NUMERICAL-MODEL OF SEISMIC RUPTURE

Simple numerical models of the cellular automaton type have been proposed recently, as an analogy for seismic faults. Those showed interesting features of spontaneous rupture evolution (Lomnitz-Adler and Lemus-Diaz, 1989) or even seismic recurrence (Bak and Tang, 1989). It is possible to incorporate realistic rheology and tensorial physics into this kind of model, to extend it to a portion of crust instead of a single fault-plane and to simulate its time evolution. A numerical model based on physics of continuum media, instead of acellular automaton, can simulate dynamic rupture in two dimensions. The medium can be submitted to increasing load which is introduced by an imposed displacement at the boundaries, space and time being discretized by a finite difference scheme. The equation of dynamics is used at each time step. A rupture criterion allows each node in the grid of the medium to fail if a threshold is reached. The brittle threshold is allowed to fluctuate from point to point in the medium according to a chosen distribution. Failure is represented by a loss of shear stiffness in the rock element concerned. Hence we distinguish two states in our medium (the unbroken, viscoelastic rheology allowing for a slight attenuation and the broken state, similar to a viscous fluid) the viscosity allows introduction of a kind of dynamic friction at the broken point. When failure takes place at a point, elastic stress is then locally released and radiates, sometimes causing rupture of neighbor points and localization of fracture along fissures or faults. This gives realistic synthetic seismograms and source slip history.