## 6 Characterization of the Pulse-Like Seismic Motion for Chi-Chi Event  
In order to investigate the characterization of the multi-pulse near-fault seismic motion, the author's method was applied to the 221 sets records for the Chi-Chi event collected from the Strong-Motion Virtual Data Center. Fifty-three sets of records qualified as pulse-like motions with a varied number of dominant pulses. Figure 13 shows the distribution of the closest distance-to-fault for the 53 sets pulse-like strong ground motions. The cumulative frequency for the records whose closest distance-to-fault was within 30 km was 92.45%, which took up the majority of the qualified records. This result agrees well with the commonly adopted engineering assumption that the near-fault earthquake motions are mainly located within 30 km from the epicenter. Nevertheless, it should be noted that there are still many records located within 30 km from the epicenter that do not qualify as pulse-like, such as the records shown in Figure 5c,d. Thus, the commonly used engineering assumption of 30 km is not suited for the classification of a specific set of strong ground motion. For near-fault earthquake motions, the largest pulse energy theoretically lies in the direction normal to the strike line [7]. The strike angle is 5\({}^{\circ}\) for the Chi-Chi event, namely the horizontal direction corresponding to the largest pulse energy in the direction of 95\({}^{\circ}\)/275\({}^{\circ}\) for the Chi-Chi event. The identified directions containing the largest pulse energy are plotted in Figure 14 to illustrate the relationship between \(\theta_{max}\) and the closest distance-to-fault. In the figure, the theta axis is the value of the parameter \(\theta_{max}\), the radius axis for the closest distance-to-fault is limited to 30 km to facilitate the comparison with the theoretical direction. The dashed line represents the direction that is perpendicular to the strike of the earthquake event. These data show that there are some seismic motions existing in the directions that are deviated from the dashed line, which indicate that the pulse-like seismic motions were not limited to the direction normal to the fault, other directions that were not perpendicular to the fault may still contain prominent pulse-like motions. Figure 14 also shows that the horizontal direction \(\theta_{max}\) was not limited to the EW/NS direction. Thirty-three set records were located within the range between \(\pm 15^{\circ}\sim\pm 75^{\circ}\), which took up 62.26% of the total number of the qualified pulse-like earthquake motions. Only 9.43% of the qualified earthquake motions lay in the direction with an error smaller than 10\({}^{\circ}\) with respect to the direction normal to the strike. This meant that the majority of horizontal directions containing the largest pulse energy did not coincide with the EW/NS direction at the seismic station for the Chi-Chi event. The use of single one components recorded at the seismic station (EW/NS) may underestimate the energy level of the input seismic signal. The varied relative orientation of the engineering structure with respect to the identified \(\theta_{max}\) may impose a different level of seismic energy on the structure. Figure 13: The relative frequency distribution of the closest distance-to-fault, for the 53 sets of seismic motions, qualified as pulse-like motions. The number of dominant pulses embedded in \(S_{0}\) was a key parameter that greatly influenced the seismic response of structures. The number of dominant pulses was closely related to the non-uniform distributed fracture along the fault, which was difficult to estimate a priori. For the Chi-Chi event, the extraction result using the author's method showed that 29 sets of earthquake motions were represented by one mother wavelet (listed in Table 2), 18 sets were represented by two mother wavelets (listed in Table 3), and six sets were represented by three mother wavelets (listed in Table 4).