CHARACTERIZATION OF LONG-RANGE CORRELATIONS IN COMPLEX DISTRIBUTIONS AND PROFILES

Characterizing long-range correlations in complex distributions, such as the porosity logs of field-scale porous media, and profiles, such a s the fracture surfaces of rock and materials, is an important problem . We carry out an extensive analysis of such distributions represented by synthetic and real data to determine which method provides the mos t efficient and accurate tool for characterizing them. The synthetic d ata and profiles are generated by a fractional Brownian motion (FBM) a nd the real data analyzed are a porosity log of an oil reservoir and t ime variations of the pressure fluctuations in three-phase flow in a f luidized bed. The FBM is generated by three different numerical method s and the data are analyzed by seven different techniques. Our analysi s indicates that the size of the data array greatly influences the acc uracy of characterization of its long-range correlations. We also find that if the size of the data array is large enough, the commonly used rescaled-range (R/S) method of analyzing FBM series fails to provide accurate estimates of the Hurst exponent, although it can provide a re asonably accurate analysis of a data array that is generated by a frac tional Gaussian noise. In contrast, the maximum entropy and wavelet de composition methods offer highly accurate and efficient tools of chara cterizing long-range correlations in complex distributions and profile s. New methods that an somewhat similar to the R/S method are also sug gested.