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Fractals, chaos, self‐organized criticality and tectonics
Author(s) -
Turcotte Donald L.
Publication year - 1992
Publication title -
terra nova
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.353
H-Index - 89
eISSN - 1365-3121
pISSN - 0954-4879
DOI - 10.1111/j.1365-3121.1992.tb00444.x
Subject(s) - fractal , geology , statistical physics , scale invariance , tectonics , criticality , induced seismicity , slider , multifractal system , simple (philosophy) , fractal analysis , mathematics , fractal dimension , statistics , seismology , physics , mathematical analysis , engineering , mechanical engineering , philosophy , epistemology , nuclear physics
Some geological structures have simple geometrical forms and can be analysed using deterministic equations. Examples include alluvial fans and many sedimentary basins. But most geological structures are complex and appear to defy mathematical analyses. Yet in the complexity there is an order. Complex geological structures generally obey fractal statistics. Examples include topography, distributions of earthquakes and faults, and mineral deposits. An unresolved question is whether the fractal order is simply the result of scale invariance or the result of governing equations that yield deterministic chaos. In order to try to answer this question a variety of slider‐block models have been considered. The stick‐slip behaviour of slider‐block models is a simple analogy to earthquakes. A pair of slider‐blocks has been shown to behave chaotically. Models that use many slider‐blocks exhibit self‐organized criticality and generate fractal statistics similar to the statistics of regional seismicity.