Modeling Exact Frequency-Energy Distribution for Quakes by a Probabilistic Cellular Automaton

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.