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Applica'on of Earthquake Simulators to Assessments of Earthquake Probabili'es
Jim Dieterich, Keith Richards-‐Dinger
There are many methods for predicting the future. For example, you can read horoscopes, tea leaves, tarot cards, or crystal balls. Collectively, these methods are known as "nutty methods." Or you can put well-researched facts into sophisticated computer models, more commonly referred to as "a complete waste of time." (Scott Adams, The Dilbert Future)
One view on the use of computer models for forecasts
1) Brief review of what goes into an assessment of 'me-‐dependent probabili'es
2) Limita'ons and problems with current methods
3) Current status of simulators
4) Near-‐term applica'ons of simulators
Outline
Simplified view of how long-‐term 'me-‐dependent probabilis'c
assessments are made
Goal is to build a model of regional seismicity, together with an assessment of current state, and it project it into the future
Long-term model of earthquake rates by fault sections
(historic seismicity, fault slip rates, paleoseism., deformation
observations)
Current state of fault sections: Elapsed time since last large EQ
(Historic EQs, paleoseism.)
Model for recurrence of slip In large earthquakes
Probability Density Distr. (PDF)
Conditional probability of earthquake in some coming
Interval of time
Some%mes 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”)
Limitations of Current Methods for Long-Term Forecasts
Working group studies of California earthquake probabilities
Date Geographic coverage Number of pages
1988 San Andreas fault system 62
1990 San Francisco Bay Region 51
1994 San Andreas Fault System (expanded) 60
2000 San Francisco Bay Region 235
2007 Statewide UCERF 2 682
Some%mes 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”)
Limitations of Current Methods for Long-Term Forecasts 1. Models have become exceedingly complex. Consequence of introducing more processes into the analyses, and desire to relax especially restrictive assumptions. (Are we reaching limit of useful development?)
2. Probability density distributions for recurrence of slip in large earthquakes are not known. Statistics of large earthquakes very poorly defined because large earthquakes are rare events. Large numbers of events ≥100 are needed to define the shape of a pdf.
Possible approaches: • Guess the type of the pdf, based on statistical models (Poisson,
clustered, quasi-periodic?) • Extrapolate statistics of smaller earthquakes to large events. (possible
magnitude dependence?)
• Extrapolate by stacking sparse data sets from different parts of the world. (Shape of distribution may depend on stress interactions, which are unique to geometry of fault systems, and on magnitude of earthquakes)
• Extrapolate using simulations that incorporate our current understanding of physical processes (example later)
Limitations of Current Methods for Long-Term Forecasts
Limitations of Current Methods for Long-Term Forecasts 3. Some additional specific issues with current methods
The 50-50-90 rule: Anytime you have a 50-50 chance of getting something right, there's a 90% probability you'll get it wrong. (Andy Rooney)
Contribu)ng problem: Current approaches tend to treat these items independently, when in fact they are o:en coupled
• Interpreta'on of empirical model • Moment balancing • Improper implementa'on of elas'c rebound concept for 3D fault systems Spring slider: Δt = Δτ / τ = D/V ; in 3D: Δt = Δτ / τ ≠ D(Δτ, L)/V
• Strict use of characteris'c earthquakes and segmenta'on is problema'c • Point characteriza'ons of segments when proper'es governing recurrence and slip are not constant along the segment
• Fault to fault jumps, rupture branching • Par''oning of seismic and aseismic slip • Non-‐linear loading processes (viscoelas'city, fault creep, off-‐fault relaxa'on) • Stress interac'ons, clock reset • Earthquake clustering and coupling of event probabili'es
Earthquake Simulators Pioneered by Steve Ward, John Rundle
• Can be tuned to be consistent with recurrence observations from paleoseismology
Characteristics of Simulators • Fault systems represented as arrays of boundary elements → accurate
representation of elastic fault interactions • Earthquake slip events arise spontaneous from stress conditions and fault
constitutive properties → result in stress redistribution • Repeated simulations of long catalogs over a range of earthquake magnitudes
• Generate robust model statistics on recurrence • Internally consistent • Statistics of multi-segment ruptures, rupture jumps, branching,
Inputs for simulator-based earthquake rate models • Fault system geometry + seismic depth • Long-term fault slip rates • If available information on recurrence intervals (adjusted by stress drop) • Constitutive properties (explicit or implicit to simulation of slip during EQs)
Color indicates long-‐term slip rate
