Abstract
The EpidemicType Aftershock Sequence (ETAS) model is widely used to describe the occurrence of earthquakes in space and time, but there has been little discussion dedicated to the limits of, and influences on, its estimation. Among the possible influences we emphasize in this article the effect of the cutoff magnitude, M_{cut}, above which parameters are estimated; the finite length of earthquake catalogs; and missing data (e.g., during lively aftershock sequences). We analyze catalogs from southern California and Italy and find that some parameters vary as a function of M_{cut} due to changing sample size (which affects e.g. Omori’s c constant) or an intrinsic dependence on M_{cut} (as M_{cut} increases, absolute productivity and background rate decrease). We also explore the influence of another form of truncation—the finite catalog length—that can bias estimators of the branching ratio. Being also a function of Omori’s pvalue, the true branching ratio is underestimated by 45% to 5% for 1.05<p<1.2. Finite sample size affects the variation of the branching ratio estimates. Moreover, we investigate the effect of missing aftershocks and find that the ETAS productivity parameters (α and K_{0}) and the Omori’s c and pvalues are significantly changed for M_{cut}<3.5. We further find that conventional estimation errors for these parameters, inferred from simulations that do not account for aftershock incompleteness, are underestimated by, on average, a factor of eight.
Original language  English 

Pages (fromto)  449469 
Number of pages  21 
Journal  Journal of Geophysical Research: Solid Earth 
Volume  122 
Issue number  1 
Early online date  13 Jan 2017 
DOIs  
Publication status  Published  Jan 2017 
Keywords
 Statistical seismology
 ETAS
 ETAS parameter estimation
 Branching ratio
 Incomplete aftershocks
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Profiles

Dr Max Werner
 School of Earth Sciences  Associate Professor of Geophysics and Natural Hazards
 Geophysics
 Cabot Institute for the Environment
Person: Academic , Member