## 2 Ground Motion Record Selection
### Two- and Three-Directional Ground Motion Selection Considering the Vertical Component  
In this section, multi-directional GM selection was discussed utilizing the code-based UHS and scenario-based spectrum for two- and three-directional NDAs. In code-based selection, two different approaches were used. In the first approach, only matching of target horizontal and target vertical spectra was considered. In the second approach, not only mean spectra but also standard deviations (0.5- and 2.0-times the target) of the records were considered, while this is not specified by most codes. In both approaches, different combinations of GM orientations (e.g., XZ or YZ and XYZ directions) were used. On the other hand, the distribution of the standard deviations (SDs) of selected GM records for multiple GM orientations conformed to the standard deviations calculated from the GMM and aligned with the target spectrum in horizontal and vertical directions. Accordingly, the topics discussed in this section can be divided into two categories: code-based two- or three-directional GM selection and scenario-based GM selection. Two-directional GM selection represents the XZ or YZ components of GMs. For instance, if the X or Y horizontal component of a GM record (e.g., 101x or 101y) is selected then the vertical component of this record (e.g., 101z) is considered for matching. Three-dimensional GM selection requires using a combined horizontal spectrum such as the SRSS (e.g., 101, which is the SRSS of 101x and 101y). Once again, the vertical component of the same record (viz, 101z) is used for spectral matching. It is important to highlight that the solution model relies not only on the SRSS; other combined spectra, such as the geometric mean and period-dependent rotated spectra, can also be easily implemented and utilized. During selection, two different target and mean spectra (i.e., vertical and horizontal) are computed and checked simultaneously and the number of selected GM components changes depending on two- or three-directional analysis. For example, let us say that we use seven GM components for GM sets (i.e., EC8-based selection). The number of selected GM components is 14 (7 components \(\times\) 2 orientations) for two-dimensional analysis while it is 14 for three-dimensional analysis (7 component pairs for horizontal and 7 components for vertical orientation). When the selection is extended for scenario-based selection, the number of selected GM components remains the same but the computation and controlling of the matching of target spectra are doubled. In other words, four different target spectra, namely two for target spectral accelerations and two for target SDs of spectral accelerations of horizontal and vertical orientations, are obtained.  
A typical representation of the alignment of target and mean spectra of selected GMs is shown in Figure 6 as an example. Target and mean spectra can be either horizontal or vertical. The enhanced solution algorithm utilized in this study is designed to minimize the areas between the mean spectrum and the target spectrum. Given the stochastic and random nature of the algorithm, the area between the mean of the selected scaled/unscaled GMs and the target spectrum can be substantial (refer to Figure 6a). However, the area between the mean and the target spectrum is minimized (see Figure 6b) with the increasing iterations of the algorithm. The same idea applies to the SD of selected GMs and the target SD at the considered period ranges, as demonstrated in Figure 7. Detailed information about the algorithm and definition of the problem is given in Section 3.