Importance of small earthquakes for stress transfers and earthquake   triggering
  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. 
A. Helmstetter (UCLA), Y. Y. Kagan (UCLA), and D. D. Jackson (UCLA)