Multifractal Analysis of Geological Data Using a Moving Window Dynamical Approach - Gil Silva; Fernando Pellon de Miranda; Mateus Michelon; Ana Ovídio; Felipe Venturelli; Letícia Moraes; João Ferreira; João Parêdes; Alexandre Cury; Flávio Barbosa (Fractal and Fractional)
Fractal dimension has proven to be a valuable tool in the analysis of geological data. For instance, it can be used for assessing the distribution and connectivity of fractures in rocks, which is important for evaluating hydrocarbon storage potential. However, while calculating a single fractal dimension for an entire geological profile provides a general overview, it can obscure local variations. These localized fluctuations, if analyzed, can offer a more detailed and nuanced understanding of the profile’s characteristics. Hence, this study proposes a fractal characterization procedure using a new strategy based on moving windows applied to the analysis domain, enabling the evaluation of data multifractality through the Dynamical Approach Method. Validations for the proposed methodology were performed using controlled artificial data generated from Weierstrass–Mandelbrot functions. Then, the methodology was applied to real geological profile data measuring permeability and porosity in oil wells, revealing the fractal dimensions of these data along the depth of each analyzed case. The results demonstrate that the proposed methodology effectively captures a wide range of fractal dimensions, from high to low, in artificially generated data. Moreover, when applied to geological datasets, it successfully identifies regions exhibiting distinct fractal characteristics, which may contribute to a deeper understanding of reservoir properties and fluid flow dynamics.