砂岩粒度分布分形特征研究方法探讨

按照分形理论的基本思想，分析了分形理论应用于砂岩粒度分布特征研究的可行性，介绍了粒度分形分布的判别方法，应用砂岩薄片粒度统计数据研究了粒度分布分形特征，提出了无标度区容量维的计算方法，并结合粒度序列关联维算法对某钻井分段岩芯砂岩样品薄片进行了粒度统计和分形维数计算．结果表明，砂岩粒度分布多数为正态分布和分形分布之间的过渡类型，即粒度分布仅在一定粒度区间内符合分形分布，据此计算得出的无标度区分形维数是描述砂岩形成环境差别及形成背景复杂性的定量参数，为利用粒度分析方法进行沉积环境解释提供了新的参考依据．

Research Method of About Fractal Feature of the Grain Size Distribution of Sandstone

Following the basic thought of fractal theory, the feasibility of application of fractal theory in the research on grain size distribution of sandstone is introduced, and the method in judging the fractal distribution of sand grain is presented. Researches into the fractal characteristics of the distribution of grain size of sandstone have been done for the first time by means of statistical data based on sandstone slices. And the calculation method of capacity dimension within a non-scaled interval has been put forward. The fractal dimension of grain size distribution of sandstone sampling from a well core has been calculated together with the correlation dimension algorithm. The results show that the distribution law of the grain size of most sandstone is between 'Normal' and 'Fractal', that is, the 'fractal' distribution exists only within a certain grain size interval. The non-scaled interval fractal dimension calculated accordingly is a quantitative parameter in describing the difference of forming environment and the complexity of forming background of sandstones, which does good to the traditional grading analysis of sandstone.