Dynamic seismic ruptures on melting fault zones

We present a physical model which describes the behavior of spontaneous earthquake ruptures dynamically propagating on a fault zone and which accounts for the presence of frictional melt produced by the sliding surfaces. First, we analytically derive the solution for the temperature evolution inside the melt layer, which generalizes previous approximations. Then we incorporate such a solution in a numerical code for the solution of the elasto–dynamic problem. When a melt layer is formed, the linear slip–weakening law (initially governing the fault and relying on the Coulomb friction) is no longer valid. Therefore we introduce on the fault a linearly viscous rheology, with a temperature–dependent dynamic viscosity. We explore through numerical simulations the resulting behavior of the traction evolution in the cohesive zone before and after the transition from Coulomb friction and viscous rheology. The predictions of our model are in general agreement with data field from exhumed faults. We also find that the fault, after undergoing the breakdown stress drop controlled by the slip–weakening constitutive equation, experiences a second traction drop controlled by the exponential weakening of fault resistance due to the viscous rheology. This further drop enhances the instability of fault, increasing the rupture speeds, the peaks in fault slip velocity and the fracture energy density