Fractal and multifractal analysis of pore-scale images of soil

Abstract.We use multifractal analysis to estimate the Rényi dimensions of river basins by two different partition methods. These methods differ in the way that the Euclidian plane support of the measure is covered, partitioning it by using mutually exclusive boxes or by gliding a box over the plane.Images of two different drainage basins, for the Ebro and Tajo rivers, located in Spain, were digitalized with a resolution of 0.5 km, giving image sizes of 617×1059 pixels and 515×1059, respectively. Box sizes were chosen as powers of 2, ranging from 2×4 pixels to 512×1024 pixels located within the image, with the purpose of covering the entire network. The resulting measures were plotted versus the logarithmic value of the box area instead of the box size length.Multifractal Analysis (MFA) using a box counting algorithm was carried out according to the method of moments ranging from −5

Section: Generalized Dimensions Using the Box Counting Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Comparison of gliding box and box-counting methods in river network analysis

Saa¹,

Gascó²,

Grau

et al. 2007

“…It is expected that, as the object fills the space in 3-D, D m will approach the Euclidean dimension (E) of three. Given the relation (1) it is now instructive to seek bounds on the values the function N(δ) can take based on Bird et al (2006) work. We denote the fraction of the image occupied by pore phase at the finest resolution (i.e.…”

Section: Mass Fractal Dimensionmentioning

confidence: 99%

“…Several authors maintain that the exact value of the mass fractal dimension cannot be readily calculated Bird et al, 2006;Perrier et al, 2006). Tel and Vicsek (1987), for instance, proposed practical methods to compute it, indicating that the standard methods for determining fractal dimensions must be applied with some caution.…”

Section: Introductionmentioning

confidence: 99%

Influence of thresholding in mass and entropy dimension of 3-D soil images

Tarquis

Heck

Grau³

et al. 2008

Abstract. With the advent of modern non-destructive tomography techniques, there have been many attempts to analyze 3-D pore space features mainly concentrating on soil structure. This analysis opens a challenging opportunity to develop techniques for quantifying and describe pore space properties, one of them being fractal analysis.Undisturbed soil samples were collected from four horizons of Brazilian soil and 3-D images at 45 µm resolution. Four different threshold criteria were used to transform computed tomography (CT) grey-scale imagery into binary imagery (pore/solid) to estimate their mass fractal dimension (D m ) and entropy dimension (D 1 ). Each threshold criteria had a direct influence on the porosity obtained, varying from 8 to 24% in one of the samples, and on the fractal dimensions. Linear scaling was observed over all the cube sizes, however depending on the range of cube sizes used in the analysis, D m could vary from 3.00 to 2.20, realizing that the threshold influenced mainly the scaling in the smallest cubes (length of size from 1 to 16 voxels).D m and D 1 showed a logarithmic relation with the apparent porosity in the image, however, the increase of both values respect to porosity defined a characteristic feature for each horizon that can be related to soil texture and depth.

“…Mandelbrot (1982) and Takayasu (1986), was developed for the quantitative analysis of the patterns of irregular shapes and complicated phenomena. Fractal and multifractal analysis has been used in several geochemical studies to understand structures observed in sediments and soils, such as pore shapes and water distribution (Bird et al, 2006;Posadas et al, 2009;Ferreiro and Vázquez, 2010;Martínez et al, 2010;Xie et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

Inferring origin of mercury inclusions in quartz by multifractal analysis

Shibata

Maruoka

Echigo

2015

Abstract. In order to refine our understanding of how fluid inclusions were trapped in the host minerals, we nondestructively observed mercury inclusions (liquid Hg 0 ) in quartz samples using X-ray computed tomography (CT) technique. The X-ray CT apparatus can observe internal structures of the samples and give cross-sectional images from the transmission of the X-rays through the samples. From the cross-sectional images, we obtained threedimensional spatial distributions of mercury inclusions, and quantitatively analyzed them using fractal and multifractal methods. Although the samples were from different geological settings, the resultant fractal dimensions were 1.70 and 1.71 for the San Benito and Itomuka samples, respectively. The fractal dimensions were also close to those predicted by diffusion-limited aggregation models and percolation theory, which are controlled by the irreversible kinetics. Given the fractal dimension and its implied mechanism, we conclude that the mercury-bearing fluids were not primary fluid inclusions, but migrated into the pre-existing cracks of quartz crystals by diffusion processes.