the rate of aftershock density decay with distance

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