Self-organized first-order transition from foreshock to mainshock in earthquake sequences induced by heat, fluid pressure, and porosity

Earthquake cycles are studied by taking into account the interactions among slip, fluid pressure, temperature, and porosity on the fault planes, which are known to play a crucial role in earthquake dynamics. The spring-block model with a single block is employed. A first-order transition from foreshock to mainshock occurring spontaneously in earthquake sequences is discovered both analytically and numerically. This transition is induced by these interactions. It is shown that the function of the slip distance u, F(u), defined as the sum of the difference between the energies stored in the driving spring before and after the slippage, and the energy dissipated during the slippage, governs the transition. The equation, $$F(u)=0$$ F ( u ) = 0 , represents the energy balance before and after the slippage, and the solution $$u=u_f$$ u = u f describes the realized slip distance for each slippage event. The solutions discontinuously transition from small to large slippages in the sequence of earthquakes. This transition can be interpreted to be a self-organized first-order transition from small to large slippages. The former slippage is governed by pore generation, whereas the latter is governed by thermal pressurization. A phase diagram of the foreshocks and mainshocks, which is also considered a phase diagram of slow and fast earthquakes, is obtained. Graphical abstract