Probabilistic Seismic Hazard Analysis

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Probabilistic Seismic Hazard Analysis
Overview
History 1969 - Allin Cornell BSSA paper Rapid
development since that time
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Probabilistic Seismic Hazard Analysis
Overview
Deterministic (DSHA) Assumes a single
scenario Select a single magnitude, M Select a
single distance, R Assume effects due to M,
R Probabilistic (PSHA) Assumes many
scenarios Consider all magnitudes Consider all
distances Consider all effects
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Probabilistic Seismic Hazard Analysis
Overview
Probabilistic (PSHA) Assumes many
scenarios Consider all magnitudes Consider all
distances Consider all effects
Why? Because we dont know when earthquakes will
occur, we dont know where they will occur, and
we dont know how big they will be
Ground motion parameters
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Probabilistic Seismic Hazard Analysis
Consists of four primary steps 1. Identification
and characterization of all sources 2.
Characterization of seismicity of each source 3.
Determination of motions from each source 4.
Probabilistic calculations
PSHA characterizes uncertainty in location, size,
frequency, and effects of earthquakes, and
combines all of them to compute probabilities of
different levels of ground shaking
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Probabilistic Seismic Hazard Analysis
Uncertainty in source-site distance
Need to specify distance measure Based on
distance measure in attenuation relationship
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Probabilistic Seismic Hazard Analysis
Uncertainty in source-site distance
Need to specify distance measure Based on
distance measure in attenuation relationship
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Probabilistic Seismic Hazard Analysis
Uncertainty in source-site distance
Where on fault is rupture most likely to occur?
Source-site distance depends on where rupture
occurs
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Probabilistic Seismic Hazard Analysis
Uncertainty in source-site distance
Where is rupture most likely to occur? We dont
know
Source-site distance depends on where rupture
occurs
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Probabilistic Seismic Hazard Analysis
Uncertainty in source-site distance
Approach
Assume equal likelihood at any point Characterize
uncertainty probabilistically
rmin
fR(r)
rmax
r
rmin
rmax
pdf for source-site distance
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Probabilistic Seismic Hazard Analysis
Uncertainty in source-site distance
Two practical ways to determine fR(r)
Draw series of concentric circles with
equal radius increment Measure length of
fault, Li, between each pair of adjacent
circles Assign weight equal to Li/L to each
corresponding distance
rmin
rmax
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Probabilistic Seismic Hazard Analysis
Uncertainty in source-site distance
Two practical ways to determine fR(r)
Divide entire fault into equal length
segments Compute distance from site to
center of each segment Create histogram of
source-site distance. Accuracy increases
with increasing number of segments
rmin
rmax
Linear source
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Probabilistic Seismic Hazard Analysis
Uncertainty in source-site distance
Divide source into equal area
elements Compute distance from center of
each element Create histogram of source-site
distance
Areal Source
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Probabilistic Seismic Hazard Analysis
Uncertainty in source-site distance
Divide source into equal volume
elements Compute distance from center of
each element Create histogram of source-site
distance
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Probabilistic Seismic Hazard Analysis
Uncertainty in source-site distance
Unequal element areas? Create histogram using
weighting factors - weight according to fraction
of total source area
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Probabilistic Seismic Hazard Analysis
Uncertainty in source-site distance
Quick visualization of pdf? Use concentric
circle approach - lets you see basic shape of
pdf quickly
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Probabilistic Seismic Hazard Analysis
Characterization of maximum magnitude
Determination of Mmax - same as for
DSHA Empirical correlations Rupture length
correlations Rupture area correlations Maximum
surface displacement correlations Theoretical
determination Slip rate correlations
Also need to know distribution of magnitudes
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Probabilistic Seismic Hazard Analysis
Distribution of earthquake magnitudes
Given source can produce different
earthquakes Low magnitude - often Large magnitude
- rare Gutenberg-Richter Southern California
earthquake data - many faults Counted number of
earthquakes exceeding different magnitude
levels over period of many years
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Probabilistic Seismic Hazard Analysis
Distribution of earthquake magnitudes
NM
M
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Probabilistic Seismic Hazard Analysis
Distribution of earthquake magnitudes
log lM
Mean annual rate of exceedance lM NM / T
M
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Probabilistic Seismic Hazard Analysis
Distribution of earthquake magnitudes
log lM
0.01
100 yrs
Return period (recurrence interval) TR 1 / lM
0.001
1000 yrs
log TR
M
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Probabilistic Seismic Hazard Analysis
Distribution of earthquake magnitudes
log lM
10a
b
Gutenberg-Richter Recurrence Law log lM a - bM
log TR
0
M
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Probabilistic Seismic Hazard Analysis
Distribution of earthquake magnitudes
Gutenberg-Richter Recurrence Law log lM a -
bM Implies that earthquake magnitudes are
exponentially distributed (exponential pdf) Can
also be written as ln lM a - bM
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Probabilistic Seismic Hazard Analysis
Distribution of earthquake magnitudes
Then lM 10a - bM expa - bM where a
2.303a and b 2.303b. For an exponential
distribution, fM(m) b e-b m
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Probabilistic Seismic Hazard Analysis
Distribution of earthquake magnitudes
Neglecting events below minimum magnitude, mo lm
n expa - b(m - mo) m gt mo where n expa
- b mo. Then, fM(m) b e-b (m-mo)
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Probabilistic Seismic Hazard Analysis
Distribution of earthquake magnitudes
For worldwide data (Circumpacific belt), log lm
7.93 - 0.96M M 6 lm 148 /yr TR
0.0067 yr M 7 lm 16.2 TR 0.062 M 8
lm 1.78 TR 0.562 M 12 lm 0.437 TR
2.29
M gt 12 every two years?
