Abstract

A specific model of the earthquake nucleation that proceeds on a non-uniform fault is put forward to explain seismological data on the nucleation in terms of the underlying physics. The model is compatible with Gutenberg-Richter's similarity law for earthquake frequencymagnitude relation. A theoretical approach in the framework of fracture mechanics, based on a laboratory-based slip-dependent constitutive law, leads to the conclusion that the earthquake moment M0 scales with the third power of the critical slip displacement Dc and the critical size 2Lc (Lc, half-length) of the nucleation zone. This scaling relation quantitatively explains seismological data published, and it predicts that 2Lc is of the order of 10 km for earthquakes with M0 = 10 Nm, 1 km for earthquakes with M0 = 10 Nm, and 100 m for earthquakes with M0 = 10 Nm, under the assumption that the breakdown stress drop b = 10 MPa. However, Lc depends on not only Dc but also b, so that the scaling relation between Lc and Dc may be violated by b, because b potentially takes any value in a wide range from 1 to 10 MPa, depending on the seismogenic environment. The good agreement between the theoretical relation and observed results suggests that a large earthquake may result from the failure of a large patch of high rupture growth resistance, whereas a small earthquake may result from the breakdown of a small patch of high rupture growth resistance. The present result encourages one to pursue the prediction capability for large earthquakes.