Stick-slip from heterogeneous Coulomb friction

Stick-slip on pre-existing faults has long been recognized as a source of shallow earthquakes, where  "stick" is the interseismic period of elastic strain accumulation and  "slip" is the earthquake. While stick-slip behavior has long been associated with velocity-dependent and time-dependent friction, the description has not adequately addressed position-dependent friction---an aspect that is relevant to spatially complex fault zones in nature. Here we state a frame-indifferent formulation of frictional contact between heterogeneous surfaces and introduce the notion that friction is a function of the states of the two surfaces in contact, each representing roughness and microstructural details of the surface. We show how the interaction between irregular surfaces results in heterogeneous Coulomb friction along the interface. We then conduct dynamic simulations of a spring-slider model and find that heterogeneity in Coulomb friction alone is capable of reproducing a wide range of complex fault slip behaviors, from fault creep and low frequency earthquakes to ordinary earthquakes and slow slip events. The different slip behaviors produced by our model occur at a spectrum with no sharp boundaries between them, which seem to agree with observations in various subduction zones. We also find that seismic moment-duration scaling span a broad continuum with upper bounds for fast and slow earthquakes adhering to cubic and linear relations, respectively. As a whole, our framework of position-dependent friction raises the prospect of alternative approaches to simulate earthquake dynamics in multidimensional models of geologic faults.