Title: Use of Earthquake Simulators in Assessment of Earthquake Probabilities
1Use of Earthquake Simulators in Assessment of
Earthquake Probabilities
Jim Dieterich, Keith Richards-Dinger Deborah
Smith UC Riverside
2Why consider the use of earthquake simulators?
- WG02 acceptable range of aggregated 30-yr
probabilities 0.3-0.9 - Primary long term goal ? reduce the uncertainty
in probabilistic assessments - What approaches can give us the best return?
- Enormous effort and rapidly increasing complexity
of current approaches - Are we reaching useful limit for developing
current methods? - Are there less cumbersome more promising
approaches?
3Some Issues that contribute to uncertainties in
probabilities
- Model uncertainty at a very fundamental level
(Poisson, Quasi-periodic, Clustered?) - PDFs Which models best capture earthquake
occurrence? Aperiodicity parameter? - Simple conceptual models (such as,
time-predictable, slip-predictable, slip
deficits, characteristic earthquakes) do not
properly capture the intrinsic relations between
stress and fault slip in 3D systems - Seismicity off of explicity represented faults
- Characteristic earthquakes?
- Segmentation Do segments exist?
- Fault to fault jumps, branching
- Point characterizations of segments when stress,
and slip, and properties governing rupture
propagation are not constant along the segment - Moment balancing
- Observational inputs (seismicity, historic EQs,
geologic data) are not implmented in a unified or
consistent way - Partitioning of seismic and aseismic slip
- Non-linear loading processes (viscoelasticity,
fault creep, off-fault relaxation) - Stress interactions, clock reset
- Contributing problem Current approach tends to
treat these items independently, when in fact
they are generally coupled
4Possible benefits of simulators
- Unified and consistent means to employ input data
- Properly capture the intrinsic relations between
stress and fault slip in 3D systems - Illuminate and quantify emergent phenomena
arising from system-scale interactions that
cannot be represented with other approaches - PDFs Instead of the one-size-fits-all approach,
simulators can be used to generate PDFs. May be
very different from idealized model PDFs. Factors
controlling PDFs - Fault interactions Depend on fault geometry and
will be consquently region-specific, vary from
point-to-point (normal stress interactions, fault
to fault jumps, branches) - Rupture process variability
- Magnitude dependence (big earthquakes are less
influenced by perturbations - Constitutive properties
- Clustering, Poisson, and quasi-periodic behavior
are not mutually exclusive in simulators - Foreshocks and aftershocks can be modeled
deterministically (declustering and other abuses
of data are not necessary) - Use to create synthetic catalogs, and strain
records, to test/refine existing methods
5(Some) Desired Attributes of a Regional
Earthquake Simulator
- 3D stress interactions
- Representation of earthquakes slip rates
deformation - Capability to simulate wide range of EQ
magnitudes (this is more an attribute of
simulation approaches. - Long simulations to obtain statistical resolution
(100,000 events) - Appropriate resolution of fault geometry (M3.5
? 1-2 km2 elements, 104-105 fault elements in a
regional simulation) - Representation of strike-slip, normal, thrust and
mixed mode faulting - Earthquake clustering including foreshocks and
aftershocks - Off-fault seismicity and stress relaxation
- Appropriate constitutive properties
- Flexibility to accommodate new developments
alternative models
6Southern California Earthquake Center
(SCEC) Community Fault Model
7Fast fault system earthquake simulator
- Boundary elements - Okada
- 30,000 or more fault elements (single processor
G5) - Detailed representation of fault network geometry
- Simulations M3.5-8 for southern California
- 3D stress interactions
- Strike-slip, dip-slip and mixed mode fault slip
- Repeated Simulation of 100,000 events
- Basic elements of rate-state friction
- Healing by log time
- Time and stress dependent nucleation
- Full representation of normal stress history
effects - Inputs
- Fault slip rate (currently loading by backslip)
- Rate-state parameters A, B, (Dc does not enter
equations) - Elastic modulii, shear wave speed ?, stress
intensity factor for rupture
8Fast fault system earthquake simulator
- Computations are based on changes of fault
sliding state - 0 Locked fault aging by log time of stationary
contact - 1 Nucleating slip analytic solutions with
rate-state friction - 2 Earthquake slip quasi-dynamic slip speed
is fixed by shear impedance - No simultaneous equations to solve
- During earthquakes slip, the initiation or
termination of slip at an element requires one
multiply and one divide operation to update
stressing rate conditions at every element - Computation time scales by N1 where N is the
number of elements - 100,000 events with 30,000 fault elements 12hrs
9Uniform intial stress conditions are
characterized by crack like rupture processes
Stress and slip at end of event along a profile
passing through the center of the slipped region.
