A proxy implementation of thermal pressurization for earthquake cycle modelling on rate-and-state faults

The reduction of effective normal stress during earthquake slip due to thermal pressurization of fault zone pore fluids is a significant fault weakening mechanism. Explicit incorporation of this process into frictional fault models involves solving the diffusion equations for fluid pressure and temperature outside the fault at each time step, which significantly increases the computational complexity. Here, we propose a proxy for thermal pressurization implemented through a modification of the rate-and-state friction law. This approach is designed to emulate the fault weakening and the relationship between breakdown energy and slip resulting from thermal pressurization and is appropriate for fully dynamic simulations of multiple earthquake cycles. It preserves the computational efficiency of conventional rate-and-state friction models, which in turn can enable systematic studies to advance our understanding of the effects of fault weakening on earthquake mechanics. In 2.5-D simulations of pulse-like ruptures on faults with finite seismogenic width, based on our thermal pressurization proxy, we find that the spatial distribution of slip velocity near the rupture front is consistent with the conventional square-root singularity, despite continued slip-weakening within the pulse, once the rupture has propagated a distance larger than the rupture width. An unconventional singularity appears only at shorter rupture distances. We further derive and verify numerically a theoretical estimate of the breakdown energy dissipated by our implementation of thermal pressurization. These results support the use of fracture mechanics theory to understand the propagation and arrest of very large earthquakes.