1. 1 – Stress contributions 2 – Probabilistic approach 3 – Deformation transients Small earthquakes contribute as much as large earthquakes do to stress changes Extract the « influence » of small earthquakes directly from seismicity data Evaluate how anomalous a given seismicity pattern can be

2. Meier et al (JGR 2014) 1 – Stress contributions

3. Estimation of the contribution in static stress transfer from small (unresolved) sources with -1 ≤  ≤ 1, C constant r = hypocentral distances btw earthquakes M o = seismic moment r Source M o Receiver 1 – Stress contributions

4. Holtsmark (1919), Chandrasekhar (1943) Gravitational field at any given location, caused by a distribution of stars (with random masses) V g(r 1,M 1 ) R } For one star : 1 – Stress contributions

5. For normal (Gaussian) distributions : There exist other stable distributions, known as Lévy distributions, for which They have power-law decays in Stability of random distributions for addition

6. Holtsmark (1919), Chandrasekhar (1943) Gravitational field at any given location, caused by a distribution of stars (with random masses) V g(r 1,M 1 ) R For all stars : V = g 1 + g 2 +... Stable for addition 1 – Stress contributions

7. Holtsmark (1919), Chandrasekhar (1943) Gravitational field at any given location, caused by a distribution of stars (with random masses) V g(r 1,M 1 ) R } For all stars : 1 – Stress contributions

8. r = hypocentral distances btw earthquakes M o = seismic moment r Source M o Receiver 1 – Stress contributions Estimation of the contribution in static stress transfer from small (unresolved) sources with -1 ≤  ≤ 1, C constant

9. r = hypocentral distances btw earthquakes M o = seismic moment r Source M o Receiver } Stable for addition For one source: Kagan (Nonl. Proc. Geophys., 1994) 1 – Stress contributions

10. r = hypocentral distances btw earthquakes M o = seismic moment r Source M o Receiver } Stable for addition For all N(m) sources of magnitude m: 1 – Stress contributions N Marsan (GJI 2004)

11. } Stable for addition For all N(m) sources of magnitude m: Gutenberg-Richter : Kanamori : NB : far field approximation 1 – Stress contributions

12. Compute stress on a regular grid Largest earthquakes dominate D=3 1 – Stress contributions

13. M 7 6 5 4 3

14. M 7 6 5 4 3

15. M 7 6 5 4 3

16. M 7 6 5 4 3

18. Compute stress on hypocenters All earthquakes contribute D=2 1 – Stress contributions

19. Meier et al (JGR 2014) FM from Yang et al. (BSSA 2012) Hypocenters from Hauksson et al. (BSSA 2012) 1 – Stress contributions

20. Meier et al (JGR 2014) 1 – Stress contributions

21. Stress change at the hypocenters of future earthquakes : ALL magnitude bands contribute equally Uncertainty on stress change grows as cut-off magnitude decreases 1 – Stress contributions

22. probability that #i triggered #j Contribution from #i Sum of all contributions Probabilistic approach 2 – Probabilistic approach

23. Contribution from #i Distance from #i to x Time t-t i Magnitude m i Marsan and Lengliné (2008) Inversion from data by Expectation – Maximization 2 – Probabilistic approach

24. Shearer et al. (2005) catalogue N>70,000 earthquakes m ≥ 2 No decoupling between space and time Correction for lack of detection following large shocks Distances from fault to target hypocenter target main fault r 2 – Probabilistic approach

25. Mainshock magnitude 2 – Probabilistic approach

26. B C A

27. A B C A B C OROR ?????? C is an indirect aftershock of A 2 – Probabilistic approach

28. 0 – 5 km 5 – 20 km > 20 km Probability of being a direct aftershock of a M>7 earthquake 1% 1 week 3 months 60% 2 – Probabilistic approach

29. Probability of being a direct aftershock of a 3<M<4 earthquake 0 – 1 km 1 – 5 km 5 – 20 km 2 – Probabilistic approach

30. Marsan and Lengliné (JGR 2010) Direct AS Our method: Direct AS Modified from Felzer & Brodsky (2006): Background removed Linear density (1/km/day) Distance (km) 0 <  t < 15' 0.5 <  t < 1 day r -1.76 +- 0.35 3 ≤ m MS < 4 m AS ≥ 2 2 – Probabilistic approach

31. M = 3 earthquake (L = 400 m, u = 1 cm) 1 km 2 km km  CFF (bars) Q: can static stress triggering explain this distribution? 2 – Probabilistic approach

32. Rate-and-state friction Dieterich (JGR 1994) = # of direct aftershocks in time and distance 2 – Probabilistic approach

33. Rate-and-state friction Dieterich (JGR 1994) = # of direct aftershocks in time and distance 2 – Probabilistic approach Background rate – density at R 1 < r < R 2 ∝ # of background earthquakes at these distances

34. Background earthquakes Mainshock 3 ≤ m < 4 No clustering Clustering Euclidean volume (km 3 ) ~ r 1.65 2 – Probabilistic approach

35. r -2.4 r -2.2 t ~ 1 hour NOT RESOLVED 2 – Probabilistic approach

36. Observations: ~ r -1.76 ± 0.35 Static stress model: ~ r -2.30 ± 0.27 Mainshock m = 3 Aftershocks up to ~ 1 hour, at 1 < r < 30 km Mainshock m = 3 Aftershocks up to ~ 1 hour, at 1 < r < 30 km Given the uncertainties, we cannot reject triggering by static stress Given the uncertainties, we cannot reject triggering by static stress 2 – Probabilistic approach

37. 3 – Deformation transient Marsan et al. (GRL 2014) With precursory acceleration Without precursory acceleration

38. 3 – Transient deformation 3 – Deformation transient With precursory acceleration Without precursory acceleration

39. 3 – Transient deformation 3 – Deformation transient With precursory acceleration Without precursory acceleration

40. 3 – Transient deformation 3 – Deformation transient Extra aftershocks from extra foreshocks 

41. ETAS simulations 3 – Transient deformation 3 – Deformation transient

42. 3 – Transient deformation 3 – Deformation transient !!! POSTER by Thomas Reverso

43. 3 – Transient deformation 3 – Deformation transient !!! POSTER by Thomas Reverso

44. 3 – Transient deformation 3 – Deformation transient !!! POSTER by Thomas Reverso

45. Small earthquakes contribute significantly to the stress budget They add great spatial variability to stress changes caused by large sources They cannot be accounted for deterministically (lack of information, number) Probabilistic approach that can be parameterized given the observed seismicity Observation of anomalous activity reveals slow deformation transients Conclusions