  Statistical properties of the one-dimensional spring-block (Burridge-Knopoff)
model of earthquakes obeying the rate and state dependent friction law are
studied by extensive computer simulations. The quantities computed include the
magnitude distribution, the rupture-length distribution, the mainshock
recurrence-time distribution, the seismic time correlations before and after
the mainshock, the mean slip amount, and the mean stress drop at the mainshock,
etc. Events of the model can be classified into two distinct categories. One
tends to be unilateral with its epicenter located at the rim of the rupture
zone of the preceding event, while the other tends to be bilateral with
enhanced "characteristic" features resembling the so-called "asperity". For
both types events, the distribution of the rupture length $L_r$ exhibits an
exponential behavior at larger sizes, $\approx \exp[-L_r/L_0]$ with a
characteristic "seismic correlation length" $L_0$. The mean slip as well as the
mean stress drop tends to be rupture-length independent for larger events. The
continuum limit of the model is examined, where the model is found to exhibit
pronounced characteristic features. In the continuum limit, the characteristic
rupture length $L_0$ is estimated to be $\sim $100 [km]. This means that, even
in a hypothetical homogenous infinite fault, events cannot be indefinitely
large in the exponential sense, the upper limit being of order $\sim 10^3$
kilometers. Implications to real seismicity are discussed.
