Effects of non-linear weakening on earthquake source scalings

Abstract

An earthquake is usually modeled as an extension of the Dugdale approach: as in LEFM, fracture energy G_c is completely spent in a relatively small region close to the crack tip, the process zone; and the fault strength is described by a slip weakening law that reaches a residual level at a characteristic slip D_c. Beyond its regularizing properties, slip weakening is a phenomenological fact of experimental rock mechanics. Recent laboratory observations show that slip weakening can be a persistent process over large amounts of slip, in contradiction to our usual view of a finite D_c. New seismological constraints from seismic nucleation phases and from the scaling of radiated energy with magnitude, seem to point to a similar interpretation. Persistent weakening can also be viewed as a lumped representation of off-fault non linear processes occurring in the wake of the process zone. On this basis, power law weakening laws have been proposed that feature a very steep weakening rate in the short slip range followed by a long tailed, non linear, weakening process with no characteristic slip. On the other hand there is growing interest in the apparent scaling of fault properties, such as D_c and G_c, with earthquake size. This is a key issue in understanding how much can be learned about large destructive earthquakes from the observation of smaller but more frequent ones and from laboratory experiments. I explore here the possible effects of non linear strength drop on macroscopic earthquake source parameters, such as magnitude, rupture size and radiated energy, and their interrelations mainly via numerical simulation of earthquake dynamics under a general family of empirical nonlinear slip weakening laws.