The empirical Bath’s law is derived from the statistical
distribution in magnitude difference of pairs of earthquakes. It
is shown that earthquake correlations can be expressed by means
of the magnitude-difference distribution. We introduce a
distinction between dynamical correlations, which imply an
“earthquake interaction”, and purely statistical correlations,
generated by other, unknown, causes. The distribution of
dynamically correlated earthquakes is derived from the
statistical fluctuations of the accumulation time, by means of
the geometric-growth model of energy accumulation in the focal
region. The derivation of the Gutenberg-Richter statistical
distributions in energy and magnitude is presented, as resulting
from this model. It is shown that the most suitable framework for
understanding the origin of the Bath’s law is the extension of
the statistical distributions to pairs of earthquakes, where the
difference in magnitude is allowed to take negative values. The
seismic activity which accompanies a main shock, including both
the aftershocks and the foreshocks, can be viewed as fluctuations
in magnitude. The extension of the magnitude difference to
negative values leads to a vanishing mean value of the
fluctuations and to the standard deviation as a measure of these
fluctuations. It is suggested that the standard deviation of the
magnitude difference is the average difference in magnitude
between the main shock and its largest aftershock (foreshock),
thus providing an insight into the nature and the origin of the
Bath’s law. Time correlations of the accompanying seismic
activity are also presented.