Transcript How Simulators Could Be Used for Creating UCERF

Applications of Earthquake Simulators to Assessment
of Earthquake Probabilities
Jim Dieterich
Some issues/limitations with current UCERF approach
Sometimes I lie awake at night, and I ask, "Where have I gone wrong?” Then a voice says
to me, "This is going to take more than one night."
(Charles M. Schultz/Charlie Brown, in "Peanuts”)
1. Models have become exceedingly complex.
2. Probability density distributions for recurrence of slip in large
earthquakes are not known. Statistics of large earthquakes very poorly
defined. Poisson, quasi-periodic, clustered? Magnitude and position
dependence of pdfs.
3. Interpretation of empirical model.
4. Strict use of characteristic earthquakes and segmentation is problematic
5. Point characterizations of segments. Properties governing recurrence and
slip are not constant along segments. Stress interactions, clock reset.
6. Non-linear loading processes. viscoelasticity, fault creep, off-fault relaxation
7. Integration with spatiotemporal clustering
8. Fault to fault jumps and rupture branching.
Contributing problem: Current approaches tend to treat these
items independently, when in fact they are often coupled
Ned’s Priorities:
1)Relax segmentation
2)Incorporate spatiotemporal clustering
Inputs to simulators
Simulators directly produce earthquake rate models for
A- and B- type faults. Catalogs ~106 events.
•Moment-balanced
•Segmentation is not assumed or enforced
•Multiple realizations  effect of parameter uncertainties
•Multiple models
•Tuned to be consistent with paleoseismic recurrence
•Rupture jumps and branching
•Uncertainties in moment-area relations are largely avoided
Direct prediction of conditional probabilities
•Sufficient number of events in catalogs to generate empirical
pdfs for all fault sub-sections
•No apriori assumptions about clustering vs Poisson vs quasiperiodic.
•Multiple realizations – evaluate effect of parameter
uncertainties
•Multiple models
Subsection approach to determining conditional probabilities: Steps
Probability density for
recurrence of slip on fault
sub-section k
Pi  CPi Ri 

CPk = conditional probability
of event M≥6.5 on section k
Sub-catalog of n events for a
section that occur in the interval
Dt for used to determine CPk
Weighted participation rate
of event i
1
Rki 
nk
Ni

j1

Sub-catalog of n events for a
section that occur in the interval
Dt for used to determine CPk
1/ N kj
Weighted participation rate
of event i
Total probability of event i in the
conditional interval Dt
1
Rki 
Ni
Pi 
nk
Ni

1/ N kj
j1


Ni

CPk
CPk Rki 
k 1
n
k
k 1
Ni
1/ N
j 1

k
j
Spatiotemporal clustering with RSQSim
Stacked rate of seismicity relative to mainshocks 6>M<7
Decay of aftershocks follows Omori power law t -p with p = 0.77
Foreshocks (not shown) follow an inverse Omori decay with p = 0.92
Dieterich and Richards-Dinger, PAGEOPH, 2010
Inter-event Waiting Time Distributions
Space – Time Distributions
Earthquake cluster along San Andreas Fault
M7.3
43 aftershocks in 18.2days
All-Cal model – SCEC Simulator Comparison Project
Earthquake cluster along San Andreas Fault
M6.9
Followed by 6 aftershocks in 4.8 minutes
All-Cal model – SCEC Simulator Comparison Project
Earthquake cluster along San Andreas Fault
M7.2
All-Cal model – SCEC Simulator Comparison Project
Clusters of Large Earthquakes
Robs is the total number of
clusters M≥7, divided by
the number of isolated M≥7
earthquakes
Rates of M≥7 Earthquakes
following M≥7 Earthquakes
Cumulative probability of earthquake
(on San Jacinto fault segment of the San Jacinto fault)
From random time
From time of M≥6.5 on
adjacent Anza segment
M≥6.5 on San Jacinto Segment
From random time
From time of M≥6.5 on
distant Calaveras segment
M≥6.5 on San Jacinto Segment
Cumulative probability of earthquakes
(on San Jacinto fault segment of the San Jacinto fault)
From random time
From time of M≥6.5 on
adjacent Anza segment
M≥6.5 on San Jacinto Segment
From random time
From time of M≥6.5 on
adjacent Anza segment
M≥5.5 on San Jacinto Segment
Summary of some advantages of simulators
relative to current UCERF methods
• Integrated self-consistent framework for generating an earthquake rate model
• Properly captures intrinsic relations between stress and fault slip in 3D systems
and avoids the dubious use of point characterizations of spatially varying
properties (stress, slip, time since last slip, clock reset)
• Clustering is modeled deterministically and tied to constitutive parameters and
evolving stress conditions
• Framework for characterizing regional fluctuations of seismicity rates –
interpretation of empirical model
• Non-linear stressing from interactions with deep creeping zone and
viscoelasticity in some models
• Moment balancing issues are eliminated
• No assumptions are made regarding characteristic earthquakes (pro or con)
• Rupture jumps and branching occur spontaneously
Summary of Possible Near-Term Applications
1) Earthquake rate models for A and B faults (no a priori
segmentation)
2) Conditional probabilities on A and B faults (Poisson,
clustering and quasi-periodic are seen)
3) Clustering probabilities for moderate and large
earthquakes (Pre-calculate look-up table for near real-time
response)
Some other applications
• Develop and/or test algorithms and models used with current
methods
• Interpretation of empirical model and regional rate fluctuations
(Tullis talk)
• Relative weighting appropriate for quasi-periodic, clustering,
and Poisson probability models
• Evolution of b-values
• Evaluate fault rupture scenarios (“Stringing Pearls” of Biasi and
Weldon – Goal: reduce number of possible models)