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

Mainshocks

Karen Felzer1 and Emily Brodsky2

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


Outline

Outline

  • Methods

  • Observations

  • Robustness of observations

  • Physical Implications


The rate of aftershock density decay with distance

1. Methods


The rate of aftershock density decay with distance

Previous work on spatial aftershock decay include:

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

Ogata

Main

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


The rate of aftershock density decay with distance

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


The rate of aftershock density decay with distance

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

Aftershocks > M 2.


The rate of aftershock density decay with distance

The aftershocks may extend out to100 km

Aftershock from the first 5 minutes of each sequence


The rate of aftershock density decay with distance

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


The rate of aftershock density decay with distance

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


The rate of aftershock density decay with distance

B)

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


The rate of aftershock density decay with distance

C)

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


The rate of aftershock density decay with distance

Linear density ===cr-1.4

Fault Geometry

Physics

Felzer & Brodsky

Kagan & Knopoff, (1980)

Helmstetter et al. (2005)

Max. pos. for r>10 km

= r

= c

rDrcr-1.4


Solutions for

Solutions consistent with observations

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

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 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


The rate of aftershock density decay with distance

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


The rate of aftershock density decay with distance

Aftershocks from Northern Cal and Japan also follow power law decay


The rate of aftershock density decay with distance

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

Peak at time of mainshocks


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