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The rate of aftershock density decay with distance

This study examines the rate of aftershock density decay with distance following mainshocks. The research utilizes composite datasets from aftershocks of M2-3 and M3-4 mainshocks, observing a pure power-law decay pattern with an exponent slightly less than -1. The results suggest that aftershocks may extend up to 100 km and are independent of mainshock magnitude. The observations are robust, showing consistency in spatial patterns and temporal decay, while highlighting the implications for fault geometry and physics. The study contrasts aftershock physics with background fault structure and rejects triggering by static stress change and rate and state friction as explanations for the observed decay patterns.

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The rate of aftershock density decay with distance

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  1. 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

  2. Outline • Methods • Observations • Robustness of observations • Physical Implications

  3. 1. Methods

  4. 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

  5. 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

  6. 2. Observations

  7. Spatial aftershock decay follows a pure power law with an exponent slightly < -1 Aftershocks > M 2.

  8. The aftershocks may extend out to100 km Aftershock from the first 5 minutes of each sequence

  9. 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

  10. 3. Robustness of observations

  11. 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

  12. 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

  13. 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

  14. 4) Physical Implications

  15. 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

  16. 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

  17. 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

  18. Supplementary Slides

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

  20. Aftershocks from Northern Cal and Japan also follow power law decay

  21. 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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