karen felzer & emily brodsky testing stress shadows
Post on 05-Jan-2016
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Karen Felzer & Emily Brodsky
Testing Stress Shadows
If earthquake triggering is caused by static stress change, we should
see stress shadows as well as zones of seismicity rate increase.
Do we actually see these shadows?
Previous work on Stress Shadows
• Stress shadows observed by Simpson and Reasenberg (1994), Harris and Simpson (1998), Stein (1999), Wyss and Wiemer, (2000), Toda and Stein (2003), and others –
• Marsan (2003) found that rate decreases were significantly more rare than expected.
• Mallman and Zoback (2003) found little seismicity decrease after the Landers and Kobe earthquakes.
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Testing for stress shadows is very
difficult
1. If seismicity rates were low before the mainshock it’s hard to measure a rate decrease.
2. Tests for seismicity rate decreases using seismictiy rate ratios (Reasenberg & Simpson, 1992;
Wyss & Wiemer, 2000…) produce many false
positives
3. Tests for shadows by looking for sudden rate decreases on mainshock day (Parsons et al. 1999; Stein
1999; Wyss & Wiemer, 2000; Toda & Stein, 2003) also produce false positives if region boundaries are free
A sudden rate decrease over the entire predicted stress shadow area would be
indicative - but this is never seen
What a test for stress shadows needs to do
Look for a seismicity drop in any collection of spatial bins that is
sharper after the mainshock than after random points in time.
To keep our spatial boundaries fluid, we look for seismicity rate changes in all 10 by 10 km bins within 1.5 fault
lengths of the mainshock
mainshock
To measure seismicity rate changes independent of ongoing aftershock sequences
we create the time ratio statistic, R
If the earthquake after the mainshock is time advanced, R<<1
If the earthquake after the mainshock is delayed, R is close to 1
Example: Evaluating rate changes after
the 1990 M 5.4 Claremont Earthquake
To evaluate whether there are a significant number of rate decreases we histogram the R values for all bins
Ideal histogram, infinite earthquake catalog
In finite catalogs, bins may have no post-mainshock earthquakes. Corrections result in a
small hump near 1.0 even w/o a shadow
Test Sensitivity
• If the concentration of R values near 1 is statistically higher after a mainshock then after a collection of random times then a stress shadow exists.
• But if a significant difference is not seen we may just not have a sensitive enough test -- Type II error.
Test Sensitivity
• Test sensitivity is evaluated by ensuring that a stress shadow is detected when we produce simulated catalogs using measured pre-mainshock seismicity rates, calculated static stress changes, and rate and state friction (Dieterich, 1994).
Normal stress 100 bars
Initial Shear stress60 bars
Background stress 4.7*10^-10 MPa/s
A 0.012, 0.008, 0.005
Rate and state parameters
Results for Landers
No shadow detected
Results for Loma Prieta
No shadow detected
Results for Northridge
Can’t be determined
Results for Hector Mine
Can’t be determined
Mid-talk summary
• No stress shadows are observed after the Landers, Loma Prieta, Northridge, or Hector Mine earthquakes. In all cases the concentration of R near 1 is less after the mainshock than at random times.
• For Landers and Loma Prieta the absence is significant -- Type II error can be ruled out at 98% significance.
• For Northridge and Hector Mine the data is not sufficient to rule out Type II error.
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What about 1906?
There were probably on the order of at least 2 times more M≥5.5
earthquakes/year in the SF Bay area from 1850-1906 as 1906-2000. But was
this caused by a stress shadow??
The seismicity patterns do not fit the stress shadow model
The timing of the seismicity slow down does not agree with the stress shadow
hypothesis
The location of the seismicity rate slow down does not agree with the stress
shadow hypothesis
Alternate explanation for Bay Area quiescence
• Since most earthquakes are aftershocks, the seismicity rate has positive feedback: high and low seismicity rates reinforce each other.
• Independent of 1906, seismicity sometimes persists at a higher or lower rate.
• This indicates that the SF “shadow” is a result of earthquake triggering, clustering, and statistical chance, not static stress decrease.
• In this model recovery from the SF Bay quiescence will be more sudden than gradual, and unpredictable.
Inter-event times indicate that many pre-1906 earthquakes were aftershocks of each other
Pre-1906, M≥5.51000 simulated Poissonian eqs
Simulated sequences, in which earthquake timing is determined only by Omori’s law, can
produce “shadows”
shadow
Simulation Results
Conclusions
• If aftershocks are triggered by static stress changes, stress shadows should occur.
• Here we find no shadow after the Landers, Loma Prieta, Northridge, or Hector Mine mainshocks, although Type II error cannot be ruled out for Northridge and Hector Mine.
• In the SF Bay Area, the instrumental earthquake catalog has been significantly quieter than the historic one. But the timing and location of the quiescence do not fit the stress shadow hypothesis, suggesting that earthquake clustering statistics may be the cause.
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