Thermal runaway as driving mechanism of deep earthquakes – Constraints from numerical modeling

Deep-focus earthquakes occur at depths of 300-700 km below the surface where brittle failure is unlikely due to the large lithostatic pressure. Instead, they require a ductile localization mechanism that can significantly reduce rock strength and create highly localized shear zones. The feedback loop of shear heating, temperature-dependent viscosity and localization is called thermal runaway and has been linked to deep-focus earthquakes. We present one- and two-dimensional (1D and 2D) numerical, thermomechanical models that investigate the occurrence, nucleation and temporal evolution of thermal runaway in a simple shear setting. The models are characterized by a visco-elastic rheology where viscous creep is accommodated with a composite rheology of diffusion and dislocation creep as well as low-temperature plasticity. We utilize the pseudo-transient iterative method in combination with a viscosity regularization and adaptive time stepping to solve this nonlinear system of equations and avoid resolution dependencies. Varying eight input parameters, we observe two distinct types of behavior. After elastic loading, models either release stress over hundreds to thousands of years, accompanied by low slip velocities and moderate temperature increase, or they release stress within seconds to minutes while slip velocity and temperature increase drastically – Thermal runaway occurs. With nondimensional scaling analysis, we unite the eight different input parameters into two nondimensional numbers that allow inferring the behavior. The ratio tr/td describes the competition between heat generation by viscous dissipation and heat loss due to thermal diffusion whereas the ratio Uel/Uth compares the elastic and thermal energy density before stress relaxation. 2D experiments show that thermal runaway allows highly localized ductile ruptures to nucleate at small heterogeneities and propagate like brittle fractures. The ruptures accelerate during propagation and reach the highest velocities when two tips link up. Rupture trajectories are usually parallel to the direction of background deformation but bend in the vicinity of other ruptures to allow for a link up. The results demonstrate that thermal runaway can create highly localized, propagating shear zones that reach slip velocities in line with slow earthquakes at upper mantle and transition zone conditions.