We present a model which predicts seismological complexity even with no complexity in geometry or heterogeneity in material properties. Fault slip is numerically modeled using a Dieterich-type rate and state variable friction law at the planar interface of two infinitely long massless elastic slabs. A constant velocity boundary condition is imposed a distance H from each interface. No geometrical, frictional, elastic, or remote loading variations are allowed in the direction parallel to the plane of the fault. In the numerical solution a periodic boundary condition is imposed, and the fault surface is divided into N subregions each of which is represented by a mathematical point. At these N points, all of which are mutually coupled by discretized two-dimensional elasticity solutions, the fricition law differential equations are numerically solved. The character of the solutions depends on model parameter values and initial conditions. Solutions are found that are periodic, quasi-periodic, or aperiodic in time; and that are spatially homogeneous for all time, nearly homogeneous except during fast slip events, or essentially inhomogeneous for all time.

For given parameter values the solutions have a qualitative character which is nearly independent of initial conditions. At any instant in time these solutions ultimately appear roughly as some super-position of those spatial sine waves which are unstable in a linearized calculation. When spatially complex, the solutions can simultaneously exhibit regions that have steady sliding, large slip rates, and local propagating creep events. Special initial conditions can generate other solutions such as steady propagating creep waves that span the whole fault. The variety of simulated slip motions and long-term patterns of slip predicted by this spatially homogeneous nonlinear dynamical model suggests a possible role for dynamics, and not just complex geological structure, as a generator of temporal and spatial complexity in seismic phenomena. ¿ American Geophysical Union 1989