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A fractional approach to study the pure-temporal Epidemic Type Aftershock Sequence (ETAS) process for earthquakes modeling
journal contribution
posted on 2023-06-10, 06:19 authored by Lorenzo Cristofaro, Roberto Garra, Enrico Scalas, Ilaria SpassianiIn statistical seismology, the Epidemic Type Aftershocks Sequence (ETAS) model is a branching process used world-wide to forecast earthquake intensity rates and reproduce many statistical features observed in seismicity catalogs. In this paper, we describe a fractional differential equation that governs the earthquake intensity rate of the pure temporal ETAS model by using the Caputo fractional derivative and we solve it analytically. We highlight that the tools and special functions of fractional calculus simplify the classical methods employed to obtain the intensity rate and let us describe the change of solution decay for large times. We also apply and discuss the theoretical results to the Japanese catalog in the period 1965-2003.
History
Publication status
- Published
File Version
- Published version
Journal
Fractional Calculus and Applied AnalysisISSN
1311-0454Publisher
SpringerExternal DOI
Volume
26Page range
461-479Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Probability and Statistics Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes