Energy structures and nucleation effects in earthquakes

We will propose a new model of earthquakes by taking into account three basic processes; the accumulation of strains, the propagation of ruptures and the recovering process of crustʹs rigidity, where the nucleation length is proportional to the rupture size and the energy distribution obeys the inverse power law. There are four important parameters in our model; the maximum rigidity of the crust S1, the minimum rigidity of the crust S0, the characteristic recovery time of the rigidity τ and the ratio of the rupture size to the nucleation length δ. There appear sharp transitions between the propagating earthquakes and the non-propagating ones. The stable exponent depends on the maximum value of the rigidity S1 and the ratio δ. The effects of some characteristic parameters will be studied in detail, and the results will be discussed in, comparison with the data of earthquakes.