Previous studies of earthquake nucleation on faults with rate- and state-dependent friction show that nucleation process initially consists of a characteristic phase of localization to a limiting dimension, followed in some cases by a late-stage nucleation-zone expansion. Processes controlling the nucleation zone dimension are of interest for understanding scaling of the minimum earthquake dimensions and scaling of premonitory processes associated with earthquake nucleation. We examine the relationships among stressing history (loading path), initial conditions, and scaling of nucleation dimensions. Recent studies show that late-stage expansion depends strongly on the ratio of the rate-state parameters a and b. Increasing a/b to the limiting value of 1 favors expansion. We further find that initial conditions of frictional state 0 and slip rate v strongly regulate the effect of a/b on nucleation-zone expansion. Significant nucleation-zone expansion is restricted to a narrow region around a critical point in the domain of initial conditions. The critical point marks a point of divergent paths of evolving slip rate and frictional state. Away from the critical point, nucleation-zone expansion decreases rapidly and becomes rather weak. We conclude that evolution of 0 and v in natural earthquake cycles generally follows paths that significantly restrict nucleation-zone expansion, even for relatively large a/b values. This finding suggests that premonitory signals generated by a fast-slipping nucleation zone immediately before earthquakes may be small and difficult to detect.
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