Multifractal Scaling characteristics of lineament networks of a fractured sandstone aquifer system

Abstract

Underground flow in fractured aquifers depends on the connectivity of the fractures, considered as a set of conduits and the main drainage axes. Quantitative analysis of fracture networks using multifractal characterisation therefore provides the backbone for assessing the connectivity of these networks. The aim of our work is to carry out a multifractal characterisation of lineament networks while performing related geometric, spectral and fractal analyses. The approach used is based on the box counting method to estimate the multifractal spectrum using the method of moments. The generalized fractal dimensions were estimated using the partition function and the multifractal spectrum using the Legendre transform. The work was carried out using a calculation code that we developed ourselves and that we named: 2D Calculation Code for Multifractal Analysis of Fracture Networks (2D-MAFN).Four lineament maps at different scales were analyzed, corresponding to the Upper Jurassic and Cretaceous geological formations of the El Gada region in the Central Algerian Saharan Atlas. The geometric analysis of the lineament networks showed good consistency between the lineament networks and the geological structure of the Atlas Range and its fault network. It also showed that the distribution of the lengths of the lineaments fits the power law. This analysis also revealed that, on a larger scale, diffuse fracturing appears to be more prevalent. In addition, the spectral analysis, through the decrease in spectral power according to a power law, characterizes a self-similar behavior and already seems to prove the scale invariance of the lineaments. The fractal dimension values obtained reflect the extent of fracturing and the degree of complexity of the network of lineaments. These values show that the lineaments are also well correlated with each other. The partition functions show that the points line up on the adjustment lines according to a law characteristic of multifractal behavior. In addition, the curves of generalized dimensions as a function of moments show a clear decrease, highlighting the multifractal nature of the fracturing process. In addition, the multifractal spectra in the form of bell curves also confirm the multifractal process for the four lineament networks analyzed. The results obtained are very encouraging and open up the prospects of modelling fracture networks for a variety of purposes, including assessing the connectivity of a fracture network.