The rate of aftershock density decay with distance
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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
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Outline
• Methods• Observations• Robustness of observations• Physical Implications
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1. Methods
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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
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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
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2. Observations
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Spatial aftershock decay follows a pure power law with an exponent slightly < -1
Aftershocks > M 2.
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The aftershocks may extend out to100 km
Aftershock from the first 5 minutes of each sequence
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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
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3. Robustness of observations
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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
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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
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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)
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4) Physical Implications
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Linear density = = =cr-1.4
rDrcr-1.4
Fault Geometry Physics€
NaftNhyp
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Nhypdr
€
Naftdr
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Nhypdr
= r
Kagan & Knopoff, (1980)
Helmstetter et al. (2005)
Max. pos. for r>10 km
€
Nhypdr = c
Felzer & Brodsky
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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)
QuickTime™ and aTIFF (Uncompressed) decompressor
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
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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
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Supplementary Slides
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Mainshocks are moved to the origin in time and space to obtain a composite data set
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Aftershocks from Northern Cal and Japan also follow power law decay
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Another way to observe distant triggering: Time series peaks at the time of the
mainshocks in different distance annuli
Peak at time of mainshocks