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薄层砂岩的空间展布形态异常复杂，地震资料由于受分辨率限制难以精确描述薄砂岩层的形态，而传统的线性数学方法也难以描述随机的地质沉积现象。通过对大量的宏观与微观沉积资料研究和测井相分析表明，地层沉积具有分形特征，利用地质统计资料建立分形地质模型，以地震和测井资料为约束，通过分形插值算法确定出井间薄砂层的空间展布形态，这种非线性的数学描述方法具有较高的分辨率和可信度，能进一步减少薄砂层储层描述的不确定性，对预测薄砂层油气藏分布范围、厚度变化意义重大。
The spatial distribution of thin-bedded sandstone is very complicated. Because of the limited resolution of seismic data, it is difficult to precisely describe the shape of thin sandstone layer. However, the traditional linear mathematical method can not describe random geological sedimentation. A large number of macroscopic and microscopic sedimentary data studies and log facies analysis show that the stratigraphic sediments have fractal features, and fractal geological models are established by using geostatistical data. Constraints are obtained by seismic data and well logging data, and fractal interpolation algorithm is used to determine the interwell sand The spatial distribution of layers, the non-linear mathematical description of the method with high resolution and reliability, can further reduce the reservoir sandstone reservoir description of the uncertainty, the prediction of the distribution of thin sand reservoir range, Thickness change is of great significance.