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Constrained Invasion Percolation Model: Growth via Leath Bursts and the Origin of Seismic b-Value
John B Rundle1,2,3, Ronaldo Ortez1, Joachim Kønigslieb1
1Department of Physics, One Shields Avenue, University of California, Davis, California 95616, USA.
Physical Review Letters
|February 29, 2020
Summary
We introduce a new network growth model, the constrained Leath invasion percolation model, which explains earthquake frequency-magnitude scaling. This model captures burst dynamics seen in various complex systems.
Area of Science:
- Network science
- Statistical physics
- Geophysics
Background:
- Complex systems often exhibit burst dynamics.
- Understanding network growth is crucial for modeling emergent phenomena.
- Earthquake frequency-magnitude distributions follow specific scaling laws.
Purpose of the Study:
- To introduce and analyze the constrained Leath invasion percolation model.
- To investigate cluster dynamics and burst phenomena within this new model.
- To determine if the model can reproduce observed earthquake frequency-magnitude scaling.
Main Methods:
- Analysis of a constrained Leath invasion percolation model for network growth.
- Characterization of cluster dynamics in terms of spatial and temporal bursts.
- Mathematical analysis in the limit of critical bond percolation probability in two dimensions (d=2).
Main Results:
- The model exhibits significant bursts in cluster dynamics across space and time.
- Quantitative reproduction of earthquake frequency-magnitude scaling was achieved.
- The scaling is observed as the occupation probability approaches the critical bond percolation threshold in d=2.
Conclusions:
- The constrained Leath invasion percolation model successfully captures burst dynamics.
- The model provides a framework for understanding earthquake frequency-magnitude scaling.
- This model has potential applications in other systems exhibiting similar burst behaviors.
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