Tectonic tremor as friction-induced inertial vibration

Slow slip events are often accompanied by tremor but how tremor is generated is yet elusive. In this study, we test the possibility that it is an inertial vibration. In the case of a single-degree-of-freedom spring and slider system with mass per unit area M, governed by rate-and-state friction with effective normal stress σ′, excitation of inertial vibrations emerges when normal stress (σ′) is low, and loading rate (V_l) is high. Accordingly, tremor can be excited in a low effective normal stress (σ′) zone, for example, in a zone of high pore pressure, when the loading rate (V_l) is temporally increased, as can happen during a slow slip event. A high loading rate helps to sustain the vibration, but a long-lasting attenuating tremor can still be excited even with a moderate velocity perturbation as long as the normal stress is sufficiently small. We use numerical simulations to verify that this hypothesis holds for a one-dimensional fault. The dominant frequency of the tremor is close to the fundamental frequency of resonance of the frictionless shear crack at a low sliding rate. Higher frequency modes are excited at higher sliding velocity. We show simulations of spontaneous slow slip events associated with tremor radiated from inertial vibration of a fault patch with locally low effective normal stress. This model provides a possible explanation for tectonic tremor associated with slow slip events.