Non-Gaussianity of petrophysical parameters using q entropy and a multifractal random walk

Geological systems such as petroleum reservoirs can be investigated using Tsallis entropy and multiplicative hierarchical cascade models. The occurrence of non-Gaussianity is a sign of uncertainty and a phase transition, which could indicate the existence of a petroleum reservoir. Two important parameters that describe a system at any scale are determined: the degree of non-Gaussianity, q, for the entropy and the intermittency, λ2, which explains critical behavior in a system. Some petrophysical indicators can be used to characterize a reservoir, but there is a lack of methods for measuring scaling information. This study compares non-Gaussianity for three selected indicators at various scales: gamma radiation (GR), sonic transient time (DT) and neutron porosity (NPHI). The results show that GR has a fat-tailed probability distribution function (PDF) at all scales, which is a sign of phase transition in the system and indicates high q and λ2. This provides valuable information about GR. NPHI shows scale dependence and the PDF converges to a Gaussian distribution at large scales. This is indicative of separated and uncorrelated porosity at large scales. For the DT series, small λ2 and q at all scales are a hallmark of local DT correlations.