}\)/s** \\ \hline
1 & CHY006 & ’gauss2’ & 560.0 & 0.36 & 34.79 & 16 & TCU054 & ’gauss1’ & 713.0 & 0.10 & 34.83 \\
2 & CHY024 & ’gauss5’ & 681.0 & 0.17 & 35.06 & 17 & TCU063 & ’gauss6’ & 1030.0 & 0.18 & 43.03 \\
3 & CHY035 & ’gauss7’ & 337.0 & 0.71 & 35.23 & 18 & TCU065 & ’gauss7’ & 1610.0 & 0.20 & 30.60 \\
4 & CHY092 & ’gauss3’ & 846.0 & 0.21 & 35.22 & 19 & TCU075 & ’db2’ & 100.0 & 0.16 & 28.71 \\
5 & CHY101 & ’db5’ & 1370.0 & 0.17 & 39.20 & 20 & TCU076 & ’db2’ & 707.0 & 0.18 & 27.83 \\
6 & NSY & ’morl’ & 712.0 & 0.14 & 34.24 & 21 & TCU082 & ’gauss1’ & 764.0 & 0.10 & 34.74 \\
7 & TCU & ’db3’ & 543.0 & 0.17 & 20.07 & 22 & TCU087 & ’db6’ & 663.0 & 0.11 & 41.70 \\
8 & TCU029 & ’db6’ & 829.0 & 0.19 & 50.25 & 23 & TCU088 & ’db6’ & 272.0 & 0.10 & 41.88 \\
9 & TCU036 & ’gauss6’ & 965.0 & 0.21 & 47.09 & 24 & TCU096 & ’db4’ & 678.0 & 0.11 & 42.40 \\
10 & TCU038 & ’db3’ & 737.0 & 0.12 & 46.96 & 25 & TCU102 & ’gauss1’ & 1030.0 & 0.15 & 36.09 \\
11 & TCU040 & ’gauss6’ & 761.0 & 0.19 & 48.15 & 26 & TCU103 & ’db6’ & 941.0 & 0.13 & 40.63 \\
12 & TCU045 & ’db6’ & 508.0 & 0.12 & 44.82 & 27 & TCU117 & ’gauss8’ & 792.0 & 0.16 & 53.54 \\
13 & TCU046 & ’gauss5’ & 611.0 & 0.11 & 39.35 & 28 & TCU122 & ’morl’ & 585.0 & 0.13 & 35.80 \\
14 & TCU049 & ’gauss3’ & 663.0 & 0.11 & 36.07 & 29 & WGK & ’db6’ & 744.0 & 0.24 & 24.80 \\
15 & TCU051 & ’gauss3’ & 603.0 & 0.12 & 35.08 & - & - & - & - & - \\ \hline \end{tabular}
\end{table} 
Table 2: The wavelet parameters for the earthquake motions qualified as pulse-like with one mother wavelet. Figure 14: The distribution of \(\theta_{max}\) for the identified pulse-like near-fault seismic motions during the Chi-Chi event. Figure 15 shows the relative frequency distribution for the occurrence of the mother wavelets in the 53 sets qualified earthquake motions. The relative frequency of 'db6' for the first and second pulse components were 28.3% and 37.5%, respectively, which were the most frequently used types of mother wavelets for both the first and the second pulse components as shown in Figure 15a,b. The'morl' mother wavelet was more frequently used compared with other mother wavelets for the third pulse component as shown in Figure 15c. Figure 15 also shows that the 'haar' mother wavelet was not used for any pulse extraction because its shape was not similar to the common profile of the pulse waveform embedded in the seismic signals.