模糊分维及其在地震研究中的某些应用

在模糊集理论与分形理论的基础上,引进了模糊分维的概念;给出了模湖容量维D₀与模糊关联维D₂的定义与确定方法;讨论了模糊分维与常用的分维（清晰分维）的关系.给出了模糊分维在地震研究中的应用结果: 1.根据模糊容量维D₀随时间的上升趋势变化,可以划分出大地震活动的高潮期;由模糊容量维D₀与模糊关联维D₂随时间变化的曲线,可以分析识别大地震前的中长期前兆异常. 2.根据模糊容量维D₀随空间和时间的变化,可以划分出未来大震所在的地区,并可发现大震前数年D₀呈现增大或减小的趋势. 3.根据前兆数据的模糊时间分维D₀随时间的变化,可以发现大地震的短期前兆异常.

FUZZY FRACTAL DIMENSION AND ITS SOME APPLICATIONS IN EARTHQUAKE RESEARCHES

At first, based on the theory of fuzzy sets and fractal theory, the concepts of fuzzy fractal dimensions has been further introduced, the definitions and methods for determination of fuzzy Hausdorff fractal dimension D0 and fuzzy relative fractal dimension D2 were given, and the relation between fuzzy fractal dimension and usual (clear) fractal dimension was discussed.Then, three results of the applications of the fuzzy fractal dimension in earthquake researches were obtained. They are as follows:1.The characteristics of fuzzy temporal fractal dimension of the activity- of large earthquakes. According to the variation of fuzzy temporal fractal dimension D0(1) with respect to time, the periods of high seismicity of large earthquakes corresponding to the periods of increase of D0(1) can be distinguished. By using the temporal variation curves of fuzzy Hausdorff fractal dimension D0(1) and fuzzy relative fractal dimension D2 the long-medium term precursory anomalous variations in seismicity before large earthquakes may be recognized.2.The characteristics of fuzzy spatial fractal dimension of the activity of strong and moderate earthquakes. According to the temporal and spatial variations of D0(2), the riskful regions of forthcoming large earthquakes corresponding to the regions of increase or decrease of D0(2) and the anomalous variations of seismicity in several years before large earthquakes may be recognized.3.The characteristics of fuzzy temporal fractal dimension of the earthquake precursors. According to the variation of fuzzy temporal fractal dimension D0(1) of precursors data with respect to time,the short term precursory anomalies before large earthquakes may be discovered.