Seismic interevent time: A spatial scaling and multifractality

The optimal scaling problem for the time t(L x L) between two successive events in a seismogenic cell of size L is considered. The quantity t(L x L) 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 Pure and Applied Geophysics 162 (2005), 1135 and GJI 162 (2005), 899).