INTRINSIC-PROPERTIES OF A BURRIDGE-KNOPOFF MODEL OF
AN EARTHQUAKE FAULT
CARLSON JM, LANGER JS, SHAW BE, TANG C
PHYSICAL REVIEW A
44: (2) 884-897 JUL 15 1991
Abstract:
We present a detailed numerical study of certain fundamental
aspects of a one-dimensional homogeneous, deterministic Burridge-Knopoff
model. The model is described by a massive wave equation, in which the
key nonlinearity is associated with the stick-slip velocity-weakening friction
force at the interface between tectonic plates. In this paper, we present
results for the statistical distribution of slipping events in the limit
of a very long fault and infinitesimally slow driving rates. Typically,
we find that the magnitude distribution of smaller events is consistent
with the Gutenberg-Richter law, while the larger events occur in excess
of this distribution. The crossover from smaller to larger events is identified
with a correlation length describing the transition from localized to delocalized
events. We also find that there is a sharp upper cutoff describing the
maximum large event. We identify how the correlation length and this upper
cutoff scale with the parameters in the model. We find that both are independent
of system size, while both do depend on the spatial discretization. In
addition to the magnitude distribution, we present a series of measurements
of other seismologically relevant quantities, including the event duration,
the size of the rupture zone, and the energy release, and discuss the relationship
between our measurements and the corresponding empirical laws in seismology.