  We have numerically investigated statistical properties of the so-called
interoccurrence time or the waiting time, i.e., the time interval between
successive earthquakes, based on the two-dimensional (2-D) spring-block
(Burridge-Knopoff) model, selecting the velocity-weakening property as the
constitutive friction law. The statistical properties of frequency distribution
and the cumulative distribution of the interoccurrence time are discussed by
tuning the dynamical parameters, namely, a stiffness and frictional property of
a fault. We optimize these model parameters to reproduce the interoccurrence
time statistics in nature; the frequency and cumulative distribution can be
described by the power law and Zipf-Mandelbrot type power law, respectively. In
an optimal case, the b-value of the Gutenberg-Richter law and the ratio of wave
propagation velocity are in agreement with those derived from real earthquakes.
As the threshold of magnitude is increased, the interoccurrence time
distribution tends to follow an exponential distribution. Hence it is suggested
that a temporal sequence of earthquakes, aside from small-magnitude events, is
a Poisson process, which is observed in nature. We found that the
interoccurrence time statistics derived from the 2-D BK (original) model can
efficiently reproduce that of real earthquakes, so that the model can be
recognized as a realistic one in view of interoccurrence time statistics.
