Scaling, multifractality, and long-range correlations in well log data of large-scale porous media

Three distinct methods, namely, the spectral density, the multifractal random walk approach, and the multifractal detrended fluctuation analysis are utilized to study the properties of four distinct types of well logs from three oil and gas fields, namely, the natural gamma ray emission, neutron porosity, bulk density, and the sonic transient time logs. Such well logs have never been analyzed by the methods that we utilize in the present study. The results indicate that the well logs exhibit multifractal characteristics, and the estimated Hurst exponents by the three methods are close to each other. Using multifractal detrended fluctuation analysis and the shuffled and surrogated data, we find that the source of multifractality is due to both broad probability density functions of the data and long-range correlations in them. The correlations are persistent and are characterized by a Hurst exponent H>0.5. Despite very significant differences in the geology of the three reservoirs–ranging from shaly sands to fractured carbonate reservoirs–there is a rough universality in the log data in that, the Hurst exponents for all the logs vary in a very narrow range.