Ground Motion Prediction Equations and Seismic Hazard Assessment Prof. Ellen M. Rathje, Ph.D., P.E. Department of Civil, Civil Architectural Architectural, and Environmental Engineering University of Texas at Austin

18 November 2010

Seismic Design Framework Source Characterization Ground Motion Characterization

Locations of sources (faults) Magnitude (Mw) Recurrence

Closest distance fault to site (Rcl) Local site conditions

Rrup Soil conditions Topographic conditions

Ground motion = fxn (magnitude, (magnitude distance distance, site conditions)

Predicting Ground Shaking • Ground motion prediction equations (GMPE) − Statistical models to predict ground shaking − Developed for different tectonic regions (shallow crustal regions regions, subduction zones, zones intra intra-plate) plate)

• Next Generation Attenuation (NGA) Project − GMPE GMPEs for f shallow h ll crustal t l earthquakes th k (appropriate for Haiti, based on available data) − Based on a consistently consistentl processed dataset of recordings − Five models generated by 5 separate teams

NGA Database • 3551 recordings • 173 earthquakes • Mw = 4.2 - 7.9

Recordings available at http://peer.berkeley.edu/nga

NGA Models ln (Y) = fsource (M, mechanism) + fdistance (M, Rrup) + fsite (Vs, (Vs others) where Y = spectral acceleration at period, T

• Key Parameters − M: moment magnitude − Style of faulting (mechanism): reverse strike-slip reverse, strike slip, normal − Rrup: distance to fault rupture plane − Vs30: average shear wave velocity in top 30 m − Z1.0: depth to Vs = 1.0 km/s

PGA (g)

PGA Predictions

Motions attenuate with distance

PGA (g g)

Larger M events attenuate more slowly

Rrup (km)

Rrup (km)

Response Spectra Predictions Rrup = 10 km Vs30 = 760 m/s (R k) (Rock)

0.08 g 0.02 g

PGA: M7 is 3x larger than M5 0.25 g

Sa at T = 1.0 s: M7 is 9x larger than M5

0.18 g

Rrup (km)

Influence of Vs30: Site Effects M = 7, Rrup = 30 km Vs30 = 760 m/s (“Rock”) PGA: PGA 200 m/s is 1.4x g than 760 m/s larger Sa at T = 1.0 s: 200 m/s / iis 2 2.2x 2 larger than 760 m/s

0.14 g 01g 0.1

0.2 g 0 09 g 0.09

Scatter in Ground Motions

1994 Northridge ((Mw = 6.7)) Earthquake

From D. Boore

Peak A Acceleration (g)

• Given M, Rrup  large range of possible motions

Distance (km)

Standard Deviation • Scatter measured by standard deviation, (sigma ), (sigma, ) of normal distribution Probabilityy of x Small 

Large 

Average of x

x

Sigma for GMPEs • Ground motions are log-normally distributed (i e ln of x is normally distributed) (i.e., Probabilityy of ln(x) ( ) Small 

Large 

Average of ln(x)

ln(x)

Sigma for GMPEs • Given M, Rrup  GMPE provides average motion and its sigma (scatter)  ~ 0.55 to 0.70

Ln PGA (g g)

Mw=7, R=10 km

10 km

Ln R (km)

For  = 0.55, 90% chance value will fall within ithi (1/3)·avg (1/3) t to 3·avg For example, if avg = 0.1 g, 90% chance value is between 0.03 and 0.3 g

Seismic Hazard Assessment • Seismic hazard: expected ground motions − Deterministic and Probabilistic approaches

• Deterministic Seismic Hazard Assessment (DSHA) − Select one (or two) most likely M, Rrup scenarios − Predict ground shaking from GMPE (avg or +1)

• Probabilistic Seismic Hazard Assessment (PSHA) − Consider all M, Rrup scenarios, their expected ground motions, and how likely they are

DSHA M = 7.0, R = 10 km  Response spectrum from GMPE

1

Spe ectral Accele eration (g)

Avg +1 Std Dev

0.8 0.6 0.4 0.2 0 0.01

0.1

1 Period (s)

10

Seismic Hazard Assessment • Probabilistic Seismic Hazard Assessment (PSHA) − Consider all M, Rrup scenarios − Consider all potential ground motion levels − Consider how likely each scenario and ground motion are to occur (i (i.e., e probability) − Compute seismic hazard curve

• B Building ildi code d d design i ground d motions ti are derived from PSHA

PSHA • Product: ground motion level and its annual rate of exceedance ( = # times per year gm level exceeded) 1E-01

Mean Annu ual Rate of Exc ceedance,  [1/yr]

Return period ~ (1 / ) 500 yr return period   ~ 0.002 0 002

1E-02

2500 yr return period   ~ 0.0004

1E-03 1E 03

1E-04 0.0

0.2

0.4

0.6

PGA (g)

