Fractal Metrology for biogeosystems analysis

Abstract

Abstract. The solid-pore distribution pattern plays an important role in soil functioning being related with the main physical, chemical and biological multiscale and multitemporal processes of this complex system. In the present research, we studied the aggregation process as self-organizing and operating near a critical point. The structural pattern is extracted from the digital images of three soils (Chernozem, Solonetz and "Chocolate" Clay) and compared in terms of roughness of the gray-intensity distribution quantified by several measurement techniques. Special attention was paid to the uncertainty of each of them measured in terms of standard deviation. Some of the applied methods are known as classical in the fractal context (box-counting, rescaling-range and wavelets analyses, etc.) while the others have been recently developed by our Group. The combination of these techniques, coming from Fractal Geometry, Metrology, Informatics, Probability Theory and Statistics is termed in this paper Fractal Metrology (FM). We show the usefulness of FM for complex systems analysis through a case study of the soil's physical and chemical degradation applying the selected toolbox to describe and compare the structural attributes of three porous media with contrasting structure but similar clay mineralogy dominated by montmorillonites.

Characterization and Analysis of Porosity and Pore Structures

“…While much of the application of this approach has been in fi elds such as geography and organic/biological systems, several authors have investigated the utility of this measure for evaluating porosity and permeability in reservoir modeling (Garrison et al 1993a,b;Cai et al 2014), soils (Zeng et al 1996;Millán 2004;Chun et al 2008;Zamora-Castro et al 2008;Luo and Lin 2009;Torres-Arguelles et al 2010;Ulthayakumar et al 2011), fractures (MirandaMartinez et al 2006, porous silica (Denoyel et al 2006), sediments (Bube et al 2007), oil mobilization (Hamida and Babadagli 2008), and sandstones (Anovitz et al 2013a(Anovitz et al , 2015a in both two and three dimensions.…”

Active Faults sources of the Morelia-Acambay Fault System, Mexico based on Paleoseismology and the estimation of magnitude <i>M<sub>w</sub></i> from fault dimensions

“…In time-series the Hurst exponent measures the growth of the standardized range of the partial sum of deviations of a data set from its mean (Ellis, 2007). The Hurst exponent is especially suitable to characterize stochastic processes (Mandelbrot and Van Ness, 1968) and there are basic differences between persistent 130 (H > 0.5) and antipersistent (H < 0.5) processes, while the white noise is characterized by H = 0.5 (Torres-Argüelles et al, 2010). For estimating the Hurst Exponent we use the Wavelet transform (Rehman and Siddiqi, 2009), where the characteristic measure of wavelet variance analysis is the wavelet exponent, H w (Malamud and Turcotte, 1999).…”