Deterministic chaos in a simulated sequence of slip events on a single isolated asperity

Abstract

Numerical simulation of repeated occurrences of slip events on a fault patch (asperity) is used to interpret the mechanism of irregular sequences of slip events. The fault is uniformly shear loaded at a constant rate, and the frictional stress acting on the fault is assumed to obey a rate-and state-dependent friction (RSF) law. A circular patch with velocity-weakening frictional property is embedded in the fault, which apart from this has velocity-strengthening frictional property. The numerical simulations are conducted using various characteristic slip distances L of the RSF law. For small values of L seismic slip events (earthquakes) repeatedly occur at regular intervals. With increasing L, the recurrence of slip events becomes more complex. A period doubled slip pattern, where seismic and aseismic slip events alternately occur, multiperiodic patterns and aperiodic patterns occur. At the same time, slip tends to become aseismic with increasing L. The distributions of shear stress on the fault just before slip events are variable because of variation in the residual stress of the preceding slip event and the shear stress generated by aseismic sliding during interseismic periods. These variations in shear stress cause the complex sequence of slip events seen here. An iteration map of the recurrence intervals of slip events for an aperiodic sequence of slip events is expressed by a simple curve, indicating that the timing of an event is predictable from the previous time interval, and the sequence of slip events exhibits deterministic chaos. To help interpret these results for a sequence of slip events on a velocity-weakening patch embedded in a velocitystrengthening region, a numerical simulation is conducted of slip on a velocity-weakening patch enclosed by a permanently locked region. In this case, no complex recurrence of slip events is observed. When L is less than a critical value, seismic slip events repeatedly occur at a constant interval. Stable sliding occurs when L is larger than the critical value. This result indicates that the complex slip behaviour seen for a velocity-weakening patch embedded in a velocity-strengthening region is caused by the interaction between the velocity-weakening and velocity-strengthening regions. © The Author 2014. Published by Oxford University Press on behalf of The Royal Astronomical Society.