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