The rate of aftershock density decay with distance
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The rate of aftershock density decay with distance. Mainshocks. Karen Felzer 1 and Emily Brodsky 2. 1. U.S. Geological Survey 2. University of California, Los Angeles. Outline. Methods Observations Robustness of observations Physical Implications. 1. Methods.

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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


  • Methods

  • Observations

  • Robustness of observations

  • Physical Implications

Previous work on spatial aftershock decay include:

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



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

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

Temporal stack

Spatial stack, M 3-4 mainshocks

Mainshocks = gray star

Mainshocks are shifted to the origin in time and space

2 observations
2. Observations M 3-4 mainshocks

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

Aftershocks > M 2.

The aftershocks may extend out to100 km exponent slightly < -1

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

3. Robustness of observations of mainshock magnitude

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


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

B) from background fault structure?

Does the result hold at longer times than 30 minutes?

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

C) from background fault structure?

Do we have power law decay in the near field?

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

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

4 physical implications
4) Physical Implications from background fault structure?

Linear density  from background fault structure?===cr-1.4

Fault Geometry


Felzer & Brodsky

Kagan & Knopoff, (1980)

Helmstetter et al. (2005)

Max. pos. for r>10 km

= r

= c


Solutions for

Solutions consistent with observations from background fault structure?

Static stress triggering not consistent with observations

Joan Gomberg

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)

r -2.4using 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.

Solutions for

Conclusions from background fault structure?

  • 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 probabilityof having an aftershock  amplitude of shaking.

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

Supplementary slides
Supplementary Slides from background fault structure?

Another way to observe distant triggering: Time series peaks at the time of the mainshocks in different distance annuli

Peak at time of mainshocks