Implementation into earthquake sequence simulations of a rate-and state-dependent friction law incorporating pressure solution creep

Abstract

Pressure solution creep (PSC) is an important elementary process in rock friction at hightemperatures where solubilities of rock-forming minerals are significantly large. It significantlychanges the frictional resistance and enhances time-dependent strengthening. A recentmicrophysical model for PSC-involved friction of clay-quartz mixtures, which can explain atransition between dilatant and non-dilatant deformation (d-nd transition), was modified hereand implemented in dynamic earthquake sequence simulations. The original model resultedin essentially a kind of rate-and state-dependent friction (RSF) law, but assumed a constantfriction coefficient for clay resulting in zero instantaneous rate dependency in the dilatantregime. In this study, an instantaneous rate dependency for the clay friction coefficient wasintroduced, consistent with experiments, resulting in a friction law suitable for earthquakesequence simulations. In addition, a term for time-dependent strengthening due to PSC wasadded which makes the friction law logarithmically rate-weakening in the dilatant regime. Thewidth of the zone in which clasts overlap or, equivalently, the interface porosity involved inPSC plays a role as the state variable. Such a concrete physical meaning of the state variableis a great advantage in future modelling studies incorporating other physical processes suchas hydraulic effects. Earthquake sequence simulations with different pore pressure distributionsdemonstrated that excess pore pressure at depth causes deeper rupture propagation withsmaller slip per event and a shorter recurrence interval. The simulated ruptures were arresteda few kilometres below the point of pre-seismic peak stress at the d-nd transition and did notpropagate spontaneously into the region of pre-seismic non-dilatant deformation. PSC weakensthe fault against slow deformation and thus such a region cannot produce a dynamic stressdrop. Dynamic rupture propagation further down to brittle-plastic transition, evidenced bygeological observations, would require even smaller frictional resistance at coseismic slip rate,suggesting the importance of implementation of dynamic weakening activated at coseismicslip rates for more realistic simulation of earthquake sequences. The present models producedmuch smaller afterslip at deeper parts of arrested ruptures than those with logarithmic RSFlaws because of a more significant rate-strengthening effect due to linearly viscous PSC. Detailedinvestigation of afterslip would give a clue to understand the deformation mechanismwhich controls shear resistance of the fault in a region of arrest of earthquake ruptures.