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

TL;DR

This paper models earthquake source processes considering interactions between thermal pressurization and dilatancy, revealing a phase transition with universal power-law behavior and a critical exponent of 1/2, independent of specific porosity laws.

Contribution

It introduces a novel phase transition framework in earthquake modeling, linking fluid pressure dynamics with universality and critical phenomena.

Findings

Identifies phase transition with power-law universality in earthquake slip dynamics.

Derives a universal critical exponent of 1/2, independent of porosity law details.

Suggests earthquake processes can be viewed as phase transitions with order parameters.

Abstract

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.