The rate of aftershock density decay with distance

Karen Felzer1 and Emily Brodsky2

1. U.S. Geological Survey 2. University of California, Los Angeles

Mainshocks

Outline

• Methods• Observations• Robustness of observations• Physical Implications

1. Methods

Previous work on spatial aftershock decay include:

What’s different about our work?• Relocated catalog (Shearer et al. (2003))

• Small mainshocks (& lots of ‘em!)

• Only the first 30 minutes of each aftershock sequence used

• Ichinose et al. (1997), Ogata(1998), Huc and Main(2003)

OgataMain

We make composite data sets from aftershocks of the M 2-3 & M 3-4 mainshocks

Mainshocks are shifted to the origin in time and space

Spatial stack, M 3-4 mainshocksTemporal stack

Mainshocks = gray star

2. Observations

Spatial aftershock decay follows a pure power law with an exponent slightly < -1

Aftershocks > M 2.

The aftershocks may extend out to100 km

Aftershock from the first 5 minutes of each sequence

The distribution of aftershocks with distance is independent of mainshock magnitude

Data from 200 aftershocks of M 2-3

mainshocks and from 200 aftershocks of M 3-4 mainshocks are plotted together

3. Robustness of observations

Is our decay pattern from actual aftershock physics, or just from background fault structure?

A)

Random earthquakes have a different spatial pattern: Our results are from aftershock physics

Does the result hold at longer times than 30 minutes?

B)

Aftershocks from 30 minutes to 25 days

Yes: the power law decay is maintained at longer times but is lost in the background at r > two fault lengths

Yes -- the same power law holds until within 50 m of the fault plane

Distances to mainshock fault plane calc. from focal mechs. of Hardebeck & Shearer (2002)

Do we have power law decay in the near field?C)

4) Physical Implications

Linear density = = =cr-1.4

rDrcr-1.4

Fault Geometry Physics€

NaftNhyp

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Nhypdr

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Naftdr

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Nhypdr

= r

Kagan & Knopoff, (1980)

Helmstetter et al. (2005)

Max. pos. for r>10 km

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Nhypdr = c

Felzer & Brodsky

Solutions consistent with observations

Solutions for

r -1.4 using D=1 from Felzer and Brodsky. This agrees with max. shaking amplitudes (based on our work with Joan Gomberg & known attenuation relationships)

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Joan Gomberg

r -2.4 using D=2 from Helmstetter et al. (2005).

Static stress triggering plus rate and state friction predicts exp(r-3) at short times (Dieterich 1994). This is not consistent with the observations.

Static stress triggering not consistent with observations

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NaftNhyp

Conclusions

• The fraction of aftershocks at a distance, r, goes as cr -1.4.

• Aftershocks of M 2-4 mainshocks may extend out to 100 km.

• Our results are consistent with probability of having an aftershock amplitude of shaking.

• Our results are inconsistent with triggering by static stress change + rate and state friction

Supplementary Slides

Mainshocks are moved to the origin in time and space to obtain a composite data set

Aftershocks from Northern Cal and Japan also follow power law decay

Another way to observe distant triggering: Time series peaks at the time of the

mainshocks in different distance annuli

Peak at time of mainshocks