Earthquake slip distribution: A statistical model

The purpose of this paper is to interpret slip statistics in a framework of extended earthquake sources. We first discuss deformation pattern of the Earth's surface from earthquakes and suggest that continuum versus block motion controversy can be reconciled by a model of the fractal distribution of seismic sources. We consider earthquake slip statistical distributions as they can be inferred from seismic moment‐frequency relations and geometrical scaling for earthquakes. Using various assumptions on temporal earthquake occurrence, these distributions are synthesized to evaluate the accuracy of geologic fault slip determinations and to estimate uncertainties in long‐term earthquake patterns based on paleoseismic data. Because the seismic moment distribution is a power law (Pareto), a major part of the total seismic moment is released by major earthquakes, M ≥ 10 19.5 N m (moment magnitude m ≥ 7); for these large earthquakes the rupture is confined to the upper brittle crust layer. We review the various moment‐frequency and earthquake scaling relationships and apply them to infer the slip distribution at area‐ and site‐specific regions. Simulating the seismic moment and strain accumulation process demonstrates that some synthetics can be interpreted as examples of a quasiperiodic sequence. We demonstrate the application of the derived slip statistical relations by analyzing the slip distribution and history of the San Andreas fault at Wrightwood, California.