测井多尺度分析方法中最优小波基的选取

不同的小波基具有不同的时频特征,用不同的小波基分析同一问题会产生不同的结果。因此,小波基的选取和优化在实际应用中是一个重要问题。本文详细分析了小波基的基本性质,并以相关系数作为选取最优小波基的依据,分别选取4种常用小波基函数进行分析和对比,通过比较相关系数的大小,选定了适合测井多尺度分析方法的最优小波基。对实际测井信号的多尺度加权重构表明,最优小波基的选取是合理的;相关系数法作为选取小波基的一种方法是可行的。 

Selection of optimum wavelet base of multiscale analysis in well logging

Different wavelet bases have different time-frequency characteristics.Different results will come out while analyzing the same problem with different wavelet bases.So the selection and the optimization of wavelet base are important in the application of wavelet analysis.In this paper basic features of wavelet base are expounded and the correlation coefficient is regarded as the basis of selecting optimum wavelet base;four wavelet base functions are chosen to be analyzed respectively and the optimum wavelet base of multiscale analysis in well logging is determined by analyzing the magnitudes of correlation coefficients.Reconstructing the original logging curves using multiscale anlysis shows that the selection of optimum wavelet base is reasonable and the correlation coefficient as a method of selecting wavelet base is feasible.