We present analytic and numerical studies of rupture propagation in a one-dimensional model of an earthquake fault. In the case of a fault that is uniformly at its slipping threshold, the propagation speed is determined by a dynamic selection mechanism elsewhere identified as ‘‘marginal stability.’’ At any nonzero distance below threshold, however, a solvability principle appears to be applicable. We describe the way in which these two mechanisms turn out to be consistent with each other and comment upon the unusual role of the short-wavelength cutoff.

• Received 19 April 1991

DOI:https://doi.org/10.1103/PhysRevLett.67.1043