Epistemic Uncertainty on the Median Ground Motion of

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 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: d – 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 -RRUP bins – USGS – Watson-Lamprey and Abrahamson • Variance of mean prediction – Boore and others (1997, SRL) • Monte Carlo simulation – This study: analytical formula

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

Watson-Lamprey & Abrahamson (For A Site in Idaho, USA) = intra-event residual t = 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 (Xo) Predicted mean Variance of predicted mean

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

Example: d for the Chiou and Youngs NGA Model • Seismic conditions considered – M: 5 to 8 – RRUP: 1 to 100 km – Faulting style: • Vertical strike-slip earthquake • Reverse earthquake: 45º dip angle – Rock condition: VS 30 = 760 m/sec, Z 1. 0 = 24 m – PGA

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Conclusions • Evaluated three different estimates of d • We prefer the variance-of-predicted-mean approach – More accurate, for a small price – Computed d reflects the distribution of data – Much less judgment is involved • 0. 4 used in USGS; selection of (M-RRUP) bins – Not limited to just M & RRUP • HW • Other soil condition

Conclusions • d depends moderately on M & RRUP • d 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 – d as a smooth function of M, RRUP, VS 30, etc. – Possibility of double counting • When both d and have large values (e. g. HW) – Is the epistemic uncertainty symmetrical?

Thank You