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

Meier et al (JGR 2014) 1 – Stress contributions

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

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

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

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 Stable for addition 1 – Stress contributions

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

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

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

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)

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

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

M

M

M

M

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

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

Meier et al (JGR 2014) 1 – Stress contributions

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

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

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

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

Mainshock magnitude 2 – Probabilistic approach

B C A

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

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

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

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 ≤ m MS < 4 m AS ≥ 2 2 – Probabilistic approach

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

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

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

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

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

Observations: ~ r ± 0.35 Static stress model: ~ r ± 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

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

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

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

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

ETAS simulations 3 – Transient deformation 3 – Deformation transient

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

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

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

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