10M8 events on fault with 10,000 fault elements
2x vertical exaggeration
- M8 events
- Duration 215s, 204s
- Rupture speed 2.22.4 km/s
- Simulation
- 50,000 events
- M3.5-8.0
- Computation time 60 minutes on Mac G5 using a
single 2.2 GHz CPU
11-106
Complex event with foreshocks and aftershocks
from Dieterich, 1995
12Mainshocks M5.7
Composite plot of earthquake clustering formed by
stacking the records of seismic activity relative
to mainshock times from Dieterich, 1995. Events
in excess of the background rate, normalized by
the number of mainshocks.
13Clustering Earthquake Pairs by Distance and Time
Synthetic Catalog M6
14Magnitude Frequency
Flat fault, 1500 fault elements
15200 m Compressive Stepover All events M6.0
16- End of first M7 event 27.9 s
- 21 aftershocks in interval between first and
second M7 events - Start of second M7 event 169 s
17Status
- Basic model fully implemented for multiple
non-planar faults - Tested with 10,000 fault elements (single
processor G5) - Computation time for l00,000 events M3.5-M8 is
about 4 hours - Currently limited by memory to about 25,000
elements - Estimated computation time 100,000 events M3.5-M8
is about 10 hours - Could in principle run state-wide fault model at
about 2x2km resolution fault resolution by summer - Plans
- Focus on understanding characteristics of model
and model testing - Implement off-fault stress relaxation coupled to
slip explicity modeled faults - Implement attenuation relations for amplitude and
duration seismic waves to capture 1st order
effects of wave propagation on triggering
18Emergent system-scale phenomena require off-fault
stress relaxation
Individual faults exhibit approximately
self-similar roughness
19Random Fractal Fault Model
Solve for slip using boundary elements. Simple
Coulomb friction with ? 0.6 Periodic B.C, or
slip on a patch
20Hurst exponent H 1.0 Roughness amplitude ?
0.1 Average sli 100 simulations
21Fault slip and stress changes
Smooth fault
Fault with self-similar roughness
22Yielding and Stress Relaxation
- Stresses due to heterogeneous slip cannot
increase without limit - some form of
steady-state yielding and stress relaxation must
occur - Slope of 0.01 ? shear strain ???.01,
?????? brittle failure - In brittle crust, stress relaxation may occur by
faulting and seismicity off of the major faults. - Instantaneous failure and slip during earthquake
- Post-seismic aftershocks
- Interseismic background seismicity
- Yielding will couple to the failure process, by
relaxing the back stresses
23Steady-state yielding by earthquakes EQ rate
µ Coulomb stress rate µ Long-term slip rate
????????
24Average long-term earthquake rate by
distance from fault with random fractal roughness
- Stressing due to fault slip at constant long-term
rate - Model assumes steady-state seismicity at the
long-term stressing rate, in regions where
25Average long-term earthquake rate by
distance from fault with random fractal roughness
Scaling
26Aftershocks Earthquake rates following a stress
step
Earthquake rate , Following a stress
step Immediate aftershocks at t0
Dieterich, JGR (1994), Dieterich, Cayol, Okubo,
Nature, (2000)
27Initial Aftershock Rate / Background Rate
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28????????
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29Delayed onset of stress shadow
30Rate-State Stress Relaxation
- Concept for on-fault stress relaxation
- Assume stresses fluctuate around a steady-state
condition where the growth of interaction
stresses due to fault slip is balanced by
off-fault yielding.
Change of stress during earthquake
Relaxed state ( tectonic stressing)
31Rate-State Stress Relaxation
Earthquake rate
Stress relaxation of individual stress components
32Rate-State Stress Relaxation
Earthquake rate
t/trecurrence
Stress relaxation for each
1.0
0.5
0.1
Scale factor C is set by long-term slip rate
Elastic solution no relaxation
33ta11 yr, T150 yr 1001 elements
t0 Coulomb stress prior to slip Background
heterogeneity removed Co-seismic stress
drop Interseismic loading Tectonic stress
Off-fault stress relaxation tT Co-seismic
stress drop Interseismic loading
34ta10 yr, T50 yr
Co-seismic stress relaxation Interval 0 -
60sec Aftershock stress relaxation Interval
60s - ta Interseismic stress relaxation Interval
ta-T Total stress relaxation Interval 0 -T
35Fault Slip Effects of Fault Roughness, Tectonic
loading and Off-Fault Stress Relaxation
Remote loading Off-fault relaxation
Slip due to remote tectonic loading (no stress
relaxation)
(?0.5)
Increasing roughness
36Asig2 bar
37(No Transcript)
38Evidence for Time Dependence of Stress
Heterogeneity
Modified from (Woessner, 2005)
39Decrease of Stress Heterogeneity with Time and
Distance (Background Deviatoric Stress 100
bars)