## 2 Intensity Measures for MS-AS Sequences  
In this study, four categories of IMs were used to represent MS-AS sequences based on 22 classic IMs. They are \(PGA\)[46], \(I_{A}\)[47], \(P_{a}\)[48], \(E_{a}\)[49], \(a_{rms}\)[50], \(a_{rs}\)[51], \(I_{c}\)[44], \(I_{a}\)[52], \(PGV\)[46], \(P_{v}\)[48], \(P_{D}\)[53], \(E_{v}\)[49], \(v_{rms}\)[50], \(v_{rs}\)[51], \(I_{v}\)[52], \(I_{F}\)[54], \(PGD\)[46], \(P_{d}\)[48], \(E_{d}\)[49], \(d_{rms}\)[50], \(d_{rs}\)[51], \(I_{d}\)[52]. The 22 classic IMs have also been used in [38], which can be divided into three groups related to acceleration (see Figure 1), velocity (see Figure 2), and displacement (see Figure 3), respectively. It is noteworthy that the structure-specific IMs are not included in this study since they are commonly related to the structural fundamental period that would be elongated due to the MS-induced damage. In other words, two different structural periods are needed to define a structure-specific IM for the MS and the following AS. Thus, this study only adopts IMs associated with the basic properties of ground motions. The considered four MS-AS IM categories include the mainshock IM, i.e., \(IM^{\text{MS}}\), and aftershock IM, i.e., \(IM^{\text{AS}}\), which are taken as the important intensity indicators for predicting the damage potential of MS-AS sequences according to [PERSON] et al. [42] and [PERSON] et al. [43], respectively. Besides \(IM^{\text{MS}}\) and \(IM^{\text{AS}}\), two new types of IMs for MS-AS sequences were proposed herein, which are briefly represented by \(IM_{1}{}^{\text{MS-AS}}\) and \(IM_{2}{}^{\text{MS-AS}}\). Using the considered 22 classic IMs, \(IM_{1}{}^{\text{MS-AS}}\) is defined by taking the entire MS-AS sequence as one nominal time history of ground motion acceleration. In particular, the peak amplitude-related IMs, including \(PGA\), \(PGV\), and \(PGD\), are used to determine \(IM_{1}{}^{\text{MS-AS}}\) by max (\(IM^{\text{MS}}\), \(IM^{\text{AS}}\)). As for the other IMs related to ground motion duration, they are used to define \(IM_{1}{}^{\text{MS-AS}}\) using the combined duration of the MS and the associated AS ground motions. As for \(IM_{2}{}^{\text{MS-AS}}\), it is defined by the ratio of \(IM^{\text{AS}}\) to \(IM^{\text{MS}}\), i.e., \(IM_{2}{}^{\text{MS-AS}}=IM^{\text{AS}}/IM^{\text{MS}}\). It is clear that \(IM_{2}{}^{\text{MS-AS}}\) is a dimensionless and compound parameter by combing \(IM^{\text{AS}}\) and \(IM^{\text{MS}}\) together. Tables 1-3 provide the considered IMs related to acceleration, velocity, and displacement, respectively, and the corresponding definitions for MS-AS ground motions. \begin{table}
\begin{tabular}{c c c c} \hline
**IMs** & \(IM^{\text{MS}}\) & \(IM^{\text{MS}}\) & \(IM^{\text{MS-AS}}\) & \(IM^{\text{MS-AS}}_{1}\) \\ \hline \(PGA\) & \(PGA^{\text{MS}}=Max\!\left[a(  
Figures 1-3 show the obtained values of the 22 classic \(IM^{\text{MS}}\) and \(IM^{\text{AS}}\) by using the acceleration-, velocity-, and displacement-related IMs, respectively. It is found that most of the selected MS ground motions have larger intensities than the corresponding AS ground motions regardless of the IMs adopted, indicating significantly higher hazard caused by MSs compared to ASs. As observed, approximately over 90% (except only 89.32% of \(PGA^{\text{MS}}\) values is greater than the corresponding \(PGA^{\text{AS}}\) values, as shown in Figure 1a) of the considered MS ground motions show larger IMs than the corresponding AS ground motions. This result shows the larger damage potential of MSs than the corresponding ASs. Since the \(I_{A}\), \(E_{a}\) and \(a_{rs}\) have similar definition equations (see Table 1), their percentages corresponding to \(I_{A}^{\text{MS}}>I_{A}^{\text{AS}}\) (Figure 1b), \(E_{a}^{\text{MS}}>E_{a}^{\text{AS}}\) (Figure 1c), and \(a_{rs}^{\text{MS}}>\ a_{rs}^{\text{AS}}\) (Figure 1d), respectively, are almost the same.