中国断层系分维及其灰色预测研究

doi:10.11867/j.issn.1001-8166.2006.05.0496

地球科学进展 ›› 2006, Vol. 21 ›› Issue (5): 496 -503. doi: 10.11867/j.issn.1001-8166.2006.05.0496

中国断层系分维及其灰色预测研究

朱晓华 ¹,蔡运龙 ²

1.中国科学院地理科学与资源研究所，北京 100101；2.北京大学资源与环境地理学系，北京 100871

收稿日期:2004-10-08 修回日期:2006-02-09 出版日期:2006-05-15
通讯作者: 朱晓华 E-mail:zhuxh@igsnrr.ac.cn
基金资助:
国家自然科学基金重点项目“西南喀斯特山区土地利用/土地覆被变化及其对土地资源利用可持续性的影响”（编号：40335046）；国家自然科学基金项目“土地结构的分形性质与尺度转换研究”（编号：40301002）资助.

Fractal Dimensions of Faults of China and Their Grey Forecast

Zhu Xiaohua ¹,Cai Yunlong ²

1.Institute of Geographical Science and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China; 2.Department of Resources, Environments, Geography, Peking University, Beijing 100871, China

Received:2004-10-08 Revised:2006-02-09 Online:2006-05-15 Published:2006-05-15

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应用分形理论和灰色系统理论方法，对中国断层系分维及其灰色预测问题进行了探讨。首先，计算并分析了中国断层系分维及其空间变化特征；其次，在计算中国大陆和南岭地区不同地质历史时期断层系分维、揭示断层系具有的跨尺度分形特征的基础上，对分维变化进行了灰色预测，其结果表明：分形理论与灰色理论结合是研究断层系时空间特征的有力工具，中国大陆下一期断层系分维预测值为1.5995，预示中国大陆下一期断层系空间结构的复杂程度将有所增加。

关键词: 分形, 分维, 灰色系统, 断层系, 中国

Based on extensive and thorough observation of a large amount of geographical, geological and economic phenomena such as coastline, earthquake, stock etc, Mandelbrot discovered the inherent character in nature that he called fractal, and he also considered the fractal dimension as the quantitative parameter to describe numerous irregular phenomena in nature. As a new tool to picture the complexity of nature, the fractal theory has been widely used in many fields. As to the study of fault, it has made progress in many fields such as the fractal character, the spatial distribution model, movement, classification, calculation of fractal dimension of fault, the relation between fault and earthquake, the fractal character of rock, and scaling between short and large fault, etc. Researches on the fractal dimensions of China's faults, the prediction of dynamic change, have not been attempted till now. These questions are discussed in this paper.
Based on the fractal theory and grey theory, the fractal character of faults of China has been quantitatively analyzed in this paper. Firstly, fractal dimensions of faults of China's mainland are calculated and compared. The fractal dimension of the whole faults of China's mainland is 1.7682, with active faults is 1.5989, and 1.6755 for less active faults. The fractal dimension of faults of the Qinghai Tibet Plateaus the largest in eight natural regions of China. Secondly, relationship of fractal dimensions between faults and mountains is discussed, and the quantitative relationship between faults and mountains is established. Thirdly, fractal dimensions of faults of China's mainland in different geological periods are calculated, and grey forecast models of fractal dimensions are established, too. It indicates that the fractal theory and grey theory are useful to the study of the characteristics of faults. The fractal dimension of faults of China's mainland for next geological periods may be 1.5995, and the complexity of faults will be increased correspondingly.

Key words: Fractal, Fractal dimension, Grey system, Faults, China.

中图分类号:

P941.7

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