Sigma - Background Norm Abrahamson Sep 30, 2009

Sigma for CEUS EPRI (2006) –Truncation of log-normal distribution –Evaluation of Application of NGA sigma to CEUS Rhoades (2008) –Deviation from log-normal for the upper tail

PGA Standard Deviation WUS vs CEUS

2005 versions of NGA Models for WUS Show Constant Sigma

EPRI (2004) models and AS NGA (2005 version)

Depth Effects on Rjb-Based Models

Rjb-Based residuals

Flinn-Engdahl regionalization Red = active Blue = Oceanc Yellow = Stable Green = Classified Stable but considered active or oceanic

Half Durations RegionNStd dev of half duration (ln units) Active ± 0.01 Stable subset ± 0.02 Stable subset ± 0.02 Stable subset ± 0.03

Additional Source Parameters in NGA models NGA has additional parameters –Style-of-faulting –Hanging wall / foot wall Small impact on total std dev –Increase by less than 0.01 if these are ignored

Path Term Variability Effects of Crustal Structure differences –Used Simulations for range of crustal structures –Compared std dev of resulting ground motions

Comparison of velocity structures

Stations used for Simulations

SCR Simulations

WUS Simulations

Std Dev for Path Effects ActiveStable PGA Hz Hz Hz Hz Hz Hz

Site Term Variability F=25 Hz Std Dev for Hard -rock (0.55) is larger than for soft-rock (0.51) 5-10 hz for soft-rock is

Std Dev from Stress-Param Variability High Freq Inter-Event Std Dev = 0.43 Compared to NGA values of 0.4

EUS Sigma Models Intra-Event Std Dev (R>20 km) –NGA models considered to be applicable with following modifications Increase the std dev to account for source parameters included in NGA that are not available for CEUS (0.01 units) Increase std dev at high frequencies to account for freq content difference –Alternative models More homogeneous crust in CUES (reduce 0.03 units) No reduction

EUS Sigma Models Inter-Event Std Dev models –NGA models are applicable without change based on teleseismic comparison –Use std dev from point-source stress parameters distribution

EUS Sigma Models Intra-Event Standard Deviation at Short distances –No increase –Some Increase Based on trends from European data –Increase Increase

EPRI (2006) model R>20 km

Short Distance Sigma Adjustment Model

Total Std Dev Models

EPRI (2004) models and AS NGA (2005 version)

Mag Dependent Sigma? After EPRI (2006) study, some NGA models revised to use mag-dependent sigma –AS08, CY08, I08 –Based on inclusion of aftershocks

Standard Deviation (RJB=30 km, VS30=760)

Rhoades et al (2008) Method

Problems Using Total Residuals

AS08 Model Using Intra-Event Residuals

AS08 Intra-Event std dev

Standard Deviation (M=7, VS30=270)

Non-linear site effects T=0.15 sec

Evaluation of Inter-Event