Effects of shear heating, slip‐induced dilatancy and fluid flow on diversity of 1‐D dynamic earthquake slip

We theoretically study effects of thermal pressurization, slip‐induced dilatancy and fluid flow on slip evolution assuming 1‐D fault model. We generalize the analysis made in our former papers by introducing an upper limit for the inelastic porosity evolution. The expression for nondimensional parameter T a , which is related to the upper limit, is derived in the present paper. We find that the parameter T a together with two nondimensional parameters S u and S u ′ derived in our former papers completely determine the qualitative nature of system behavior once the initial condition is given. For example, changes in S u and T a generate two qualitatively different slip behaviors, both of which can be models for ordinary earthquake. The slip is accelerated with time after experiencing an initial deceleration in one of them, while the slip ceases after monotonic deceleration in the other. The initial slip deceleration observed in the former case may be interpreted as a dynamic event preceding the main shock in seismological observations. We mathematically derive the expression for the ranges of the nondimensional parameters in which the above two slip behaviors appear. Slow earthquakes are also modeled in the same framework, and nonzero values of the nondimensional parameter S u ′ together with relatively large values of S u and T a are found to contribute to the generation of such slow earthquakes. The mathematical framework constructed here can be applied to understanding of some other natural phenomena such as a kind of reaction‐diffusion system.