Éditeur(s) : HAL CCSD Oxford University Press (OUP): Policy P - Oxford Open Option A Oxford University Press (OUP)
Résumé : International audience
It is well known that sedimentary rocks having same porosity can have very different pore size distribution. The pore distribution determines many characteristics of the rock, among which its transport properties are often the most useful. Multifractal analysis is a powerful tool that is increasingly used to characterize the pore space. In this study, we performed multifractal analysis of pore distribution on simulated sedimentary rocks using the relaxed bidisperse ballistic deposition model (RBBDM). The RBBDM can generate a 3-D structure of sedimentary rocks of variable porosity by tuning the fraction p of particles of two different sizes. We also performed multifractal analysis on two samples of real sedimentary rock to compare with the simulation studies. One sample, an oolitic limestone is of high porosity (40 per cent) while the other is a reefal carbonate of low porosity, around 7 per cent. 2-D sections of X-ray microtomographs of the real rocks were stacked sequentially to reconstruct the real rock specimens. Both samples show multifractal character. The results from analysis of real rock agree quite well with the simulated structure of low porosity. The simulated rock of high porosity showed a weak multifractal nature though the real rock sample of similar porosity was found to be strongly multifractal. We propose a ‘structure parameter’ ξ which is a function of porosity and the generalized dimensions, and controls the transport properties of the rock.
ISSN: 0956-540X

hal-01174142
https://hal.archives-ouvertes.fr/hal-01174142
DOI : 10.1093/gji/ggu417

Éditeur(s) : HAL CCSD Oxford University Press (OUP)
Résumé : International audience
Several studies, both theoretical and experimental, show that sedimentary rocks have a fractal pore-grain interface. In this paper a computer simulated 3-D sedimentary rock structure generated by the Relaxed Ballistic Bidisperse Deposition Model (RBBDM), is investigated to characterize the micro structure of its pores. The pore volume and the rock-pore interface show the same fractal dimension indicating that the pore volume is a fractal. The two point density correlation is computed for the pore space and the results compare favourably with the range reported from experiments. An array of 2-D X-ray tomography micrograph sections of a real sedimentary rock, an oolitic limestone (pure calcite) from the Mondeville formation of Middle Jurassic age (Paris Basin, France), was used to generate a 3-D bitmap. The 3-D real rock sample generated in this manner, was analysed for similar studies as the simulated structure. The results were compared with those obtained from simulation. The simulation results agree qualitatively with the real rock sample. Diffusion through the connected pore space of the simulated structure was studied using a random walk algorithm and the results compared with the similar simulation study done on the 3-D oolitic limestone specimen. In both cases diffusion was found to be anomalous indicating that the sedimentary rock has a fractal geometry. The favourable comparability of results between the simulated and real rock supports the usefulness of the model of sedimentary rock generation which can be applicable to transport phenomena.
ISSN: 0956-540X

hal-00823061
https://hal.archives-ouvertes.fr/hal-00823061
DOI : 10.1093/gji/ggs084

Éditeur(s) : HAL CCSD American Geophysical Union
Résumé : International audience
This paper presents a multicontinuum approach to model fractal temporal scaling of catchment response in hydrological systems. The temporal scaling of discharge is quantified in frequency domain by the transfer function HðxÞ, which is defined as the ratio between the spectra of catchment response and recharge time series. The transfer function may scale with frequency x as HðxÞ x2b. While the classical linear and Dupuit models predict exponents of b52 and b51, observations indicate scalings with noninteger exponents b. Such behaviors have been described by multifractal models, which, however, often lack a relation to the medium characteristics. We revisit and extend the classical linear Dupuit aquifer models and discuss their physical meanings in the light of the resulting aquifer dynamics. On the basis of these classical models, we derive a multicontinuum approach that provides physical recharge models which are able to explain fractal behaviors with exponents 1=2 < b < 2. Furthermore, this approach allows to link the fractal dynamics of the discharge process to the physical aquifer characteristics as reflected in the distribution of storage time scales. We systematically analyze the catchment responses in the proposed multicontinuum models, and identify and quantify the time scales which characterize the dynamics of the catchment response to recharge.
ISSN: 0043-1397

insu-00952537
https://hal-insu.archives-ouvertes.fr/insu-00952537
https://hal-insu.archives-ouvertes.fr/insu-00952537/document
https://hal-insu.archives-ouvertes.fr/insu-00952537/file/russian.pdf
DOI : 10.1002/2013WR014255

