FRACTALS, CHAOS, SELF-ORGANIZED CRITICALITY AND TECTONICS

被引:26
作者
TURCOTTE, DL
机构
[1] Department of Geological Sciences, Cornell University, Ithaca, New York
关键词
D O I
10.1111/j.1365-3121.1992.tb00444.x
中图分类号
P [天文学、地球科学];
学科分类号
07 ;
摘要
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.
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页码:4 / 12
页数:9
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共 33 条
[11]  
Gutenberg B., Richter C.F., Seismicity of the Earth and Associated Phenomenon, (1954)
[12]  
Hewett T.A., Fractal distributions of reservoir heterogeneity and their influence on fluid transport, Pap. Soc. Petrol. Eng., 15386, (1986)
[13]  
Huang J., Turcotte D.L., Are earthquakes an example of deterministic chaos, Geophysical Research Letters, 17, pp. 223-226, (1990)
[14]  
Huang J., Turcotte D.L., Evidence for chaotic fault interactions in the seismicity of the San Andreas fault and Nakai trough, Nature, 348, pp. 234-236, (1990)
[15]  
Ito K., Matsuzaki M., Earthquakes as self‐organized critical phenomena, J. geophys. Res., 95, pp. 6853-6868, (1990)
[16]  
Kadanoff L.P., Nagel S.R., Wu L., Zhou S.M., Scaling and universality in avalanches, Phys. Rev., 39 A, pp. 6524-6533, (1989)
[17]  
Lorenz E.N., Deterministic nonperiodic flow, Journal of the Atmospheric Sciences, 20, pp. 130-141, (1963)
[18]  
Mandelbrot B.B., How long is the coast of Britain? Statistical self‐similarity and fractional dimension, Science, 156, pp. 636-638, (1967)
[19]  
Mandelbrot B.B., The Fractal Geometry of Nature, (1982)
[20]  
May R.M., Simple mathematical models with very complicated dynamics, Nature, 261, pp. 459-467, (1976)