Agnes Helmstetter

We estimate the rate of aftershocks triggered by a heterogeneous stress change, using the rate-and-state model of Dieterich [1994].We show that an exponential stress distribution Pt(au) ~exp(-tautau_0) gives an Omori law decay of aftershocks with time ~1/t^p, with an exponent p=1-A sigma_n/tau_0, where A is a parameter of the rate-and-state friction law, and \sigma_n the normal stress. Omori exponent p thus decreases if the stress "heterogeneity" tau_0 decreases. We also invert the stress distribution P(tau) from the seismicity rate R(t), assuming that the stress does not change with time. We apply this method to a synthetic stress map, using the (modified) scale invariant "k^2" slip model [Herrero and Bernard, 1994]. We generate synthetic aftershock catalogs from this stress change.The seismicity rate on the rupture area shows a huge increase at short times, even if the stress decreases on average. Aftershocks are clustered in the regions of low slip, but the spatial distribution is more diffuse than for a simple slip dislocation. Because the stress field is very heterogeneous, there are many patches of positive stress changes everywhere on the fault.This stochastic slip model gives a Gaussian stress distribution, but nevertheless produces an aftershock rate which is very close to Omori's law, with an effective p<=1, which increases slowly with time. We obtain a good estimation of the stress distribution for realistic catalogs, when we constrain the shape of the distribution. However, there are probably other factors which also affect the temporal decay of aftershocks with time. In particular, heterogeneity of A\sigma_n can also modify the parameters p and c of Omori's law. Finally, we show that stress shadows are very difficult to observe in a heterogeneous stress context.

We estimate the relative importance of small and large earthquakes for static stress changes and for earthquake triggering, assuming that earthquakes are triggered by static stress changes and that earthquakes are located on a fractal network of dimension D. This model predicts that both the number of events triggered by an earthquake of magnitude m and the stress change induced by this earthquake at the location of other earthquakes increase with m as ∼10^Dm/2. The stronger the spatial clustering, the larger the influence of small earthquakes on stress changes at the location of a future event as well as earthquake triggering. If earthquake magnitudes follow the Gutenberg‐Richter law with b > D/2, small earthquakes collectively dominate stress transfer and earthquake triggering because their greater frequency overcomes their smaller individual triggering potential. Using a southern California catalog, we observe that the rate of seismicity triggered by an earthquake of magnitude m increases with m as 10^αm, where α = 1.05 ± 0.05. We also find that the magnitude distribution of triggered earthquakes is independent of the triggering earthquake's magnitude m. When α ≈ b, small earthquakes are roughly as important to earthquake triggering as larger ones. We evaluate the fractal correlation dimension D of hypocenters using two relocated catalogs for southern California. The value of D measured for distances 0.1 < r < 5 km is D = 1.54 for the Shearer et al. catalog and D = 1.73 for the Hauksson et al. catalog. The value of D reflects both the structure of the fault network and the nature of earthquake interactions. By considering only those earthquake pairs with interevent times larger than 1000 days, we can largely remove the effects of short‐term clustering. Then D ≈ 2, close to the value D = 2α = 2.1 predicted by assuming that earthquake triggering is due to static stress. The value D ≈ 2b implies that small earthquakes are as important as larger ones for stress transfers between earthquakes and that considering stress changes induced by small earthquakes should improve models of earthquake interactions.

We estimate the relative importance of small and large earthquakes for static stress changes and for earthquake triggering, assuming that earthquakes are triggered by static stress changes and that earthquakes are located on a fractal network of dimension D. This model predicts that both the number of events triggered by an earthquake of magnitude m and the stress change induced by this earthquake at the location of other earthquakes increase with m as \~10^(Dm/2). The stronger the spatial clustering, the larger the influence of small earthquakes on stress changes at the location of a future event as well as earthquake triggering. If earthquake magnitudes follow the Gutenberg-Richter law with b>D/2, small earthquakes collectively dominate stress transfer and earthquake triggering, because their greater frequency overcomes their smaller individual triggering potential. Using a Southern-California catalog, we observe that the rate of seismicity triggered by an earthquake of magnitude m increases with m as 10^(alpha m), where alpha=1.00+-0.05. We also find that the magnitude distribution of triggered earthquakes is independent of the triggering earthquake magnitude m. When alpha=b, small earthquakes are roughly as important to earthquake triggering as larger ones. We evaluate the fractal correlation dimension of hypocenters D=2 using two relocated catalogs for Southern California, and removing the effect of short-term clustering. Thus D=2alpha as predicted by assuming that earthquake triggering is due to static stress. The value D=2 implies that small earthquakes are as important as larger ones for stress transfers between earthquakes.