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Correlation of Response Spectral Values for Multicomponent Ground Motions

¹ Department of Civil and Environmental Engineering
Stanford University
Stanford, California 94305-4020

View larger version (24K): [in a new window]   Figure 1. Effect of smoothing on the empirical correlation matrix for horizontal epsilons in perpendicular directions at two periods (T1 and T2). (a) Before smoothing. (b) After smoothing.

View larger version (23K): [in a new window]   Figure 2. Correlation coefficients for perpendicular horizontal epsilons at the same period. Empirical results, the prediction from equation (7), and the correlations implied from the ratios of standard deviations in Boore et al. (1997) and Spudich et al. (1999).

View larger version (18K): [in a new window]   Figure 3. Correlation coefficients between horizontal epsilons and vertical epsilons at the same period. Empirical results and the prediction from equation (8).

View larger version (55K): [in a new window]   Figure 4. Correlation contours for horizontal epsilons in the same direction at two periods (T1 and T2). (a) Smoothed empirical results. (b) The prediction from equation (9). (c) The prediction from Abrahamson et al. (personal comm., 2003). (d) The prediction from Inoue and Cornell (1990).

View larger version (30K): [in a new window]   Figure 5. Correlation contours for vertical epsilons in the same direction at two periods (T1 and T2). (a) Smoothed empirical results. (b) The prediction from equation (10).

View larger version (25K): [in a new window]   Figure 6. Correlation contours for horizontal epsilons in perpendicular directions at two periods (T1 and T2). (a) Smoothed empirical results. (b) The prediction from equation (11).

View larger version (22K): [in a new window]   Figure 7. Correlation contours of vertical epsilons with horizontal epsilons at two periods (T1 and T2). (a) Smoothed empirical results. (b) The prediction from equation (12).

View larger version (20K): [in a new window]   Figure 8. Correlation coefficient between vertical epsilons and horizontal epsilons when the period in the vertical direction is 0.1 sec.

View larger version (31K): [in a new window]   Figure 9. Overlaid contours at four correlation levels for the empirical correlations, the prediction from equation (9) and the prediction from Abrahamson et al. (personal comm., 2003).

View larger version (27K): [in a new window]   Figure 10. Contours of vector-valued probabilistic seismic-hazard analysis. The contours denote the mean annual rate of exceeding both the Savertical and the Sahorizontal values. P.E., Probability of exceedance.

View larger version (55K): [in a new window]   Figure 11. Samples of 20 response spectra from magnitude 6.5 earthquakes with a source-to-site distance of 8 km. The simulated spectra use means and variances from Abrahamson and Silva (1997). (a) Simulated spectra using correlation coefficients equal to zero between all periods. (b) Simulated spectra using correlation coefficients equal to one between all periods. (c) Simulated spectra using correlation coefficients from equation (9). (d) Real spectra from recorded ground motions with magnitude 6.5 and distance 8 km.