  The optimal scaling problem for the time t(LxL) between two successive events
in a seismogenic cell of size L is considered. The quantity t(LxL) is defined
for a random cell of a grid covering a seismic region G. We solve that problem
in terms of a multifractal characteristic of epicenters in G known as the
tau-function or generalized fractal dimensions; the solution depends on the
type of cell randomization. Our theoretical deductions are corroborated by
California seismicity with magnitude M>2. In other words, the population of
waiting time distributions for L = 10-100 km provides positive information on
the multifractal nature of seismicity, which impedes the population to be
converted into a unified law by scaling. This study is a follow-up of our
analysis of power/unified laws for seismicity (see PAGEOPH 162 (2005), 1135 and
GJI 162 (2005), 899).
