Correlated Avalanche-Burst Invasion Percolation: Multifractal Origins of a Characteristic Self-Organized Critical System
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917574937149440 |
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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 |
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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 |