dorsal/arxiv
View SchemaErgodicity in Natural Earthquake Fault Networks
| Authors | K. F. Tiampo, J. B. Rundle, W. Klein, J. Holliday, J. S. Sa Martins, C. D. Ferguson |
|---|---|
| Categories | |
| ArXiv ID | physics/0604053 |
| URL | https://arxiv.org/abs/physics/0604053 |
| DOI | 10.1103/PhysRevE.75.066107 |
Abstract
Numerical simulations have shown that certain driven nonlinear systems can be characterized by mean-field statistical properties often associated with ergodic dynamics [C.D. Ferguson, W. Klein, and J.B. Rundle, Phys. Rev. E 60, 1359 (1999); D. Egolf, Science 287, 101 (2000)]. These driven mean-field threshold systems feature long-range interactions and can be treated as equilibrium-like systems with dynamics that are statistically stationary over long time intervals. Recently the equilibrium property of ergodicity was identified in an earthquake fault system, a natural driven threshold system, by means of the Thirumalai-Mountain (TM) fluctuation metric developed in the study of diffusive systems [K.F. Tiampo, J.B. Rundle, W. Klein, J.S. Sa Martins, and C. D. Ferguson, Phys. Rev. Lett. 91, 238501 (2003)]. In this work we analyze the seismicity of three naturally-occurring earthquake faults networks from a variety of tectonic settings in an attempt to investigate the range of applicability of effective ergodicity, using the TM metric and other, related statistics. Results suggest that, once variations in the catalog data resulting from technical and network issues are accounted for, all of these natural earthquake systems display stationary periods of metastable equilibrium and effective ergodicity that are disrupted by large events. We conclude that a constant rate of events is an important prerequisite for these periods of punctuated ergodicity, and that while the level of temporal variability in the spatial statistics is the controlling factor in the ergodic behavior of seismic networks, no single statistic is sufficient to ensure quantification of ergodicity. Specifically, we demonstrate that stationarity, while a necessary condition, is not sufficient to ensure ergodicity in fault systems.
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"abstract": "Numerical simulations have shown that certain driven nonlinear systems can be\ncharacterized by mean-field statistical properties often associated with\nergodic dynamics [C.D. Ferguson, W. Klein, and J.B. Rundle, Phys. Rev. E 60,\n1359 (1999); D. Egolf, Science 287, 101 (2000)]. These driven mean-field\nthreshold systems feature long-range interactions and can be treated as\nequilibrium-like systems with dynamics that are statistically stationary over\nlong time intervals. Recently the equilibrium property of ergodicity was\nidentified in an earthquake fault system, a natural driven threshold system, by\nmeans of the Thirumalai-Mountain (TM) fluctuation metric developed in the study\nof diffusive systems [K.F. Tiampo, J.B. Rundle, W. Klein, J.S. Sa Martins, and\nC. D. Ferguson, Phys. Rev. Lett. 91, 238501 (2003)]. In this work we analyze\nthe seismicity of three naturally-occurring earthquake faults networks from a\nvariety of tectonic settings in an attempt to investigate the range of\napplicability of effective ergodicity, using the TM metric and other, related\nstatistics. Results suggest that, once variations in the catalog data resulting\nfrom technical and network issues are accounted for, all of these natural\nearthquake systems display stationary periods of metastable equilibrium and\neffective ergodicity that are disrupted by large events. We conclude that a\nconstant rate of events is an important prerequisite for these periods of\npunctuated ergodicity, and that while the level of temporal variability in the\nspatial statistics is the controlling factor in the ergodic behavior of seismic\nnetworks, no single statistic is sufficient to ensure quantification of\nergodicity. Specifically, we demonstrate that stationarity, while a necessary\ncondition, is not sufficient to ensure ergodicity in fault systems.",
"arxiv_id": "physics/0604053",
"authors": [
"K. F. Tiampo",
"J. B. Rundle",
"W. Klein",
"J. Holliday",
"J. S. Sa Martins",
"C. D. Ferguson"
],
"categories": [
"physics.geo-ph",
"physics.comp-ph"
],
"doi": "10.1103/PhysRevE.75.066107",
"title": "Ergodicity in Natural Earthquake Fault Networks",
"url": "https://arxiv.org/abs/physics/0604053"
},
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