2005/12/29 by G. Molchan, Molchan, G., T. Kronrod +1
Physics and Astronomy · #FOS: Physical sciences #Geophysics (physics.geo-ph) #Other Condensed Matter (cond-mat.other) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.other #cond-mat.stat-mech #physics.geo-ph
paper · pdf · doi:10.48550/arxiv.physics/0512264
arxiv created 2006/01/11 · arxiv updated 2009/12/01
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).