Transcript Document

Chapter 5: Calculating
Earthquake Probabilities
for the SFBR
Mei Xue
EQW March 16
Outline
• Introduction to Probability
Calculations
• Calculating Probabilities
• Probability Models Used in the
Calcuations
• Final calculation steps
Introduction to Probability
Calculations
Introduction to Probability
Calculations
• Earthquake probability is calculated
over the time periods of 1-, 5-, 10-, 20-,
30- and 100-year-long intervals
beginning in 2002
• The input is a regional model of the
long-term production rate of
earthquakes in the SFBR (Chapter 4)
• The second part of the calculation
sequence is where the time-dependent
effects enter into the WG02 model
Introduction to Probability
Calculations
• Review what time-dependent
factors are believed to be
important and introduce several
models for quantifying their
effects
• The models involve two interrelated areas: recurrence and
interaction
Introduction to Probability
Calculations
• Express the likelihood of occurrence of
one or more M6.7 EQs in the SFBR in
the time periods in five ways:
• The probability for each characterized large
EQ rupture source (35)
• The probability that a particular fault
segment will be ruptured by a large EQ (18)
• The probability that a large EQ will occur
on any of the 7 characterized fault systems
• The probability of a background EQ (on
faults in the SFBR, but not on one of the 7)
• The probability that a large EQ will occur
somewhere in the region
Calculating Probabilities
• Primary input: the
rupture source
mean occurrence
rate (Table 4.8)
• The probability
rupture source,
each fault,
combined with
background -> the
probability for the
region as a whole
Calculating Probabilities
• They model EQs that rupture a fault
segment as a renewal process:
independent
• Probability Models
• Poisson: the probability is constant in time
and thus fully determined by the long-term
rate of occurrence of the rupture source
• Empirical model: a variant of the Poisson,
the recent regional rate of EQs
• Time-varying probability models: BPT, BPTstep (1906, 1989), and Time-predictable
(1906), take into account information about
the last EQ
Calculating Probabilities
Survivor function: gives the probability that at least
time T will elapse between successive events
hazard function: gives the instantaneous rate of
failure at time t conditional upon no event having
occurred up to time t
Conditional probability: gives the
Probability that one or more EQs will occur on a rupture
source of interest during an interval of interest, conditional
upon it not having occurred by T (year 2002)
Five Probability Models:
1 Poisoon Model
 - the mean rupture rate of each rupture source
• The hazard function is constant
• Fails to incorporate the most basic physics
of the earthquake process: reloading
• Fails to account for stress shadow
• Reflects only the long-term rates
• Conservative estimate for faults that timedependent models are either too poorly
constrained or missing some critical
physics (interaction)
Five Probability Models:
2 Empirical Model
(t) – not stationary, estimated from the
historical EQ record (M  3.0 since 1942
and M  5.5 since 1906)
- the long term mean rate
• Complements the other models as M 
5.5 is not used by other models
• Take into account the effect of the
1906 EQ stress shadow
• Specifies only time-dependence,
preserving the magnitude distribution
of the rupture sources
The shape of the magnitude distribution on each fault
remains unchanged; the whole distribution moves up and
down in time
Summary of rates and 30-year probabilities of EQs (M6.7)
in SFBR calculated with various models
Assumptions:
1. Fluctuations in the rate of M  3.0 and M  5.5 EQs reflect
fluctuations in the probability of larger events
2. Fluctuations in rate on individual faults are correlated
(though stress shadow is not homogeneous in space,
affected seismicity on all magjor faults in the region)
3. The rate function (t) can be sensibly extrapolated
forward in time
Five Probability Models:
3 BPT Model
μ – the mean recurrence interval, 1/
α – the aperiodicity, the variability of recurrence
times, related to the variance 2, equals /μ
A Poisson process when α=1/sqrt(2)
1. For smaller α, strongly peaked, remains close to zero longer
2. For larger α, “dead time” becomes shorter, increasingly
Poisson-like
Estimates of aperiodicity α obtained by Ellsworth et al. (1999)
for 37 EQ secquences (histogram) and the WG02 model
(solid line)
Five Probability Models:
4 BPT-step Model
• A variation of the BPT model
• Account for the effects of stress
changes caused by other
earthquakes on the segment under
consideration (1906, 1989)
• Interaction in the BPT-step model
occurs through the state variable
1. A decrease in the average stress on a segment lowers the
probability of failure, while an increase in average stress
causes an increase in probability
2. The effects are strongest when the segment is near failure
Assumptions:
1. The model represents the statistics of recurrence intervals
for segment rupture
2. The time of the most recent event is known or constrained
3. The effects of interactions are properly characterized (BPTstep, 1906, 1989 San Andreas only)
Five Probability Models:
5 Time Predictable Model
• The next EQ will occur when
tectonic loading restores the stress
released in the most recent EQ
• Dividing the slip in the most recent
EQ by the fault slip rate
approximates the expected time to
the next earthquake
• Only time of next EQ not size
• Only for the SAF fault
Five Probability Models:
5 Time Predictable Model
Four extensions:
1. Model the SFBR as a network of
faults
2. Strictly gives the probability that a
rupture will start on a segment
3. Fault segments can rupture in more
than one way
4. Use Monte Carlo sampling of the
parent distributions to propagate
uncertainty through the model
Five Probability Models:
5 Time Predictable Model
Six-step calculation sequence:
1. Slip in the most recent event
2. Slip rate of the segment
3. Expected time of the next rupture
of the segment
4. Probability of a rupture starting on
the segment (4 segments, ignoring
interaction, BPT model) – Epicentral
probabilities
5. Convert epicentral probabilities into
earthquake probabilities
Five Probability Models:
5 Time Predictable Model
6. Compute 30-year source
probabilities
Final calculation steps
• Probabilities for fault segments
and fault systems
• Probabilities for earthquakes in
the background
• Weighting alternative probability
models (VOTE)
• Probabilities for the SFBR model
Paper recommendataions
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Reasenberg, P.A., Hanks, T.C., and Bakun, W.H., 2003, An
empirical model for earthquake probabilities in the San
Francisco Bay region, California, 2002-2031, BSSA 93 (1):
1-13 FEB 2003
Shimazaki, K., and Nakata, T., Time-predictable
recurrence model for large earthquakes: Geophysical
Research Letters, v. 7, p. 279-282, 1980
Ellsworth, W.L., Matthews, M.V., Nadeau, R.M., Nishenko,
S.P., Reasenberg, P.A., and Simpson, R.W., A physicallybased earthquake recurrence model for estimation of
long-term earthquake probabilities: USGS, OFR 99-522,
23 p., 1999
Cornell, C.A., and Winterstein, S.R., Temporal and
magnitude dependence in earthquake recurrence
models: BSSA, v. 78, no. 4, p. 1522-1537, 1988
Harris, R.A., and Simpson, R.W., Changes in static stress
on Southern California faults after the 1992 Landers
earthquake: Nature, v. 360, no. 6401, p. 251-254, 1992