Quasi-static fault slip on an interface between poroelastic media with different hydraulic diffusivity: A generation mechanism of afterslip

We theoretically study the generation mechanism of afterslip, assuming a two-dimensional in-plane fault on a bimaterial interface that separates poroelastic half-spaces with different hydraulic diffusivities; the deformation is assumed to be quasi-static. Our study shows that the coseismic faulting triggers quasi-static fault tip growth effectively because of positive feedback between the evolving fault slip and fluid pressure buildup. A similar study was made by Yamashita (2007), but he assumed the difference to be only in the Biot-Willis coefficient and undrained and drained Poisson's ratios. A comparison with the model of Yamashita (2007) shows that the diffusivity contrast is much more effective for the generation of afterslip. We also find that the fault tip is likely to extend unilaterally in the direction of slip in the medium of higher diffusivity; the duration of fault growth is longer for a larger diffusivity contrast. We find a scaling relationship in which the moment released by the quasi-static fault extension is approximated well by a linear function of the duration of fault growth. This is largely different from the expectations from a 2-D classical dynamic fault model; the moment is proportional to the square of duration of fault growth if the classical fault model is assumed.