Emergence and seismological implications of phase transition and universality in a system with interaction between thermal pressurization and dilatancy

摘要

A dynamic earthquake source process is modeled by assuming interaction amongfrictional heat, fluid pressure, and inelastic porosity. In particular, fluidpressure increase due to frictional heating (thermal pressurization effect) andfluid pressure decrease due to inelastic porosity increase (dilatancy effect)play important roles in this process. Two nullclines become exactly the same inthe system of governing equations, which generates non-isolated fixed points inthe phase space. These lead to a type of phase transition, which produces auniversality described by the power law between the initial value of onevariable and the final value of the other variable. The universal criticalexponent is found to be 1/2, which is independent of the details of theporosity evolution law. We can regard the dynamic earthquake slip process as aphase transition by considering the final porosity or slip as the orderparameter. Physical prediction of phase emergence is difficult because theporosity evolution law has uncertainties, and the final slip amount isdifficult to predict because of the universality. Finally, nonlinearmathematical application of the result is also discussed.