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 10th Anniversary of the Chi-

Chi Earthquake, 2009

• Backgrounds

• Proposed approaches

• Preliminary results for one NGA model

• Conclusions

NGA – Next-Generation Ground-Motion Attenuation Model

• Partnerships with USGS and SCEC

• 2002 - 2007

• Executed through the PEER-Lifelines Program

Caltrans

Pacific Gas & Electric Company

California Energy Commission

PEER Center

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

100 101 102

10-2

10-1

100

R X (km)

PG

A

Abrahamson & SilvaBoore, Joyner, & FumalCampbellSadigh and others

M 7.5, Strike-Slip

1997 SRL Set

100 101 102

10-2

10-1

100

R X (km)

PG

A

Abrahamson & SilvaBoore & AtkinsonCampbell & BorzogniaChiou & Youngs

M 7.5, Strike-Slip

2008 NGA Set

1997 SRL Set: 4 ground motion attenuation models for crustalearthquakes, 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:

– This additional uncertainty should reflect reflect mainly the lack of data constraints on a mainly the lack of data constraints on a modelmodel

– 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

USGS 2008 National Seismic Hazard Mapping Project

(M-R RUP ) Range N eq 1.6 N eq 1.6

5 M < 6, RRUP < 10 24 0.22 4 0.535 M < 6, 10 RRUP < 30 50 0.15 15 0.275 M < 6, RRUP ≥ 30 26 0.21 14 0.286 M < 7, RRUP < 10 24 0.22 19 0.246 M < 7, 10 RRUP < 30 26 0.21 20 0.246 M < 7, RRUP ≥ 30 23 0.22 18 0.25M ≥ 7, RRUP < 10 7 0.40 7 0.40M ≥ 7, 10 RRUP < 30 8 0.37 9 0.35M ≥ 7, RRUP ≥ 30 10 0.33 13 0.29

Chiou & Youngs Campbell & Bozorgnia

Engineering JudgmenteqN

7

6.1

4.0

Bin

sel

ecti

on is

arb

itra

ry

Watson-Lamprey & Abrahamson (For A Site in Idaho, USA)

eqobs NN

22

Chiou & Youngs(M-R RUP ) Range

5 M < 6, RRUP < 10 0.125 M < 6, 10 RRUP < 30 0.065 M < 6, RRUP ≥ 30 0.076 M < 7, RRUP < 10 0.096 M < 7, 10 RRUP < 30 0.076 M < 7, RRUP ≥ 30 0.06M ≥ 7, RRUP < 10 0.13M ≥ 7, 10 RRUP < 30 0.11M ≥ 7, RRUP ≥ 30 0.07

= 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.

)( Xby

b̂b̂

Variance of Predicted Mean for New Observations (Xo)

oTT

o

oT

o

o

oo

XXVXX

XbVarX

yVar

bXy

11

2

][

]]ˆ[[

]ˆ[)(

ˆˆ

Predicted mean

Variance of predicted mean

Random Earthquake Effect (Abrahamson and Youngs, 1992)

0

000

0

0

00

22

22

22

12

12

nMnM

nn

nn

II

II

II

V

= intra-event residual = inter-event residual

Example: 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: VS30 = 760 m/sec, Z1.0 = 24 m

– PGA

4 5 6 7 8 9M

00.

10.

20.

30.

40.

5

R < 10 km

Strike-Slip Reverse (FW) USGS WL&A

4 5 6 7 8 9M

00.

10.

20.

30.

40.

5

10 < R < 30 km

4 5 6 7 8 9M

00.

10.

20.

30.

40.

5

R > 30 km

100 101 102

Distance (km)

00.

10.

20.

30.

40.

5

M 5.5

Strike-Slip Reverse (FW) Reverse (HW) USGS WL-A

100 101 102

Distance (km)

00.

10.

20.

30.

40.

5

M 6.5

100 101 102

Distance (km)

00.

10.

20.

30.

40.

5

M 7.5

100 101 102

Distance (km)

00

.10

.20

.30

.40

.5

ds m

M 5.5

1 2 3 4

100 101 102

Distance (km)0

0.1

0.2

0.3

0.4

0.5

ds m

M 6.5

100 101 102

Distance (km)

00

.10

.20

.30

.40

.5

ds m

M 7.5

4

321

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-RRUP) bins

– Not limited to just M & RRUP

• HW

• Other soil condition

Conclusions

• depends moderately on M & RRUP

• 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, RRUP,VS30, etc.

– Possibility of double counting• When both and have large values (e.g. HW)

– Is the epistemic uncertainty symmetrical?

Thank You

Distance to surface trace

RRUP

Bridge site

Dipping fault plane

Surface

Distance Measures

RxRJB