A frictional-viscous-mixing fault model and its implications for a single slow slip event rupture

Recent geological observations imply that slow slip events (SSEs) occur in fault zones with finite thickness of ~100s of meters. The bulk matrix of the fault zone deforms viscously, while pervasive frictional surfaces are distributed in the viscous matrix. In this theoretical study, we investigate the rupture behaviors of a frictional-viscous-mixing fault model and explore its potential to generate a single SSE. To simultaneously consider both the 10s-kilometer-scale rupture propagations and the 100s-meter-scale frictional-viscous features in the same model, we treat a fault zone as a zero-thickness surface embedded in an elastic medium. The frictional-viscous characteristics are parameterized into a constitutive relation, or friction law, where fault strength is partitioned into a frictional and a viscous component. For simplicity, the frictional strength is set to be slip weakening, while the viscous strength increases linearly as the bulk shear rate (slip rate) increases (Eq1 in Figure below). We explore the rupture behaviors of the above model both analytically and numerically. We find that: Final slip is proportional to the static stress drop and slipping area length, as in regular earthquakes (Eq2). Peak slip rate increases with dynamic frictional stress drop, while a high viscous coefficient can significantly reduce slip rate, leading to slow slip behaviors (Eq3). Rupture propagation speed is mainly controlled by the radiation damping factor and viscous coefficient, and can be significantly reduced compared to typical fast earthquakes when viscous coefficient is high. (Eq4). The slip rate decay time increases with the viscous coefficient and slipping area length (Eq5), which eventually predicts M~T^3 scaling. When frictional stress drop is ~1MPa and viscous coefficient is smaller than the radiation damping factor /(2), the above models predict fast slip behavior of regular earthquakes. Our model predicts slow slip behaviors in a wide range of parameter space when stress drop is low and viscous coefficient is high. In particular, a frictional strength drop of ~10 kPa and viscous coefficient of 10^4-10^5 /(2) can simultaneously explain many independent characteristic rupture parameters of SSEs. Our model can be further tested with future geophysical, geological and experimental data.