Epistemic Uncertainty on the Median Ground Motion of Next-Generation Attenuation (NGA) Models Brian Chiou and Robert Youngs The Next Generation of Research on Earthquake-Induced Landslides: An International Conference in Commemoration of 10 th Anniversary of the Chi-Chi Earthquake, 2009

Backgrounds Proposed approaches Preliminary results for one NGA model Conclusions

NGA’s Programmatic Goal Develop a new set of ground-motion prediction models for shallow crustal earthquakes –Satisfy needs of current practice of earthquake engineering –Make significant improvement

Next Generation of Attenuation (NGA) Program Products: –NGA strong-motion database: 3551 recording, 173 earthquakes –Set of 5 ground-motion prediction models for estimation of PGA, PGV, and spectral acceleration (0.02 to 10 sec) –Publications: Comprehensive PEER report for each NGA model Earthquake Spectra –2008 special issue on NGA models, February 2008

Uncertainties on Ground-Motion Prediction (Toro et al, 1997) Aleatory variability (inherent random variability) –Random variability about the predicted mean (  ) –Characterized by the residual standard deviation (  T ) of regression model Epistemic uncertainty in  &  T (due to incomplete data) –  ,  

Reduction of Uncertainty Alteatory variability  –By definition,  can not be reduced by the collection of more data –But, estimate of  can be improved Epistemic uncertainty –   can be improved by collecting more data and improved knowledge about the earthquake processes

Is Reduced   a Result of NGA Research? For –Use of a larger, higher-quality database –Guidance from the state-of-the-art seismological/geotechnical simulations –Recent advancements in earthquake and geotechnical engineering Against –Close interaction may lead to cross influence –Large magnitude (M > 7.5) & close distances

1997 SRL Set: 4 ground motion attenuation models for crustal earthquakes, published in Seismological Research Letters, April 1997

Recommendation by the NGA Project Team To use NGA models, additional epistemic uncertainty on the mean prediction (  ) should be considered:   reflect mainly the lack of data constraints on a model –This additional uncertainty should reflect mainly the lack of data constraints on a model –No recommendation by the NGA project team.

Proposed Approahces Variance of sample mean for pre-defined M-R RUP bins –USGS –Watson-Lamprey and Abrahamson Variance of mean prediction –Boore and others (1997, SRL) Monte Carlo simulation –This study: analytical formula

USGS 2008 National Seismic Hazard Mapping Project Engineering Judgment Bin selection is arbitrary

Watson-Lamprey & Abrahamson ( For A Site in Idaho, USA )  = intra-event residual  = inter-event residual

Variance of Predicted Mean (This Study) Estimate of model coefficient ( ) is subject to estimation uncertainty. Var[ ], though usually not reported, can be reconstructed.

Variance of Predicted Mean for New Observations (X o ) Predicted mean Variance of predicted mean

Random Earthquake Effect (Abrahamson and Youngs, 1992)  = intra-event residual  = inter-event residual

Example:   for the Chiou and Youngs NGA Model Seismic conditions considered –M: 5 to 8 –R RUP : 1 to 100 km –Faulting style: Vertical strike-slip earthquake Reverse earthquake: 45º dip angle –Rock condition: V S30 = 760 m/sec, Z 1.0 = 24 m –PGA

Conclusions Evaluated three different estimates of   We prefer the variance-of-predicted-mean approach –More accurate, for a small price –Computed   reflects the distribution of data –Much less judgment is involved 0.4 used in USGS; selection of (M-R RUP ) bins –Not limited to just M & R RUP HW Other soil condition

Conclusions   depends moderately on M & R RUP   depends strongly on hanging wall (HW) location –HW effect is poorly constrained; more HW data are needed Dependence on period and other source variables (as shown in the conference abstract)

Future Work Will be extended to other NGA models –Results to be shared with NGA developers –To serve as one basis for the final recommendation by the NGA project team Implementation issues –   as a smooth function of M, R RUP,V S30, etc. –Possibility of double counting When both   and   have large values (e.g. HW) –Is the epistemic uncertainty symmetrical?

Thank You