EARTHQUAKE SIZE-FREQUENCY RELATIONS FROM AN ANALYTICAL STOCHASTIC RUPTURE MODEL

An analytical stochastic model of earthquake rupture is presented. Alt hough the general formulation makes no a priori self-similarity assump tion, scale independent earthquake size-frequency (ESF) statistics eme rge from the interaction between fault strength heterogeneity and rupt ure mechanics. The model also gives theoretical derivations for scale dependent ESF statistics, including gradual frequency saturation for s mall earthquakes, and a continuum of possible transitions in the stati stics of large earthquakes. A model fault is characterized as a surfac e composed of a large number of asperities, defined as small discrete contact surfaces of finite strength. An earthquake rupture grows via s uccessive asperity-breaking subevents. The probability of rupture to a certain size earthquake or greater is the total product of incrementa l rupture growth probabilities. These are governed by a new asperity f ailure probability distribution, derived as a mixture of Weibull distr ibutions. By including fracture mechanics, the resulting mixture distr ibution, characterized by the scale and shape parameters Lambda and Ga mma, is written in terms of the rupture size. The important difference between the mixture distribution and the Weibull distribution is that the mixture results in power law ESF statistics. Self-similarity occu rs when material heterogeneity and rupture mechanics are mutually ''tu ned'' to give Lambda=Gamma=1. Frequency saturation for small earthquak es is shown to be a simple consequence of a general aseismic nucleatio n process. The nucleation magnitude m(nu) defines the roll-off point i n ESF statistics that occurs when the area of seismic rupture equals t he area of precursory, aseismic rupture growth. By fitting the model t o the Parkfield earthquake data set, m(nu)=0.9 is obtained. The change in ESF scaling for the transition from moderate to large earthquakes depends on the changes in stress at the growing rupture front. The Nor thern California Earthquake Data Center seismicity data set is fitted for a transition at magnitude m similar or equal to 5 with Lambda'=0.4 and Gamma'=0.75. This result indicates that the change in the ESF rel ation associated with the transition from moderate to large earthquake s in California and Nevada is caused by surface rupture accompanied by partial width and slip saturation.