Apparent stress scaling for tectonic and induced seismicity: Model and observations

A macroscopic model of seismic sources provides a scaling relationship for the apparent stress, treated as a function of three independent parameters: seismic moment, rupture area size, and average slip acceleration. These parameters represent three different factors: kinematic, geometric and material. This relationship allows us to distinguish and explain the following statistical characteristics of the log apparent stress versus log seismic moment plot. The regional trends, represented by a series of 1/2 slope lines, are related to the averaged shape of slip velocity pulses, so they reflect kinematic characteristics of the rupture process. The global trend, represented by the 1/6 slope line, is expected to characterize sets of events of wide range of rupture area sizes and assumes dependence of rupture area size on total slip, so it is related to the rupture initiation, propagation and arrest conditions; therefore, it reflects earthquake rupture dynamics. Additional shiftings among the trend lines obtained for the smallest induced tremors, larger tectonic earthquakes, and slow tsunami earthquakes, reflect differences between the intact rock failure and the frictional slip failure, that is, between fracture energies of these different earthquake classes.