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We introduce a Random Domino Automaton model to explain earthquake statistics, linking the Gutenberg-Richter and Omori laws to earthquake waiting times. This model successfully fits seismic data, accounting for localized seismic property variations.

Keywords:
earthquake statisticsmagnitude-frequency distributionmodelingmodeling Gutenberg-Richter lawprobabilistic cellular automatasolvable modelsstochastic processestoy model of earthquakes

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Area of Science:

  • Earthquake statistics
  • Complex systems modeling
  • Geophysics

Background:

  • The Gutenberg-Richter law and Omori law describe earthquake frequency-magnitude and decay rates, respectively.
  • Understanding the interrelation between these laws and earthquake waiting times requires a mechanistic model.
  • Probabilistic cellular automata offer a framework for modeling complex spatiotemporal phenomena like seismicity.

Purpose of the Study:

  • To develop a probabilistic cellular automaton model, the Random Domino Automaton, for earthquake statistics.
  • To provide a mechanistic explanation for the observed relationships between the Gutenberg-Richter law, Omori law, and earthquake waiting time distributions.
  • To solve the inverse problem for the model and apply it to real seismic data.

Main Methods:

  • Development of the Random Domino Automaton, a probabilistic cellular automaton.
  • Derivation of a general algebraic solution for the inverse problem of the model.
  • Application of the model and its inverse solution to seismic data from the Legnica-Głogów Copper District, Poland.

Main Results:

  • The Random Domino Automaton provides a mechanistic basis for the interrelation of key earthquake laws.
  • The algebraic solution to the inverse problem was successfully derived.
  • The model demonstrated adequacy when applied to seismic data, accurately reflecting localized seismic properties and deviations from the Gutenberg-Richter law.

Conclusions:

  • The Random Domino Automaton is a viable model for earthquake statistics.
  • The developed inverse problem solution allows for model calibration to site-specific seismic characteristics.
  • The study highlights the model's ability to capture deviations from the Gutenberg-Richter law due to localized seismic properties.