0.8

1.0

As  , ground motions  because tthey ey a are e less ess likely ey

PSHA • PSHA accounts for 4 things that DSHA does not − Large scatter () in ground motion prediction − More small earthquakes than large − Activity rates (i.e., Number EQ/yr) vary from fault to fault − Increased hazard from multiple faults Sit A Site M=7

M=7

R=10 km R=10 km

DSHA: Hazard A = Hazard B PSHA: Hazard A > Hazard B

Sit B Site M=7

R=10 km

Requirements for PSHA • Rate of earthquakes and their distribution across magnitudes: − Magnitude recurrence

• GMPE to t predict di t ground d shaking h ki llevels l and d standard deviation given M, Rrup Activity rate: No. of Eqs /yr

GMPE

GM ( z )  MREGM ( z )  o    PGM  z m, r f M (m) f R (r )  dmdr m r

Annual rate of exceedance of gm level = “z”

P [Mi] P [Rj] Mag Recurrence

PSHA • Magnitude Recurrence − Number of small earthquakes vs vs. large  

Numbe er ofEQs m (1/yr)/ yr (1/yr)

1.E+00

Defined using: 1.E‐01

• Geodetic slip rates

1.E‐02

Max Mw

• Rates of small EQs

1.E‐03

• Fault length (Mmax)

1 E‐04 1.E 04 5

6

7 Magnitude

8

9

PSHA Calculation Magnitude Distribution Derived from magnitude recurrence 0.8 0.7

Ground Motion Prediction How likely is PGA > 0.2 g for each M?

0.675

PGA=0.2 g

0.5 0.4 0.3

0.225

0.2

0.075

0.1 0

4

5

6

0.025 7

Log PGA (g L g)

Probab bility

P [M M]

0.6

Mw=7

Magnitude

Magnitude, M

Rrup = 10 km for all earthquakes Activity rate = 0 0.5 5 per yr

Mw=5 10 km

Log R (km) ( )

Probabilityy [[M=5]] > Probabilityy [M=7] [ ] Prob [PGA > 0.2 g given M = 5] < Prob [PGA > 0.2 g given M = 7]

PSHA Calculation 



PGA (0.2 g )  o   P PGA  0.2 g mi , rj  P[mi ]  P[rj ] mi

rj

M

P[mi]

P[r = 10 km]

P[PGA>0.2|m,r]

P[M] · P[PGA>0.2 g]

4

0.675

1.0

0.01

0.00675

5

0.225

1.0

0.05

0.02025

6

0 075 0.075

10 1.0

0 25 0.25

0 01875 0.01875

7

0.025

1.0

0.58

0.01450 Sum = 0.06025 0 06025 (0.2 g) = o · 0.06025  (0.2 g) = 0.03012 Return Period ~ 33 yr

Hazard Curve • Perform hazard calculation for multiple values of PGA to generate hazard curve ~ 0.002  500 y yr return p period  10% probability of exceedance in 50 yrs

Mean An nnual Rate of E Exceedance,  [1/yr]

1E-01

1E-02

~ 0.0004  2500 yr return period  2% probability of exceedance in 50 yrs

1E-03

1E-04 0.0

0.2 0.6 g 0.8 0.36 0 36 g0.4 0.58 PGA (g)

1.0

Disaggregation • What magnitudes and distances contribute most to ground motion hazard?? M

P[mi]

P[r = 10 km]

P[M] · P[PGA>0.2 g]

% Contribution

4

0.675

1.0

0.00675

13%

5

0.225

1.0

0.02025

22%

6

0 075 0.075

10 1.0

0 01875 0.01875

37%

7

0.025

1.0

0.01450

28%

M = 6 has the largest contribution and M = 4 smallest

Disaggregation Oakland, CA Disaggregation for 10% probability of exceedance in 50 yrs (500 yr return period)

Uniform Hazard Spectrum Develop hazard curves for multiple response spectrum periods  

1 Annual Ratte of Exceeda ance (Lambd da)

PGA Sa at T=0.3 s S att T=1.0 Sa T 10s

0.1

Sa at T=2.0 s

0.01

0.001

0.0001 0

0.5

1 Acceleration (g)

1.5

2

Uniform Hazard Spectrum Plot Sa value from each hazard curve at its appropriate spectral period

Sa (g)

1.5 1 0.5 0 0

1

2

Period (s)

3

4

Summary • Ground motion prediction equations (GMPE) − Statistical models to predict ground shaking − Model the effects of M, Rrup, style of faulting, site conditions − NGA models represent the state-of-the-art in GMPEs for shallow crustal earthquakes − NGA models are currently believed to best represent ground shaking in Haiti (but recordings in Haiti will help confirm this!)

Summary • Seismic Hazard Assessment − Deterministic seismic hazard analysis (DSHA) provides an “EQ scenario” of ground shaking − Probabilistic seismic hazard analysis (PSHA) considers all uncertainties (e.g., all potential earthquakes, q , rate of earthquakes, q , etc.)) − PSHA has become the standard for defining ground motions used in design g g