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从渗透率、孔隙度的概率分布特征入手，结合现有的分形插值理论，对分形插值的各个环节进行了细致的理论分析，并提出了改进方法。引入Box-Cox变换，将非正态分布转化为正态分布，提高了计算分形特征指数H和进行分形模型识别的准确度。同时将分形模拟工作集中在分维Brown运动（Fbm）和分维Gauss噪声（Fgn）模型上，便于插值后数据结构的检验，大大简化了分形建模和模拟工作。给出了Fbm和Fgn模型识别的定量标准，即可以用谱分析方法加以识别，当谱分析斜率1≤β≤3时，数据序列为Fbm，当-1≤β≤1时，数据序列为Fgn。此外，论述了对分形插值理论可采用3种插值方式进行分形模拟。同时，简单介绍了分形特征指数的求取方法及应注意的若于问题。最后，对分形模拟的具体步骤及插值结果的检验方法作了详细的介绍。
Beginning with the probability distribution of permeability and porosity, combined with the existing fractal interpolation theory, the fractal interpolation in all aspects of a detailed theoretical analysis, and propose improved methods. The Box-Cox transformation is introduced to transform the non-normal distribution into a normal distribution, which improves the accuracy of calculating the fractal index H and identifying the fractal model. At the same time, the fractal simulation work is focused on fractal Brownian motion (Fbm) and fractal Gaussian noise (Fgn) model to facilitate the test of the data structure after interpolation, which greatly simplifies the fractal modeling and simulation work. The quantitative criteria of Fbm and Fgn model identification are given, which can be identified by spectral analysis. When the slope of the spectrum is 1≤β≤3, the data sequence is Fbm. When -1≤β≤1, the data sequence is Fgn . In addition, the paper discusses fractal interpolation theory can be used three kinds of interpolation fractal simulation. At the same time, simply introduced the method of calculating the fractal characteristic index and should pay attention to if the problem. Finally, the concrete steps of fractal simulation and the test method of interpolation result are introduced in detail.