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