分形分析在测井数据应用中的几个问题

Some Remarks on Application of Fractal Analyses in Well Logging Data

讨论了测井数据的分形分析中经常遇到而又容易产生误差的问题,特别是重标度极差分析和功率谱分析方法中的不一致性以及在分形分析中如何处理原始测井数据。在此基础上又进一步讨论了全域标度指数与局部奇异性指数之间的关系,进而引入分析了测井数据的多重分形特征。研究表明实测的测井数据的多重分形谱很少是对称的,一般是左侧奇异值小的分支比右侧奇异值大的分支的斜率要大,显示了较奇异的点的分数维(或相对含量)随着奇异值的变化而有较快的变化。最后讨论了地球物理数据中普遍存在的1/fβ现象的成因问题,明确了其多成因的可能性,然而单纯的沉积作用也可以形成多重分形沉积地层。

This paper discusses applications of fractal analyses in well logging data, and particularly some related problems which are prone to causing misunderstandings and errors. One of the most troublesome issues is the inconsistency between the rescaledrange method and the power spectrum method, mainly due to the incorrect preprocessing of the raw well data. Then discussed is the relationship between the global scaling exponent (H) and the local singularity exponent (Hu), followed by the introduction of multifractal properties of well logging data. Studies show that multifractal spectra of log data are rarely symmetrical, but have steepened slopes on their left branches where the singularity strengths are higher. This indicates more rapid variations in fractal dimensions (or relative portions) for highly singular data points in the data series. Further discussed are the causes for the universal 1/f~~β phenomenon, and we come to see that while the causes might be multiple and intertwined, sedimentary process alone can produce multifractal sedimentary sequences.