Slip-dependent friction law and nucleation processes in earthquake rupture

Matsu'ura, M., Kataoka, H. and Shibazaki, B., 1992. Slip-dependent friction law and nucleation processes in earthquake rupture. In: T. Mikumo, K. Aki, M. Ohnaka, L.J. Ruff and P.K.P. Spudich (Editors), Earthquake Source Physics and Earthquake Precursors. Tectonophysics, 211: 135–148. We developed a physical model that interprets slip-strengthening and slip-weakening processes in brittle shear fracture by considering the microscopic interaction between statistically self-similar fault surfaces. Our model successfully describes general features of the constitutive behaviour observed in laboratory experiments of stick-slip. With the progress of fault slip, frictional stress first increases rapidly up to a peak value, and then decreases gradually to a constant level. The first slip-strengthening process can be explained by the increase of frictional resistance in transition from the in-phase contact to the random-phase contact of fault surfaces. The latter slip-weakening process can be explained by the decrease of frictional resistance due to the abrasion of surface asperities. The trade-off between these two processes determines the peak stress and the critical displacement over which the slip-weakening proceeds. We examined the nucleation process proceeding in a seismogenic zone with the increase of external shear stress through numerical simulations. In our model the seismogenic zone is represented by a broad weak zone with a locally strong part (asperity) on a fault plane. The basic equations governing the nucleation process are the equation of equilibrium and the constitutive relation between frictional stress and fault slip. We obtained the following results. The nucleation process first proceeds quasi-statically at the weak portions with the increase of external shear stress. Then, if the constitutive relation at the asperity has a high and narrow peak of stress, brittle dynamic rupture occurs in a limited area around the asperity. When the constitutive relation has a low and broad peak, the dynamic rupture of the asperity does not occur. The process is completely aseismic. When the peak of stress is high and broad, the dynamic rupture of the asperity leads to the catastrophic rupture which extends over the whole region. From these results it is concluded that diversity in the nucleation process can be ascribed to difference in the variation of constitutive behaviour along the fault.