A physical scaling relation between the size of an earthquake and its nucleation zone size

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 frequency-magnitude 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 M-o, scales with the third power of the critical slip displacement D-c and the critical size 2L(c) (L-c, half-length) of the nucleation zone. This scaling relation quantitatively explains seismological data published, and it predicts that 2L, is of the order of 10 km for earthquakes with M-o = 10(21) Nm, 1 km for earthquakes with M-o = 10(18) Nm, and 10 km for earthquakes with M-o = 10(15) Nm, under the assumption that the breakdown stress drop Delta tau (b) = 10 MPa. However, L-c, depends on not only D-c, but also Delta tau (b), so that the scaling relation between L-c and D-c, may be violated by Delta tau (b) because Delta tau (b) potentially takes any value in a wide range from 1 to 10(2) 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.