  Spatiotemporal correlations of the one-dimensional spring-block
(Burridge-Knopoff) model of earthquakes, either with or without the viscosity
term, are studied by means of numerical computer simulations. The continuum
limit of the model is examined by systematically investigating the model
properties with varying the block-size parameter a toward a\to 0. The Kelvin
viscosity term is introduced so that the model dynamics possesses a sensible
continuum limit. In the presence of the viscosity term, many of the properties
of the original discrete BK model are kept qualitatively unchanged even in the
continuum limit, although the size of minimum earthquake gets smaller as a gets
smaller. One notable exception is the existence/non-existence of the
doughnut-like quiescence prior to the mainshock. Although large events of the
original discrete BK model accompany seismic acceleration together with a
doughnut-like quiescence just before the mainshock, the spatial range of the
doughnut-like quiescence becomes narrower as a gets smaller, and in the
continuum limit, the doughnut-like quiescence might vanish altogether. The
doughnut-like quiescence observed in the discrete BK model is then a phenomenon
closely related to the short-length cut-off scale of the model.
