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The rate of aftershock density decay with distance Karen Felzer 1 and Emily Brodsky 2 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: Whats 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) Ogata Main

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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 mainshocks Temporal 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 r D r cr -1.4 Fault Geometry Physics = r Kagan & Knopoff, (1980) Helmstetter et al. (2005) Max. pos. for r>10 km = 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) 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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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

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