The rate of aftershock density decay with distance
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Transcript of 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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are needed to see this picture.
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