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
In this paper, we have presented a spectral and a multifractal analysis performed on 412 time series of wind speed data each of duration of 350 s and sampled at 20 Hz. The average spectrum for the wind speed displays a scaling behavior, in the inertial range, over two decades, with b ¼ 1:68 close to the Kolmogorov value À 5/3. A multifractal analysis has been motivated by the presence of scaling invariance in data set. Then we have considered their scaling properties in the framework of fully developed turbulence and multifractal cascades. The results obtained for wind speed confirm that the exponent scaling function z V ðqÞ is nonlinear and concave. This exponent characterizes the scaling functions in the inertial range indicating that the wind speed is intermittent and multifractal. Moreover the theoretical quadratic relation for lognormal multifractals is well fitted. We investigate the consequence for wind energy production: we generate stochastic simulations of a multifractal random walk, and using a power curve derived from experimental data, we generate the associated power time series. We show that, due to the saturation of the power curve for large speed values, when the input time series (turbulent wind speed) is multifractal, the output can be almost monofractal.
ISSN: 0167-6105

hal-01527886
https://hal.archives-ouvertes.fr/hal-01527886
DOI : 10.1016/j.jweia.2012.06.002

Éditeur(s) : HAL CCSD
Résumé : International audience
This paper deals with image processing. This study takes place in a segmentation process based on texture analysis. We use the multifractal ap-proach to characterize the textures. More precisely we study a particular multi-fractal spectrum called the large deviation spectrum. We consider two statistical methods to numerically compute this spectrum. The resulting spectrum, com-puted by both methods over an image, is a one dimension spectrum. In the scope of this article, we extend these methods in order to obtain a two dimen-sions spectrum which could be assimilated to an image. This 2D spectrum al-lows a local characterization of the image singularities while a 1D spectrum is a global characterization. Moreover, the computation of the spectrum requires the use of a measure. We introduce here a pre processing based on the gradient to improve the measure. We show results on both synthetic and real world images. Finally, we remark that the resulting 2D spectrum is close to the resulting im-age of an edge detection process while edge detection using one dimension spectrum requires post processing methods. This statement will be used for fu-ture works.
SITIS Proceedings
Hammamet, Tunisia

hal-00602273
https://hal.archives-ouvertes.fr/hal-00602273

Éditeur(s) : HAL CCSD Springer
Résumé : The analysis of gamma ray measurements provides valuable information about the basement's lithospherical model and the radioactive elements contained in the subsurface. To be exploited, the raw data need pre-processing operations which consist of corrections of the Compton effect, altimetry and the aircraft background, and 2D interpolations. These transformations may modify the data's stochastic component which reflects heterogeneities of the investigated medium. In this study, a fractal analysis is carried out on airborne gamma ray data measured in the Hoggar's area (Algeria). First, it is shown that the analyzed data exhibit fractal properties. Due to the dependence of the latter on the spatial location of the measures, the data can be considered as paths of multifractional Brownian motions. Another result worth noting is that the fractal nature of the raw data is not modified by the pre-processing operations. The fractal analysis can be then performed on the raw spectrometric measurements without submitting them to any pre-processing; thus, the stochastic component of the measurements is kept intact.
ISSN: 1866-7411

hal-00817494
https://hal.archives-ouvertes.fr/hal-00817494
DOI : 10.1007/s12517-011-0407-3

Éditeur(s) : HAL CCSD American Geophysical Union
Résumé : International audience
An analytical solution in the Laplace domain is derived for modeling anomalous pressure diffusion during pumping tests in aquifer displaying hierarchical fractal fracture networks. The proposed solution generalizes all of the analytical models for fractal flow published previously by combining multifractal diffusion and nested multiporosity with transient exchanges, interface skin effects, and well storage effect. Solutions are derived for fracture-delimited blocks with planar, cylindrical, and spherical shapes, as well as with any fractional dimensional shapes. Any combinations of these shapes can be defined in order to model a large range of situations. Within each permeability level, the fractal properties of the fracture network can be specified and the fractal dimension can be distinct from the shape dimension of the block.
ISSN: 0043-1397

hal-00411549
https://hal.archives-ouvertes.fr/hal-00411549
DOI : 10.1029/2008WR007125