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 Mo 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 Mo 1021 Nm, 1 km for earthquakes with Mo 1018 Nm, and 100 m for earthquakes with Mo 1015 Nm, under the assumption that the breakdown stress drop Dtb 10 MPa. However, Lc depends on not only Dc but also Dtb, so that the scaling relation between Lc and Dc may be violated by Dtb, because Dtb potentially takes any value in a wide range from 1 to 102 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.