## 4 Application of Record Selection Model
The _MSE_ values of uni-directional selection between the individual GMs in the set were calculated as 17.71% and 3.37% for the horizontal and vertical GM sets, respectively. When the variation is constrained, these values dramatically decreased to 3.25% and 0.60% for horizontal and vertical directions. The same trend was also observed when constraints were applied to bi-directional selection. The _MSE_ values were 30.83% and 6.32% when record-to-record variability is ignored  
In addition to the above assessments, three components of GM selection according to the scenario-based target spectrum were also considered. It is worth reminding that scenario-based three-component compatible GM selection requires definition of four different targets. The first two are about the target horizontal and vertical target acceleration spectrum. The other two are about the dispersion of horizontal and vertical target acceleration spectra. Dispersion of acceleration spectra versus natural periods can be determined by GMMs proposed in the literature. Therefore, in addition to the compatibility between the mean spectrum of the selected horizontal and vertical spectrum and their corresponding target spectrum, dispersion (or the standard deviation of the acceleration spectrum) of the horizontal and vertical GM spectra must be also compatible with the corresponding target dispersion. Since there is no explicit definition for the compatibility of the spectrum according to scenario-based selection, the ratio between the mean spectrum and the target spectrum was assumed to range from 0.80 to 1.25 in both orientations. The same assumption was also made for horizontal and vertical GMs regarding the compatibility of SD distribution. In this study, the period range for scenario-based GM selection was assumed as 0.2 s-2.0 s and 0.1 s-1.5 s for horizontal and vertical directions, respectively. Based on the period range considered, and the selection constraints defined in Section 4, a solution model is run for GM record sets and the initially and finally obtained results according to a scenario-based earthquake are plotted in Figure 15. In Figure 15a,b, both the mean and SD of the selected horizontal/vertical GM spectrum were not compatible with their corresponding target spectrum since the initial steps of the model are created with a random variable. In this step, the \(MSE\) values in Figure 15a were computed as 0.98% and 23.15% for the mean and SD of the selected GMMs in the horizontal direction, respectively. In addition, the \(MSE\) values in Figure 15b were also determined as 0.36% and 21.31% for the mean and SD of the selected GMMs in the vertical direction, respectively. After a certain number of iterations repeated between Step 3 and Step 5, as shown in Figure 8, the compatibility of GM sets with target spectra increased and the termination creation is satisfied, as seen in Figure 15c,d. It is important to highlight that all constraints were met during all runs for both code- and scenario-based selections. It is clear in Figure 15c,d that the mean and SD of the selected horizontal/vertical GM spectra are highly compatible with the corresponding targets after selection and scaling. The \(MSE\) values for the mean and SD of selected GMMs at the final stage were calculated as 0.04% and 0.04% (Figure 15c) for the horizontal direction, respectively. Similarly, the \(MSE\) values for the mean and SD of selected GMMs at the final stage were determined as 0.05% and 0.06% (Figure 15c) for the  
Figure 14: GM selection for bi-directional selection according to the TBEC for soil class ZD considering the record-to-record variability (**left**: SRSS spectrum of horizontal GMs; **right**: scaled GM of the Z direction). vertical direction, respectively. Starting from the initial step to the final step, the _MSE_ values decreased from 23.15% to 0.04% for the standard deviation of accelerations for both directions by the proposed solution model.