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

Abstract

In response to Cocco and Bizzarri’s (2002) argument that “there is no need to assume that friction must become independent of slip rate at high speeds to resemble slip weakening”, I remarked in my previous paper (Ohnaka, 2004) that “this argument seems logically inconsistent, because the effect of high velocity cutoff has been incorporated into the equation used in their simulation.” The most recent comment by Bizzarri and Cocco (2006) represents their counterargument to this remark. The basis of their reasoning is that even if the +1 term was included in the argument of the logarithm in equations (1c) and (1d) described in the paper (Ohnaka, 2004), the traction dependence on slip rate would remain in the governing equation, because the state variable depends on the fault slip velocity (Bizzarri and Cocco, 2006). I feel the need to point out, however, that their counterargument still appears to be logically inconsistent. In their simulations of the dynamic rupture regime within the framework of the rateand state-dependent formulation, they used the equation from which the direct effect of high slip rates on the shear traction had been cut off, which they admit in their comment (Bizzarri and Cocco, 2006). In addition, they also used the equation from which the effect of slip rate on state evolution had been removed; it would seem they are unaware of this fact. The state variable has the dimensions of time and is interpreted to be the age of the load supporting contacts across the fault surface (see Dieterich and Kilgore, 1996). According to Dieterich and Kilgore (1996), the evolution of state at constant slip speed under constant effective normal stress is given by