SPATIAL CORRELATION OF SPECTRAL ACCELERATIONS Paolo Bazzurro Jaesung

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

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 PGA residuals from the 1999 Chi-Chi earthquake 2

Ground-motion models are used to characterize groundmotion intensities at individual sites Ground-motion models are used to predict the distribution of the ground-motion intensities as a function of magnitude, source-tosite distance, etc. for each earthquake Spect ral ac c Predi elera ti cted on at s mean ite “i ” USGS hazard map PGA with 10% probability of exceedance in 50 years Intra (log) s -even pectr a Inter t resi l acce -even dual t resi dual (at al at sit l sites e “i” ) lerati on 3

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 PGA ε’s from the 1999 Chi -Chi earthquake 4

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) Site i Site j 5 Jayaram and Baker (2010)

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 PGA ε’s from the 1999 Chi -Chi earthquake ε’s at two sites separated by a specified distance 6

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

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

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 Hypo. C 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 2 s) 9

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

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 Sa(2 s) ε’s from the simulated ground motions 11

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

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:

Directional semivariograms are reasonably similar at short separation distances Aagaard Song. Mod set, Sa(10 s) Aagaard Random Hypo. C set, Sa(5 s) 14

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

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

The ranges corresponding to pulse-like and non-pulse-like ground motions are drastically different for Random Hypo. C set Aagaard Random Hypo. C 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 17

Conclusions • This study used simulated ground motions to estimate spatial correlations • Near-fault ground motions (within 10 km 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