Exploring the Impact of Non-Gaussian Properties in Petrophysical Data Using q-Entropy and Multifractal Models

The analysis of non-Gaussian properties in petrophysical data is crucial for a comprehensive understanding of subsurface geological processes and in this study, we explore the potential of integrating q-Entropy and multifractal models to characterize the complex behavior of petrophysical properties and the methodology involves rigorous data collection from rock models, well logs, and seismic surveys, followed by preliminary statistical analysis to detect deviations from Gaussian distributions through skewness, kurtosis, and advanced tests such as the Shapiro-Wilk test and QQ-plots. q-Entropy is computed across a range of entropic indices to quantify the system’s non-linear dynamics, while multifractal detrended fluctuation analysis (MF-DFA) is employed to derive the singularity spectrum, thereby capturing the multiple scaling behaviors inherent in the data ,our results demonstrate significant non- Gaussian features, with optimal q values indicating enhanced sensitivity to underlying long-range correlations and the broad multifractal spectrum further confirms the presence of heterogeneous structures within the reservoir and these findings not only advance the theoretical understanding of petrophysical data but also offer practical implications for improving reservoir characterization and modeling and the integrated approach provides a powerful framework that can be extended to other geoscience fields, including hydrology, and suggests promising avenues for future research through the incorporation of machine learning techniques.