Theoretical modeling of slow slip in terms of dilatants strengthening and fluid flow

We have made theoretical modeling of slow slip, in which dilatants strengthening and fluid flow are two key factors.
I first mention some features of slow slip and tremor obtained by seismological and geodetic observations. I then review our simulation results for which fluid flow in the direction perpendicular to fault is assumed. Such fluid flow is widely assumed in theoretical and numerical studies. Our analysis was successful to simulate the slow fault growth and some other features associated with slow slip. However, the simulated backward propagating velocity of tremor is found to be much larger than observed seismologically. Our study shows that this occurs because the assumption of fluid flow perpendicular to fault. We show some simulation results in which the permeability anisotropy is taken into account. We assume, in the above studies, a fault in a homogeneous medium to study how nonlinear system dynamics gives rises to complex earthquake phenomena. However, some mechanical heterogeneity will certainly exist in reality. Finally, we shortly mention our recent simulation results in which mechanical heterogeneity and rheology of plate interface is considered.