A Physical Scaling Relation Between the Size of an Earthquake and its Nucleation Zone Size

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 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 _c is of the order of 10 km for earthquakes with M _o = 10²¹ Nm, 1 km for earthquakes with M _o = 10¹⁸ Nm, and 100 m for earthquakes with M _o = 10¹⁵ 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 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.