Apparent stress scaling and statistical trends

Statistical relations between different earthquake parameters, such as M0 (seismic moment), ES (seismic energy), τa (apparent stress), A (rupture area), g (average slip acceleration), are investigated. For this purpose, a kinematic earthquake model representing averaged earthquake rupture process is formulated. The model implies a scaling relationship for τa as a function of three other parameters, related to kinematic (M0), geometric (A) and material (g) source characteristics, which, according to the model, can change independently. This scaling relation is used to explain statistical trends that characterize different earthquake data sets (including micro-, small, moderate and large events) plotted in the log τa − log M0 space, and to determine the area in this space, where typical earthquakes occur. The scaling relationship is interpreted in terms of the apparent stress minimum (i.e., the most uniform among the possible earthquake rupture patterns). It is concluded that, although the apparent stress increases on an average with increasing seismic moment, small and large earthquakes are essentially similar.