Dynamics of an expanding circular fault

Abstract

We study a plane circular model of a frictional fault using numerical methods. The model is dynamic since we specify the effective stress at the fault. In one model we assume that the fault appears instantaneously in the medium; in another, that the rupture nucleates at the center and that rupture proceeds at constant subsonic velocity until it suddenly stops. The total source slip is larger at the center and the rise time is also longer at the center of the fault. The dynamic slip overshoots the static slip by 15 to 35 per cent. As a consequence, the stress drop is larger than the effective stress and the apparent stress is less than one half the effective stress. The far-field radiation is discussed in detail. We distinguish three spectral regions. First, the usual constant low-frequency level. Second, an intermediate region controlled by the fault size and, finally, the high-frequency asymptote. The central region includes the corner frequency and is quite complicated. The corner frequency is shown to be inversely proportional to the width of the far-field displacement pulse which, in turn, is related to the time lag between the stopping phases. The average corner frequency of S waves v₀^s is related to the final source radius, a, by v₀^s = 0.21 β/α. The corner frequency of P waves is larger than v₀^s by an average factor of 1.5.