1. SPATIAL CORRELATION OF SPECTRAL ACCELERATIONS Paolo Bazzurro, Jaesung Park and Nimal Jayaram 1

2. Motivation Ground-motion intensities at multiple sites during the same earthquake exhibit spatial correlation Spatial correlation is a key input parameter for risk analysis of spatially-distributed systems such as lifelines and building portfolios Researchers have used recorded ground motions to develop models for this spatial correlation We are interested in estimating spatial correlation using simulated ground motions 2 PGA residuals from the 1999 Chi-Chi earthquake

3. Ground-motion models are used to characterize ground- motion intensities at individual sites Ground-motion models are used to predict the distribution of the ground-motion intensities as a function of magnitude, source-to- site distance, etc. for each earthquake 3 Spectral acceleration at site “i”Predicted mean (log) spectral acceleration Intra-event residual at site “i” Inter-event residual (at all sites) USGS hazard map PGA with 10% probability of exceedance in 50 years

4. Observed “residuals” from well-recorded earthquakes Observations of past earthquakes shows that these residuals are correlated at nearby sites, due to – Common source earthquake – Similar location to asperities – Similar wave propagation paths – Similar local-site effects 4 PGA ε’s from the 1999 Chi-Chi earthquake

5. A typical approach for estimating spatial correlation Ideally, we would like to have many observations at every site pair of interest Lacking that, the following assumptions are commonly made – Any pair of sites with equal separation distance within an earthquake has the same correlation (stationarity) – The correlation is independent of orientation (isotropy) 5 Site j Site i Jayaram and Baker (2010)

6. Estimation of spatial correlation The stationarity and isotropy assumptions allow us to pool many pairs of observations with comparable separation distances We can then estimate a correlation coefficient 6 PGA ε’s from the 1999 Chi-Chi earthquake ε’s at two sites separated by a specified distance

7. Spatial correlation prediction model To turn these observations into a predictive model, we need: An equation to predict correlation as a function of separation distance, h: A correlation “range” R 7 Empirical semivariogram “Range”

8. Empirically estimated ranges 8 Source: Jayaram and Baker (2010)

9. Simulations used We use the following simulations – 1989 Loma Prieta earthquake from Dr. Rob Graves – 1989 Loma Prieta earthquake from Dr. Brad Aagaard – 1906 San Francisco earthquake Song-Mod set from Dr. Brad Aagaard (San Francisco hypocenter) – 1906 San Francisco earthquake Random HypoC from Dr. Brad Aagaard (Bodega bay hypocenter, random slip distribution) Source model – Beroza (1991) and Wald et al. (1991) for Loma Prieta earthquake – Song et al. (2008) for San Francisco earthquake Number of recordings – 35,547 for Aagaard simulations – 40,000 for Graves simulation We excluded soft soil sites and only considered spectral periods beyond 2s) 9

10. Correlations from simulations are comparable in some scenarios to those from recorded ground motions, larger in others 10

11. Revisiting the assumption of stationarity using simulated ground motions Zones are defined based on the distance from the rupture Correlations were separately estimated for each zone 11 S a (2s) ε’s from the simulated ground motions

12. Correlations between residuals at near-fault sites are smaller 12 Aagaard Song-Mod setAagaard Random HypoC set

13. Revisiting our assumptions: isotropy? We assumed correlations were dependent only on separation distance, and not on orientation We can revisit this using directional semivariograms: Group pairs of observations by separation distance and separation orientation:

14. Directional semivariograms are reasonably similar at short separation distances 14 Aagaard SongMod set, Sa(10s)Aagaard Random HypoC set, Sa(5s)

15. Impact of directivity effects on spatial correlation Wavelet analysis procedure of Baker (2007) used to identify pulse-like ground motions in the simulations Over 400 pulses were identified in the Aagaard’s 1989 Loma Prieta earthquake simulations, and over 2000 pulses were identified in the 1906 San Francisco earthquake simulations The spatial correlation of these near-fault pulse-like ground motions are compared to that of near-fault non-pulse-like ground motions 15

16. Reasonably similar ranges were observed using both pulse-like and non-pulse like records in two simulation sets 16 Aagaard SongMod setAagaard Loma Prieta set

17. The ranges corresponding to pulse-like and non-pulse-like ground motions are drastically different for Random HypoC set 17 Aagaard Random HypoC set The drastic difference observed in this case could be simulation specific (e.g., use of a more uniform rupture speed than proposed in the Song et al. rupture model) Further investigation is necessary, possibly using recorded ground motions, to test the impact of directivity further

18. Conclusions This study used simulated ground motions to estimate spatial correlations Near-fault ground motions (within 10km of the rupture) were seen to exhibit smaller spatial correlation The assumption of isotropy generally seems to be valid at short separation distances The effect of directivity on spatial correlation was seen to be negligible in two sets and significant in a third set Further similar investigation is necessary using recorded ground motion sets to confirm the observations discussed earlier 18