Earthquake source nucleation as self organization process

The theory of an earthquake source nucleation is discussed. Based on the assumption that self organization of damage process takes place in the zone of an earthquake source nucleation the theory incorporates the damage rheology framework of Lyakhovsky et al. and the approach of phenomenology theory of second-order phase transition. Namely, the free energy governing the process of an earthquake source nucleation depends on two collective variables α and φ in addition to the strain tensor εij. The variable α quantifies the fracture of the medium and the variable φ quantifies the interaction effect of cracks. The region ΩS is associated with a potential source of an earthquake if the damage variable α exceeds the critical value αcr(1) inside ΩS. The important feature of a potential source is that interaction of fractures causes acceleration of damage process inside the region of potential source and the material should lose stability primarily in this region. Interaction of fractures results also in occurrence of a residual stress caused by nonuniformity of fracture density. The appearance and development of the potential source result in increase of intensity of damage process not only in the region of potential source but also in a certain neighborhood of the last. It is compatible with such observed effects as acceleration of seismic energy release and growth of correlation length of weak seismicity before large earthquake. Transition of potential source to the stage of avalanche-unstable fracturing is associated with instability generated by explosive increase of interaction of fractures when the damage variable α exceeds the second critical value αcr(2) inside ΩS.