## 4 Comparison of Records Spectra and Correlation Coefficient  
The mean response spectra obtained from three different record sets are presented in Figure 6. As shown, the mean response spectra of the records are approximately matched to the target spectrum in the period range of the bridges. The SIMQKE artificial records are closely matched to the target spectrum, while the matching obtained using the natural records and the Atkinson artificial records have larger differences. Since the number of available Atkinson records are limited to 45 records in each set, it is difficult to achieve a close match with the target spectrum. This is especially true if the period range considered for matching is relatively wide. The natural records in this study were selected from a large pool of records; therefore, very good spectral matching was achieved for this case. The matching error, E, obtained at different periods is shown in Figure 6b for different record sets in terms of Ln(SAmean/SAtarg), where SAmean is the mean spectrum of the records. It should be noted that increasing the number of records will not necessarilyresult in improved matching. This is because as the number of records increases, records with larger differences (i.e., error) relative to the target spectrum need to be used. The variability of the records response spectra for different sets is shown in Figure 6c in terms of logarithmic standard deviation (i.e., record-to-record variability). As shown in the figure, the variability of the SIMQKE records are significantly smaller than that of the other two sets. The variability of the Atkinson records in the period range of 0.3 to 1.0 s is similar to that of the natural records and it is smaller in other period ranges. It should be noted that the use of the spectrum matched records results in a reduced record-to-record variability in general. Therefore, these records are only used for the prediction of the mean responses of the bridges.  
The coefficients of correlation between the horizontal components of the artificial records were computed for 140 randomly paired records. The correlation coefficients for a pool of 326 natural records selected from the PEER-NGA database were also computed. In Figure 7a,b the cumulative probabilities of the correlation coefficients were compared for the case of the as-recorded horizontal components and the maximum correlation (e.g., [32]). To predict the correlation coefficients reported in Figure 7, a computer code was developed to calculate these coefficients for different types of records based on the equations and recommendations provided by [PERSON] [32]. The results demonstrate that the correlation coefficients were much lower for the SIMQKE artificial records considered. The total cumulative probabilities of the correlation coefficients for the Atkinson records were approximately similar to those of the natural records as shown in Figure 7c. Some codes impose an upper bound of 0.3 for the correlation coefficients of the records used in analysis [27]. There is a general concern that the simultaneous use of highly correlated motions may underestimate the response in certain cases [32].  
Figure 6: Comparison of the spectrum matching for different artificial and natural records for case of: (**a**) mean response spectra; (**b**) error in spectrum matching and (**c**) logarithmic standard deviation.  
Figure 7: Correlation coefficients between the horizontal components for different record sets for the case of (**a**) as-recorded motions; (**b**) maximum correlation and (**c**) total cumulative probability.