A Fractional Model for Earthquakes
arXiv:2403.00142 · doi:10.1093/jrsssc/qlae031
Abstract
This paper extends the existing fractional Hawkes process to better model mainshock-aftershock sequences of earthquakes. The fractional Hawkes process is a self-exciting point process model with temporal decay kernel being a Mittag-Leffler function. A maximum likelihood estimation scheme is developed and its consistency is checked. It is then compared to the ETAS model on three earthquake sequences in Southern California. The fractional Hawkes process performs favourably against the ETAS model. Additionally, two parameters in the fractional Hawkes process may have a fixed geophysical meaning dependent on the study zone and the stage of the seismic cycle the zone is in.
arXiv comment16 pages, 7 figure, submitted to the Journal of the Royal Statistical Society Series C
References in corpus (7)
- Numerical evaluation of two and three parameter Mittag-Leffler functions
- Importance of small earthquakes for stress transfers and earthquake triggering
- Is Earthquake Triggering Driven by Small Earthquakes?
- Nonstationary ETAS models for nonstandard earthquakes
- Residual analysis methods for space--time point processes with applications to earthquake forecast models in California
- Scaling Laws in Earthquake Memory for Interevent Times and Distances
- A fractional Hawkes process II: Further characterization of the process