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A fractional approach to study the pure-temporal Epidemic Type Aftershock Sequence (ETAS) process for earthquakes modeling

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posted on 2023-06-10, 06:19 authored by Lorenzo Cristofaro, Roberto Garra, Enrico ScalasEnrico Scalas, Ilaria Spassiani
In 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 Analysis

ISSN

1311-0454

Publisher

Springer

Volume

26

Page range

461-479

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Probability and Statistics Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2023-02-24

First Open Access (FOA) Date

2023-03-23

First Compliant Deposit (FCD) Date

2023-02-23

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