Topological origin of the Gutenberg-Richter law: Dynamic decoupling of fault cascades and energy dissipation
Abstract
The Gutenberg-Richter (G-R) law is seismology's most robust empirical regularity, yet a first-principles derivation of its slope-the b-value-has remained elusive. Here, we present an analytical theory based on a finite hierarchical fault network composed of velocity-weakening asperities separated by velocity-strengthening creeping zones. By coupling network topology with fracture mechanics, we derive a generalized closed-form expression of b-value,(b=3/(3+2γ)log10k/log10q), where k is the threshold branching ratio and q is the area amplification factor. Crucially, we reveal a dynamic decoupling between k and q governed by energy dissipation. The empirical universality of b=1 naturally emerges as the fault network self-organizes into a critical attractor (k=q) that maximizes two-dimensional spatial filling. Furthermore, grounded in Rate-and-State Friction rheology, we demonstrate that foreshock acceleration (inverse-Omori) and aftershock decay (Omori-Utsu) are dual manifestations of the similar hierarchical cascade. In the mean-field limit, these temporal exponents are decoupled from static fracture energy, revealing a profound orthogonality between time-dependent friction and static energy release. By unifying the G-R law, Bath's law, and the foreshock-aftershock asymmetry, this framework might provide a physics-based pathway for operational earthquake forecasting.
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BibTeX
@misc{chen2026topological,
title = {{Topological origin of the Gutenberg-Richter law: Dynamic decoupling of fault cascades and energy dissipation}},
author = {Bin Chen and Mingze Zhao and Puyu Cao},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02541},
eprint = {2611.02541},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02541},
}
RIS
TY - UNPB
TI - Topological origin of the Gutenberg-Richter law: Dynamic decoupling of fault cascades and energy dissipation
AU - Bin Chen
AU - Mingze Zhao
AU - Puyu Cao
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02541
UR - https://arxiv.org/abs/2611.02541
AB - The Gutenberg-Richter (G-R) law is seismology's most robust empirical regularity, yet a first-principles derivation of its slope-the b-value-has remained elusive. Here, we present an analytical theory based on a finite hierarchical fault network composed of velocity-weakening asperities separated by velocity-strengthening creeping zones. By coupling network topology with fracture mechanics, we derive a generalized closed-form expression of b-value,(b=3/(3+2γ)log_10k/log_10q), where k is the threshold branching ratio and q is the area amplification factor. Crucially, we reveal a dynamic decoupling between k and q governed by energy dissipation. The empirical universality of b=1 naturally emerges as the fault network self-organizes into a critical attractor (k=q) that maximizes two-dimensional spatial filling. Furthermore, grounded in Rate-and-State Friction rheology, we demonstrate that foreshock acceleration (inverse-Omori) and aftershock decay (Omori-Utsu) are dual manifestations of the similar hierarchical cascade. In the mean-field limit, these temporal exponents are decoupled from static fracture energy, revealing a profound orthogonality between time-dependent friction and static energy release. By unifying the G-R law, Bath's law, and the foreshock-aftershock asymmetry, this framework might provide a physics-based pathway for operational earthquake forecasting.
ER -