Correlated Avalanche-Burst Invasion Percolation: Multifractal Origins of a Characteristic Self-Organized Critical System

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Main Authors: Ortez, Ronaldo A., Rundle, John B.
Format: Preprint
Published: 2023
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author Ortez, Ronaldo A.
Rundle, John B.
author_facet Ortez, Ronaldo A.
Rundle, John B.
contents We extend our previous model, avalanche-burst invasion percolation (AIP) by introducing long-range correlations between sites described by fractional Brownian statistics. In our previous models with independent, random site strengths, we reproduced a unique set of power-laws consistent with some of the b-values observed during induced seismicity. We expand upon this model to produce a family of critical exponents which could be characterized by the local long-range correlations inherent to host sediment. Further, in previous correlated invasion percolation studies, fractal behavior was found in only a subset of the range of Hurst exponent, $H$. We find fractal behavior persists for the entire range of Hurst exponent. Additionally, we show how multiple cluster scaling power laws results from changing the generalized Hurst parameter controlling long-range site correlations, and gives rise to a multifractal system. This emergent multifractal behavior plays a central role in allowing us to extend our model to better account for variations in the observed Gutenber-Richter b-values of induced seismicity.
format Preprint
id arxiv_https___arxiv_org_abs_2303_10272
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Correlated Avalanche-Burst Invasion Percolation: Multifractal Origins of a Characteristic Self-Organized Critical System
Ortez, Ronaldo A.
Rundle, John B.
Adaptation and Self-Organizing Systems
Statistical Mechanics
We extend our previous model, avalanche-burst invasion percolation (AIP) by introducing long-range correlations between sites described by fractional Brownian statistics. In our previous models with independent, random site strengths, we reproduced a unique set of power-laws consistent with some of the b-values observed during induced seismicity. We expand upon this model to produce a family of critical exponents which could be characterized by the local long-range correlations inherent to host sediment. Further, in previous correlated invasion percolation studies, fractal behavior was found in only a subset of the range of Hurst exponent, $H$. We find fractal behavior persists for the entire range of Hurst exponent. Additionally, we show how multiple cluster scaling power laws results from changing the generalized Hurst parameter controlling long-range site correlations, and gives rise to a multifractal system. This emergent multifractal behavior plays a central role in allowing us to extend our model to better account for variations in the observed Gutenber-Richter b-values of induced seismicity.
title Correlated Avalanche-Burst Invasion Percolation: Multifractal Origins of a Characteristic Self-Organized Critical System
topic Adaptation and Self-Organizing Systems
Statistical Mechanics
url https://arxiv.org/abs/2303.10272