Numerical simulation of three-dimensional faulting processes with heterogeneous rate- and state-dependent friction

Abstract

Miyatake, T., 1992. Numerical simulation of three-dimensional faulting processes with heterogeneous rate- and state-dependent friction. In: T. Mikumo, K. Aki, M. Ohnaka, L.J. Ruff and P.K.P. Spudich (Editors), Earthquake Source Physics and Earthquake Precursors. Tectonophysics, 211: 223–232. Numerical simulations of three-dimensional faulting processes with heterogeneous rate- and state-dependent friction were carried out by using a multi-mass-spring model. The rate- and state-dependent friction law proposed by Dieterich ∗ ∗ Dieterich (1978) and later developed by Ruina ∗∗ ∗∗ Ruina (1983) has much capability to simulate a wide variety of source processes, e.g., precursory slip, post-seismic slip, co-seismic slip, creep events and earthquake cycles. Since the original equation is a stiff ordinary equation which has rapidly decaying solutions and is difficult to solve, we modified the equation so that numerical computation are made stable. This rate- and approximate state-dependent friction law is applied to a single-degree-of-freedom elastic system to compare its dynamical behaviours with those of the original friction law and found that our friction law was a good approximation of the original formula. Then we apply this modified friction law to a multi-mass-spring model to simulate a whole earthquake source process. In this paper, we studied mainly the effect of heterogeneity of frictional parameters. Three types of barriers, i.e., a strong barrier, a weak barrier and a relaxation barrier, can be simulated by certain frictional parameters. For each case, large mainshocks occurred repeatedly. In the case of a weak barrier, the barrier region slipped with some delay time during the mainshock, i.e., the occurrence of a multiple shock. In the case of a strong barrier, the barrier region was left unslipped during the mainshock. A small part of this barrier region slipped sequentially as small aftershocks, and eventually the entire barrier region slipped as the largest aftershock. A fault with a relaxation barrier was also left unslipped during the mainshock similarly to a strong barrier case, but a small part of the barrier slipped as creep events.