Power law distribution of seismic rates: theory and data analysis

A. Saichev and D. Sornette ()

The European Physical Journal B: Condensed Matter and Complex Systems, 2006, vol. 49, issue 3, 377-401

Abstract: We report an empirical determination of the probability density functions P data (r) (and its cumulative version) of the number r of earthquakes in finite space-time windows for the California catalog, over fixed spatial boxes 5 ×5 km 2 , 20 ×20 km 2 and 50 ×50 km 2 and time intervals $\tau =10,~100$ and 1000 days. The data can be represented by asymptotic power law tails together with several cross-overs. These observations are explained by a simple stochastic branching process previously studied by many authors, the ETAS (epidemic-type aftershock sequence) model which assumes that each earthquake can trigger other earthquakes (“aftershocks”). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. We develop the full theory in terms of generating functions for describing the space-time organization of earthquake sequences and develop several approximations to solve the equations. The calibration of the theory to the empirical observations shows that it is essential to augment the ETAS model by taking account of the pre-existing frozen heterogeneity of spontaneous earthquake sources. This seems natural in view of the complex multi-scale nature of fault networks, on which earthquakes nucleate. Our extended theory is able to account for the empirical observation but some discrepancies, especially for the shorter time windows, point to limits of both our theoretical approach and of the ETAS model. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Keywords: 64.60.Ak Renormalization-group, fractal, and percolation studies of phase transitions (see also 61.43.Hv Fractals; macroscopic aggregates), 02.50.Ey Stochastic processes, 91.30.Dk Seismicity (see also 91.45.gd–in geophysics appendix), (search for similar items in EconPapers)
Date: 2006
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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DOI: 10.1140/epjb/e2006-00075-3

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