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.