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Probabilistic Seismic Hazard Analysis
Distribution of earthquake magnitudes
Every source has some maximum magnitude Distributi
on must be modified to account for Mmax Bounded
G-R recurrence law
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Probabilistic Seismic Hazard Analysis
Distribution of earthquake magnitudes
Every source has some maximum magnitude Distributi
on must be modified to account for Mmax Bounded
G-R recurrence law
log lm
Bounded G-R Recurrence Law
Mmax
M
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Probabilistic Seismic Hazard Analysis
Distribution of earthquake magnitudes
Characteristic Earthquake Recurrence Law
Paleoseismic investigations Show similar
displacements in each earthquake Inividual faults
produce characteristic earthquakes Characteristic
earthquake occur at or near Mmax Could be caused
by geologic constraints More research, field
observations needed
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Probabilistic Seismic Hazard Analysis
Distribution of earthquake magnitudes
log lm
Characteristic Earthquake Recurrence Law
Seismicity data
Geologic data
Mmax
M
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Probabilistic Seismic Hazard Analysis
Predictive relationships
Standard error - use to evaluate conditional
probability
log lm
PY gt Y MM, RR
ln Y
Y Y
ln Y
M M
R R
log R
Mmax
M
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Probabilistic Seismic Hazard Analysis
Predictive relationships
Standard error - use to evaluate conditional
probability
ln Y
PY gt Y MM, RR
ln Y
Y Y
M M
R R
log R
M
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Probabilistic Seismic Hazard Analysis
Temporal uncertainty
Poisson process - describes number of occurrences
of an event during a given time interval or
spatial region. 1. The number of occurrences in
one time interval are independent of the
number that occur in any other time
interval. 2. Probability of occurrence in a very
short time interval is proportional to
length of interval. 3. Probability of more than
one occurrence in a very short time
interval is negligible.
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Probabilistic Seismic Hazard Analysis
Temporal uncertainty
Poisson process
where n is the number of occurrences and m is the
average number of occurrences in the time
interval of interest.
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Probabilistic Seismic Hazard Analysis
Temporal uncertainty
Poisson process Letting m lt
Then
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Probabilistic Seismic Hazard Analysis
Temporal uncertainty
Poisson process
Consider an event that occurs, on average, every
1,000 yrs. What is the probability it will occur
at least once in a 100 yr period? l 1/1000
0.001 P 1 - exp-(0.001)(100) 0.0952
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Probabilistic Seismic Hazard Analysis
Temporal uncertainty
What is the probability it will occur at least
once in a 1,000 yr period? P 1 -
exp-(0.001)(1000) 0.632 Solving for l,
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Probabilistic Seismic Hazard Analysis
Temporal uncertainty
Then, the annual rate of exceedance for an event
with a 10 probability of exceedance in 50 yrs is
The corresponding return period is TR 1/l 475
yrs. For 2 in 50 yrs, l 0.000404/yr
TR 2475 yrs
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Probabilistic Seismic Hazard Analysis
Summary of uncertainties
Location Size Effects Timing
fR(r) fM(m) PY gt Y MM, RR P 1 - e-lt
Poisson model
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Probabilistic Seismic Hazard Analysis
Combining uncertainties - probability computations
PA PA PAB1PB1 PAB2PB2
PABNPBN
Total Probability Theorem
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Probabilistic Seismic Hazard Analysis
Combining uncertainties - probability computations
Applying total probability theorem,
where X is a vector of parameters. We assume
that M and R are the most important parameters
and that they are independent. Then,
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Probabilistic Seismic Hazard Analysis
Combining uncertainties - probability computations
Above equation gives the probability that y will
be exceeded if an earthquake occurs. Can convert
probability to annual rate of exceedance by
multiplying probability by annual rate of
occurrence of earthquakes.
