测井曲线的多重分形分析方法研究

On Multifractal Analysis Method in Well Logging Interpretation

单一分形在测井解释方面已有许多应用。多重分形分析可以计算出包括单一分形分维数在内的多重分形谱 ,对测井曲线进行分析时 ,多重分形分析可以提供比单一分形分析更多的信息。在研究测井曲线多重分形分析的数学原理基础上 ,研究了计算测井曲线多重分形谱的算法。该算法由FORTRAN语言实现。通过对实际测井资料的处理分析 ,发现多重分形谱在描述地层非均质性方面具有比较好的效果。测井曲线的多重分形分析方法对于复杂地层的研究具有一定的现实意义。

There are many applications of fractals in logging interpretation. However, it is not enough for only one fractal dimension to describe the characteristics of formation because the formation is a very complicated anisotropic body. The multifractal analysis can calculate a multifractal spectrum that includes many fractal dimensions. So its more information can be provided than that of fractal analysis in the logging interpretation. The algorithm calculating the multifractal spectrum of logging is studied here after the mathematical theory of logging multifractal analysis has been studied. The program is completed in FORTRAN language according to the algorithm. It is found that the multifractal spectrum has a good effect in the description of the formation's heterogeneity through the processing and analysis of logging data coming from the field. Therefore, the logging multifractal analysis method will take some practical significance in study of the complicated formation.