SCEC Seismicity Simulators Comparison and Valida'on Project
PI: Terry Tullis Nadia Lapusta Olaf Zielke Steve Ward John Rundle, Louise Kellog, Don Turcotte Jim Dieterich, Keith Richards-Dinger Fred Pollitz
RSQsim • Boundary elements
• Strike-‐slip, dip-‐slip and mixed mode fault slip
• 35,000 fault elements (single processor) ~90,000 with 8 node cluster Detailed representa'on of fault network geometry
Simula'ons of California at ≥M3.5 are feasible
• Fast algorithm → Simula'ons ≥100,000 Eqs (Dieterich, 1994)
• Seismogenic fault elements – rate-‐state fric'on Healing by log 'me
Time-‐ and stress-‐dependent nuclea'on
Full representa'on of normal stress history effects
• Fault creep elements – rate strengthening
• Inputs Fault slip rates
Rate-‐state parameters: a, b, (insensi%ve to Dc)
Elas'c modulii, shear wave speed β, stress concentra'on factor for rupture propaga'on
Fault geometry and co-‐seismic slip
Dieterich and Richards-‐Dinger, PAGEOPH, 2010
DYNA3D – Fully dynamic finite element simula'on
RSQsim – Fast simula'on
Propaga'on 'me 14.0 s
Propaga'on 'me 14.3 s
RSQsim – DYNA3D Comparison
RSQsim – DYNA3D Comparison
Foreshocks and aoershocks from a simula'on of 500,000 earthquakes spanning 16,370 years
Decay of aoershocks 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
Stacked rate of seismicity rela've to mainshocks 6>M<7
Comparison of Simulation Statistics: Inter-event Waiting Times
Inter-event Waiting Times and Distances
Working Group assessments of earthquake probabilities have become important products that are used in a variety of ways
• Economic decisions (insurance rates, earthquake retrofits), • Input for probabilistic seismic hazard assessments • Preparadness/earthquake response planning • Public policy
Abrupt changes in methodology are not desirable
Develop experience and confidence in use of simulators
Progressive implementation
Near-term applications of simulators for evaluation of earthquake probabilities
Interpretation of the empirical model
All-Cal Model – Fluctuations of Moment Release Rate
Southern California
Northern California
Interpretation of the empirical model
All-Cal Model – Fluctuations of Moment Release Rate
(Color indicates magnitude of slip)
Fault slip during large events with creeping zone at base of fault
Statistics for recurrence of earthquake slip at a specific point
Clustered (1/t)
cov = 0.1
cov = 0.9 ~ Poisson
Most large earthquakes M≥7 occur as isolated events in space and time. However, there are occasional large-event clusters.
- Joshua Tree – Landers – Big Bear – Hector Mine sequence - Nankai earthquake pairs of 1854, 1944-1946
Working Group assessments assume independence of recurrence probabilities and do not treat coupling of earthquake probabilities
PA alters PB, PC, PD, …; PB alters PA, PC, PD,…; etc
Simulations generate clusters that appear to capture clustering statistics. 0.1– 0.2 probability that a large earthquake will be followed by another large earthquake within 4 years.
This coupling of event probabilities is embedded in empirical pdf’s
Large-event earthquake pairs and clusters
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
Conclusions
• Methods in current use have become increasingly complex, apparently without a corresponding improvement in predictability
• If one accepts the possibility that recurrence sta's'cs are controlled in part by local fault geometry → require several thousand years to gather sta's'cs to define pdf for recurrence of large earthquakes
• Clustering, Poisson, and quasi-‐periodic behavior are not mutually exclusive in simulators
• PDFs: Instead of the one-‐size-‐fits-‐all approach, simulators can be used to generate empirical PDFs.
• Simulators are evolving rapidly and will con'nue to improve as our understanding of earthquake processes improves
• Simula'ons appear to be a viable means for dealing with several short-‐comings of current methods
• It is 'me to begin phasing in the use simulators into the Working Group process
Addi'onal advantages of simulators rela've to current methods
• Integrated self-‐consistent framework for genera'ng an earthquake rate model
• Properly captures intrinsic rela'ons between stress and fault slip in 3D systems
• Foreshocks and aoershocks are modeled determinis'cally and 'ed to cons'tu've
parameters and stress condi'ons
• Framework for characterizing region-‐wide fluctua'ons of seismicity rates –
interpreta'on of empirical model
• Non-‐linear stressing from interac'ons with deep creeping zone. Viscoelas'city appears to be tractable
• Moment balancing issues are reduced
• No assump'ons are made regarding characteris'c earthquakes (pro or con)
• Rupture jumps and branching occur spontaneously
• Avoids the dubious use of point characteriza'ons of spa'ally varying proper'es (stress,
slip, 'me since last slip)
Weather forecast for tonight: Dark. Continued dark overnight, with widely scattered light by morning. (George Carlin)
