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Title: Use of Earthquake Simulators in Assessment of Earthquake Probabilities


1
Use of Earthquake Simulators in Assessment of
Earthquake Probabilities
Jim Dieterich, Keith Richards-Dinger Deborah
Smith UC Riverside
2
Why 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?

3
Some 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

4
Possible 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

6
Southern California Earthquake Center
(SCEC) Community Fault Model
7
Fast 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

8
Fast 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

9
Uniform 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.
10
M8 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
12
Mainshocks 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.
13
Clustering Earthquake Pairs by Distance and Time
Synthetic Catalog M6
14
Magnitude Frequency
Flat fault, 1500 fault elements
15
200 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

17
Status
  • 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

18
Emergent system-scale phenomena require off-fault
stress relaxation
Individual faults exhibit approximately
self-similar roughness
19
Random Fractal Fault Model
Solve for slip using boundary elements. Simple
Coulomb friction with ? 0.6 Periodic B.C, or
slip on a patch
20
Hurst exponent H 1.0 Roughness amplitude ?
0.1 Average sli 100 simulations
21
Fault slip and stress changes
Smooth fault
Fault with self-similar roughness
22
Yielding 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

23
Steady-state yielding by earthquakes EQ rate
µ Coulomb stress rate µ Long-term slip rate
????????
24
Average 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

25
Average long-term earthquake rate by
distance from fault with random fractal roughness
Scaling
26
Aftershocks Earthquake rates following a stress
step
Earthquake rate , Following a stress
step Immediate aftershocks at t0
Dieterich, JGR (1994), Dieterich, Cayol, Okubo,
Nature, (2000)
27
Initial Aftershock Rate / Background Rate
????????
???????
????????
28
????????
????????
???????
29
Delayed onset of stress shadow
30
Rate-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)
31
Rate-State Stress Relaxation
Earthquake rate
Stress relaxation of individual stress components
32
Rate-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
33
ta11 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
34
ta10 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
35
Fault 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
36
Asig2 bar
37
(No Transcript)
38
Evidence for Time Dependence of Stress
Heterogeneity
Modified from (Woessner, 2005)
39
Decrease of Stress Heterogeneity with Time and
Distance (Background Deviatoric Stress 100
bars)
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