Overview:

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Overview Earthquake Segmentation,
Fault-to-Fault Jumps, and Numerical
Paleoseismology
John B. Rundle Center for Computational Science
Engineering Professor of Physics, Geology and
Engineering University of California, Davis
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The GCM Community A gt 1 Billion Research
Program Computational Simulations of Sea Surface
Temperature The climate system is regulated in
part by sea surface temperature. Simulation of
North Atlantic sea surface temperature and ocean
height over a 5 year period is shown below. Each
frame represents a time step of 3 days.
Computation is based on the Parallel Ocean Model
developed at Los Alamos National Laboratory.
Color scale scales from -2o C (purple) to 32o C
(red). At right is the history of global
temperature change since 1880.
Computations Simulations by Y. Chao B Cheng,
JPL Movie Rendered with RIVA by P. Li J. Jacob,
JPL
Courtesy NOAA
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Constraints for WGCEP Forecasts Legal requirement
is that all possible ruptures must be considered
on the fault system. Numerical simulations having
long range interactions (mean field models), such
as Virtual California, and Standard Physical
Earth Model, have the property that they are
ergodic, meaning that all possible configurations
(ruptures) are visited by the dynamics, consisten
with the assumptions of the model (JBR et al.,
Phys. Rev. Lett., 1995 D Egolf, Science, 2001).
This property implies that the legal requirement
can presumably be fulfilled by the use of these
simulations.
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Ensemble Forecasting Requires Many Models and
Approaches Simulations will never be complete
both nature and the state of the art
evolve Ensemble forecasting can be used to define
the probability distribution for possible future
events. No one model or simulation will suffice -
many different models and simulations are needed
Data assimilation and model steering are
required for any viable approach
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Segmentation Assumed in Current Models
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Simulation based methods Virtual
California Virtual California 2001 Includes All
the Major Active Strike Slip Faults in
California (Rundle, 1988 PB Rundle et al., PRL,
2002 PB Rundle et al., PAGEOPH, in press, 2006)
Faults in RED are shown superposed on a LandSat
image of California. Geologic data are used to
set the model parameters. (Image courtesy of
Peggy Li, JPL)
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Comparison of Fault Topology in UCERF and in
Virtual California
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Ensemble Forecasting with Numerical Simulations
Virtual California
Backslip model Topology of fault system does
not evolve. Stress accumulation occurs as a
result of negative slip, or backslip. Linear
interactions (stress transfer) -- At the moment,
interactions are purely elastic, but
viscoelastic interactions can easily be
added. Arbitrarily complex 3D fault system
topologies -- At the moment, all faults are
vertical strike-slip faults. Boundary element
mesh is 10 km horizontal, 15 km vertical.
Faults are embedded in an elastic half space,
but layered media are possible as well.
Friction laws -- are based on laboratory
experiments of Tullis-Karner-Marone, with
additive stochastic noise. Method of solution
for stochastic equations is therefore via
Cellular Automaton methods. Friction laws based
on general theoretical law obtained by Klein et
al. (1997). Both TKM and Rate-and-State
friction can be incorporated.
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Structure of Virtual California Family of
Codes JPL QuakeSim Project http//quakesim.jpl.n
asa.gov
The structure of a backslip code such as Virtual
California uses boundary elements or finite
elements only to compute the stress Greens
functions. The dynamics are computed, analyzed
and visualized with codes of considerable
generality. The advantage of a backslip model is
that all faults are guaranteed to have an average
slip rate equal to the observed long-term rate.
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Parameter values used in Virtual California are
taken from USGS and SCEC data bases, supplemented
by expert opinion (i.e., not us!)
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Remarks on Friction Aseismic Slip (Stress
Leakage) Factor ?
? determines fraction of total slip that is
stable aseismic slip.
Rate and State Friction has been used to model
these data.
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Stochastic CA Friction Mathematical Details
Friction experiments can be described by a
stochastic Leaky Threshold Equation, or
Hopfield Equation Friction Equation on
each segment d? / dt ?KVLoad - ? ? ?(
t tF ) ? ( ??/? t ? ) ?(t)
Rate of change of stress Rate of stress
supply Rate of stress dissipation tF
represents all times for which ?? ( t F )
?F . VLoad is the segment loading rate (long
term fault slip rate), and K is the segment
stiffness. The ? - function parametrizes the
sudden slip event. The factor ? characterizes the
rate at which stress increases on fault segments.
? is a stochastic noise.
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UCERF Proposed Ruptures
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Large Single Events from Virtual California
Simulations
Two large events on the San Andreas Fault. The
dark bar indicates the epicentral segment. Red
indicates right-lateral slip Blue indicates
left-lateral slip The epicenter is the first
segment to slip in the event.
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Aftershocks from the 1906 San Francisco
Earthquake During the Following 48 Hours (AJ
Meltzner and DJ Wald, BSSA 93, 2160-2186, 2003)
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The Great 1906 San Francisco Earthquake Extended
for 350 km Along the San Andreas Fault in
Northern California. Horizontal offsets of as
much as 8 meters were observed.
Wayne Thatcher, US Geological Survey
Three coupled spatial scales visible 1. Fault
length (430 km) 2. Slip (m) 3. Rupture
thickness (cm)
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Numerical (Computational) Paleoseismology A
Sequence of Great NSAF Earthquakes at One Site
Element 238 Moderate Frictional Variability
Model V6P10d
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Space-Time Patterns of Historic Earthquakes
Large earthquakes on major faults occur
irregularly in time
Major events on the San Andreas Fault
From K. Sieh et al., JGR, 94, 603 (1989)
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Numerical (Computational) Paleoseismology II A
Sequence of Great SSAF Earthquakes at One Site
Element 300 Moderate Frictional Variability
Model V6P10d
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Numerical (Computational) Paleoseismology - III A
Sequence of Great SSAF Earthquakes at One Site
Element 305 Larger Frictional Variability
Model V6P18d
Year 760 12.4 m max
Year 251 9.7 m max
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Pattern Analysis from Virtual California
Simulations Space-time patterns are revealed by
Principal Component Analysis. If there are N
fault segments (degrees of freedom), there will
be N characteristic patterns of activity. Each
pattern is an eigenvector of the correlation
matrix. The first 4 eigenvectors are shown.
The activity at red sites is positively
correlated in time with activity at other red
sites. Similarly for blue sites with other blue
sites. Activity at the red and blue sites is
negatively correlated. Patterns computed over
40,000 years of simulations.
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Comparisons Great Earthquakes with Most
Significant Patterns
Events from Simulations
Patterns (Correlation Eigenvectors)
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Jumps Probability that a Rupture that Starts
on N San Jacinto Jumps to Either SSAF or SMF-CF
Moderate Frictional Variability Model V6P10d
Larger Frictional Variability Model V6P18d
Anderson et al., Science, 2003
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Probability that a Rupture that Starts on SSAF
Jumps Larger Frictional Variability Model
V6P18d
Probability that rupture begins on SSAF and jumps
to N San Jacinto or SMF-CF
Probability that rupture begins on SSAF and jumps
to any other fault
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Stress Dynamics and the Optimization of Numerical
Forecasts using Data-Scoring
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