细胞自动机的多重分形特征和动力学根源

用大量弹簧滑块组成的模型可以模拟地震的复杂性,本文以细胞自动机(CA)为数学工具,结合地震学和岩石力学的结果,考虑了能量的输入和损耗,进行了地震事件的数字模拟。对模型中输出的"地震"事件进行了时间和空间的多分形分析,并对自组织临界(SOC)状态进行了讨论,进而得到事件至少在时间域里的分布呈现出层次结构,符合自相似特征。本文的CA模型属于确定性的混沌系统,而对于处在SOC状态下的大量事件的频度和大小的统计与G-R指数律很好地吻合。结果表明,虽然自组织(SO)可能是更准确的地震表征,但SOC仍然是研究地震现象的很好的模式。

MULTIFRACTAL CHARACTERISTICS AND DYNAMICAL SOURCES OF CELLULAR AUTOMATA

Using the model made from lots of spring-blocks, we may model the complication of earthquakes,In this paper,by cellular automata(CA) as mathematical tools,with the results of seismology and rock mechanics,comsidering about the energy gathering and energy losses,we do digital modelling for earthquake events,then do multifractal analysis for "earthquakes" events from this model in both time and space fields,and discuss self-organized critical(SOC)state,Further,we get the conclusion in which event distribution shows hierarchy structure,at least, in time field and is coincident with self-similarity nature.This CA model is a determinacy Chaos system, its statistics for frequency and magnitude of lots of events under the state of SOC accords with Gutenberg-Richter index law well.The results show that although self-organized (SO)state might be more accurate earthquake expression,SOC still is a very good mode in earthquake studies.