Local regularity investigation of well logs from an Algerian tight reservoir

Geophysical well logs often exhibit a complex behavior that can be described by fractal stochastic models. Since fractional Brownian motions, which are monofractals presenting a constant Hölderian regularity degree everywhere, they are not appropriate to study log data. In this view, multifractals have been introduced. Here we present a regularity analysis to describe the scaling properties of well logs recorded within an Algerian tight reservoir. This study consists of investigating the local singular behavior of data by using multifractional and fractal techniques. The local analysis aims at studying the possibility of estimating the local Hölder (H) regularity exponent [i.e., the evolution of H value with depth (z)], while the multifractal analysis leads to the definition of a singularity spectrum, D(α), which represents the distribution of the fractal dimension and does not display the spatial information. The application of both approaches to well logs data shows a clear correlation between the H(z) and the lithological units. However, it is demonstrated that the mean H-values corresponding to the three layers derived from the local approach, and the dominant H values determined by the multifractal analysis are close for all the studied logs, except for deep dual laterolog (LLD). That means that a given a specific H value cannot characterize a unique lithology.