# Seismological and Engineering Demand Misfits for Evaluating Simulated Ground Motion Records
## 4 Engineering Demand Misfits
Yet, there is variability in terms of alternative engineering demand log-scale misfits where among all types of these misfits, energy-demand dependent log-scale misfits (the upper bound being approximately 0.6) are generally larger than the other types. This can be attributed to the inherent definition of energy as a more complex phenomenon. The values of the average engineering demand log-scale misfits for each station at each study area are given in Table 6. Results for Erzincan (Table 6) present that, consistent with the mean seismological log-scale misfits (Table 4), the smallest misfit corresponds to the station ERC having the closest distance to the fault plane. The same observation is valid for the other study areas including Duzce and L'Aquila, where the least average engineering demand log-scale misfits correspond to the stations DZC and AQA having the closest distance to the fault planes as compared to the other stations. The same observation is also observed for the seismological log-scale misfits of Table 4. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Case Study** & **Station** & **Average Engineering Demand Log-Scale Misfit** \\ \hline Erzincan & ERC & 0.13 \\  & REF & 0.37 \\  & TER & 0.30 \\  & DZC & 0.12 \\  & GYN & 0.38 \\  & IZN & 0.30 \\  & IZT & 0.30 \\  & AQA & 0.13 \\  & CLN & 0.33 \\  & GSA & 0.28 \\  & MTR & 0.19 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Average engineering demand log-scale misfits at all stations for all case studies. Next, the mean engineering demand log-scale misfit for each study area is calculated by taking the average of the entire log-scale misfits at all stations of that case study. The mean log-scale misfits corresponding to the engineering demand parameters for the Erzincan, Duzce and L'Aquila regions are, respectively, calculated as 0.27, 0.28 and 0.23. The values show that the mean engineering demand  
Figure 8: Engineering demand log-scale misfits in terms of HI, ASI, VSI, E-S\({}_{a}\), IE-S\({}_{a}\), E-Ei, and IE-Ei between the real and simulated records of the Duzce event. Figure 7: Engineering demand log-scale misfits in terms of HI, ASI, VSI, E-S\({}_{a}\), IE-S\({}_{a}\), E-Ei, and IE-Ei between the real and simulated records of the Erzincan event. Figure 9: Engineering demand log-scale misfits in terms of HI, ASI, VSI, E-S\({}_{a}\), IE-S\({}_{a}\), E-Ei, and IE-Ei between the real and simulated records of the L’Aquila event. log-scale misfits corresponding to the Erzincan and Duzce, both located on alluvial basins, are greater than that corresponding to the L'Aquila mostly placed on stiff soil conditions. So, the results of engineering demand log-scale misfits are in agreement with the seismological log-scale misfits defined in this study. The maximum difference between the two types of the log-scale misfits is observed for L'Aquila as approximately 30 percent. On the other hand, for Erzincan and Duzce this difference is nearly 25 percent. Finally, GOF scores proposed by [PERSON] and [PERSON] [39] are calculated for the engineering demand parameters for all case studies in order to compare them with the GOF scores defined previously in terms of the seismological measures. Table 7 presents the results for all stations and all case studies. Similar to the seismological GOF scores, in the calculation of engineering demand GOF scores, a uniform weight is considered for all engineering demand parameters. The comparison of the results in Tables 6 and 7 reveals that there is good agreement between the engineering demand log-scale misfits and the engineering demand GOF scores for most case studies. In other words, as the average engineering demand log-scale misfit increases for a specific case study at a selected station, the engineering demand GOF score goes down. For the Erzincan and Duzce regions placed on alluvial basins, the mean engineering demand GOF scores are, respectively, 51 and 49. For the third case study, L'Aquila, which is mostly located on the rock or stiff soil conditions, the mean engineering demand GOF score is estimated as 54.