Seismic Interevent Time: A Spatial Scaling and Multifractality |
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| Authors: | G Molchan T Kronrod |
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| Institution: | (1) International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Moscow;(2) The Abdus Salam International Center for Theoretical Physics, SAND Group, Trieste, Italy |
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| Abstract: | The optimal scaling problem for the time t(L × L) between two successive events in a seismogenic cell of size L is considered. The quantity t(L × 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). |
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| Keywords: | Recurrence time fractals statistical methods seismicity |
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