1. 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

2. Outline Methods Observations Robustness of observations Physical Implications

3. 1. Methods

4. 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

5. 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

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. 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

13. 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)

14. 4) Physical Implications

15. 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

16. 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

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 probability of 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