where n expa - bmo
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Probabilistic Seismic Hazard Analysis
Combining uncertainties - probability computations
If the site of interest is subjected to shaking
from more than one site (say Ns sites), then
For realistic cases, pdfs for M and R are too
complicated to integrate analytically.
Therefore, we do it numerically.
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Probabilistic Seismic Hazard Analysis
Combining uncertainties - probability computations
Dividing the range of possible magnitudes and
distances into NM and NR increments, respectively
This expression can be written, equivalently, as
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Probabilistic Seismic Hazard Analysis
Combining uncertainties - probability computations
What does it mean?
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Probabilistic Seismic Hazard Analysis
Combining uncertainties - probability computations
NM x NR possible combinations Each produces some
probability of exceeding y Must compute PY gt
yMmj,Rrk for all mj, rk
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Probabilistic Seismic Hazard Analysis
Combining uncertainties - probability computations
Compute conditional probability for each element
on grid Enter in matrix (spreadsheet cell)
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Probabilistic Seismic Hazard Analysis
Combining uncertainties - probability computations
Build hazard by computing conditional
probability for each element multiplying
conditional probability by Pmj, Prk,
ni Repeat for each source - place values in same
cells
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Probabilistic Seismic Hazard Analysis
Combining uncertainties - probability computations
When complete (all cells filled for all
sources), Sum all l-values for that value of y
ly
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Probabilistic Seismic Hazard Analysis
Combining uncertainties - probability computations
Choose new value of y Repeat entire
process Develop pairs of (y, ly) points
Plot
Seismic Hazard Curve
log TR
log ly
y
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Probabilistic Seismic Hazard Analysis
Combining uncertainties - probability computations
Seismic hazard curve shows the mean annual rate
of exceedance of a particular ground motion
parameter. A seismic hazard curve is the
ultimate result of a PSHA.
log lamax
log TR
log ly
log TR
amax
y
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Probabilistic Seismic Hazard Analysis
Using seismic hazard curves
Probability of exceeding amax 0.30g in a 50 yr
period? P 1 - e-lt 1 -
exp-(0.001)(50) 0.049 4.9 In a 500 yr
period? P 0.393 39.3
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Probabilistic Seismic Hazard Analysis
Using seismic hazard curves
What peak acceleration has a 10 probability of
being exceeded in a 50 yr period? 10 in 50 yrs
l 0.0021 or TR 475 yrs Use seismic hazard
curve to find amax value corresponding to l
0.0021
log lamax
log TR
0.0021
475 yrs
amax0.21g
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Probabilistic Seismic Hazard Analysis
Using seismic hazard curves
Contribution of sources Can break l-values down
into contributions from each source Plot
seismic hazard curves for each source and
total seismic hazard curve (equal to sum
of source curves) Curves may not be parallel,
may cross Shows which source(s) most important
Total
log lamax
2
log TR
1
3
amax
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Probabilistic Seismic Hazard Analysis
Using seismic hazard curves
Can develop seismic hazard curves for different
ground motion parameters Peak acceleration Spectra
l accelerations Other Choose desired l-value Read
corresponding parameter values from
seismic hazard curves
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Probabilistic Seismic Hazard Analysis
Using seismic hazard curves
Can develop seismic hazard curves for different
ground motion parameters Peak acceleration Spectra
l accelerations Other Choose desired l-value Read
corresponding parameter values from
seismic hazard curves
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Probabilistic Seismic Hazard Analysis
0.1
2 in 50 yrs Peak acceleration
Crustal
0.01
lamax
Intraplate
0.001
Interplate
0.0001
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Probabilistic Seismic Hazard Analysis
0.1
2 in 50 yrs Sa(T 3 sec)
0.01
Crustal
lamax
Intraplate
0.001
Interplate
0.0001
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Probabilistic Seismic Hazard Analysis
Uniform hazard spectrum (UHS)
Find spectral acceleration values for different
periods at constant l All Sa values have same
l-value same probability of exceedance
Uniform Hazard Spectrum
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Probabilistic Seismic Hazard Analysis
Disaggregation (De-aggregation)
Common question What magnitude distance
does that amax value correspond to?
