Comment on “Earthquake cycles and physical modeling of the process leading up to a large earthquake”

The modeling of earthquake initiation and subsequent rupture propagation requires the use of a fault constitutive law controlling the traction evolution and the slip acceleration that yields a finite energy flux at the crack tip. The determination of the temporal evolution of dynamic traction during the propagation of an earthquake rupture has been the major task of many recent investigations. Ohnaka (2004) presented a detailed discussion in favor of a "rational" governing law for earthquake ruptures which is consistent with laboratory experiments and, according to the author, is based on the "physics of rock friction and fracture". He concluded that this constitutive law must be slip-dependent because the slip dependency is a "more fundamental property of the shear rupture than the ratedependency". Ohnaka (2004) also suggested that this slipdependent law model the whole seismic cycle (therefore including earthquake nucleation and long-term fault restrengthening) and considered the proposed law to be a governing relation unifying the different features of the earthquake failure process. In order to support the proposed slip-dependent law, Ohnaka (2004) presented a questionable comparison between the slip- and the rate- and state-dependent (referred to as RS hereafter) constitutive laws (see section 2 of that paper). As previously mentioned, his discussion focused on demonstrating that the slip dependency is more important than the rate dependency. The goal of the present paper is not to open a debate on the more appropriate constitutive law, neither to support RS friction in favor of slip-dependent laws. Instead, our aim is to provide an alternative interpretation of the slip dependency of shear traction as well as to discuss the reasons why RS friction laws yield a traction evolution consistent with slip-weakening (referred to as SW hereafter). Although we share a common goal with Ohnaka in our search for the best framework within which to define a unified constitutive law that models earthquake initiation, propagation and arrest, we think that the complexity and the diversity of real fault zone structures make this task difficult to accomplish. Our reasoning is explained in detail in the following discussion.