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Vere-Jones' self-similar branching model
1Mathematical Department, Nizhny Novgorod State University, Gagarin prosp. 23, Nizhny Novgorod, 603950, Russia.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2005
Summary
This study introduces a new branching process model for earthquake statistics, simplifying triggered seismicity by removing magnitude cutoffs. The model predicts observable aftershock distributions compatible with real seismic data.
Area of Science:
- Statistical Seismology
- Branching Processes
- Point-Process Theory
Background:
- Existing earthquake models (ETAS) require minimum/maximum magnitude cutoffs, posing theoretical challenges.
- Branching processes offer a framework for modeling triggered seismicity.
Purpose of the Study:
- To investigate the exactly self-similar branching process by Vere-Jones for earthquake statistics.
- To extend the ETAS model by removing magnitude cutoffs and analyze its properties.
Main Methods:
- Analysis of a two-branched magnitude distribution for first-generation daughters.
- Investigation of subcritical, critical, and supercritical regimes.
- Examination of an extended model interpolating between different processes.
Main Results:
- The model predicts a two-branched distribution for triggered event magnitudes across all generations.
- A renormalization of the exponent 'd' to 'h' is observed due to event hierarchies.
- Overall catalog magnitude distributions may appear single-branched, masking triggered event details.
Conclusions:
- The exactly self-similar Vere-Jones model offers a viable alternative to ETAS, avoiding magnitude cutoff issues.
- The predicted two-branched aftershock magnitude distribution is potentially testable with advanced reconstruction methods.
- The model's predictions are compatible with observed seismic catalog data.