Total hazard includes contributions from all
combinations of M R.
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Probabilistic Seismic Hazard Analysis
Disaggregation (De-aggregation)
Common question What magnitude distance
does that amax value correspond to?
Total hazard includes contributions from all
combinations of M R. Break hazard down into
contributions to see where hazard is coming
from.
M7.0 at R75 km
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Probabilistic Seismic Hazard Analysis
Disaggregation (De-aggregation)
USGS disaggregations
Seattle, WA 2 in 50 yrs (TR 2475 yrs) Sa(T
0.2 sec)
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Probabilistic Seismic Hazard Analysis
Disaggregation (De-aggregation)
USGS disaggregations
Olympia, WA 2 in 50 yrs (TR 2475 yrs) Sa(T
0.2 sec)
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Probabilistic Seismic Hazard Analysis
Disaggregation (De-aggregation)
USGS disaggregations
Olympia, WA 2 in 50 yrs (TR 2475 yrs) Sa(T
1.0 sec)
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Probabilistic Seismic Hazard Analysis
Disaggregation (De-aggregation)
Another disaggregation parameter
For low y, most e values will be
negative For high y, most e values will be
positive and large
e -1.6
ln Y
e -0.8
Mm2
e 1.2
e 2.2
ln Y
Y y
r1
r2
log R
r3
rN
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Probabilistic Seismic Hazard Analysis
Logic tree methods

• Not all uncertainty can be described by
  probability
• distributions
• Most appropriate model may not be clear
• Attenuation relationship
• Magnitude distribution
• etc.
• Experts may disagree on model parameters
• Fault segmentation
• Maximum magnitude
• etc.

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Probabilistic Seismic Hazard Analysis
Logic tree methods
Attenuation Model
Magnitude Distribution
Mmax
G-R (0.7)
BJF (0.5)
Char. (0.3)
G-R (0.7)
A S (0.5)
Char. (0.3)
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Probabilistic Seismic Hazard Analysis
Logic tree methods
Attenuation Model
Magnitude Distribution
Mmax
Sum of weighting factors coming out of each node
must equal 1.0
G-R (0.7)
BJF (0.5)
Char. (0.3)
G-R (0.7)
A S (0.5)
Char. (0.3)
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Probabilistic Seismic Hazard Analysis
Logic tree methods
Attenuation Model
Magnitude Distribution
Mmax
G-R (0.7)
BJF (0.5)
Char. (0.3)
G-R (0.7)
0.5x0.7x0.2 0.07
A S (0.5)
Char. (0.3)
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Probabilistic Seismic Hazard Analysis
Logic tree methods
Attenuation Model
Magnitude Distribution
w
Mmax
G-R (0.7)
BJF (0.5)
Char. (0.3)
Final value of Y is obtained as weighted average
of all values given by terminal branches of logic
tree
G-R (0.7)
A S (0.5)
Char. (0.3)
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Probabilistic Seismic Hazard Analysis
Logic tree methods
Recent PSHA logic tree included Cascadia
interplate 2 attenuation relationships 2 updip
boundaries 3 downdip boundaries 2 return
periods 4 segmentation models 2 maximum magnitude
approaches 192 terminal branches
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Probabilistic Seismic Hazard Analysis
Logic tree methods
Recent PSHA logic tree included Cascadia
intraplate 2 intraslab geometries 3 maximum
magnitudes 2 a-values 2 b-values 24 terminal
branches
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Probabilistic Seismic Hazard Analysis
Logic tree methods
Recent PSHA logic tree included Seattle Fault
and Puget Sound Fault 2 attenuation
relationships 3 activity states 3 maximum
magnitudes 2 recurrence models 2 slip rates 72
terminal branches for Seattle Fault 72
terminal branches for Puget Sound Fault
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Probabilistic Seismic Hazard Analysis
Logic tree methods
Recent PSHA logic tree included Crustal areal
source zones 7 source zones 2 attenuation
relationships 3 maximum magnitudes 2 recurrence
models 3 source depths 252 terminal branches
Total PSHA required analysis of 612 combinations
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