Models of the water retention curve for soils with a fractal pore size distribution

Perrier, Edith; Rieu, Michel; Sposito, Garrison; Marsily, Ghislain de

doi:10.1029/96wr01779

Cited by 140 publications

(91 citation statements)

References 31 publications

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“…This is due in part to the relatively small number of parameters that can define a random fractal porous medium of great complexity and rich structure. Also, fractal scaling of natural porous media has been widely anticipated on the basis of the observed power law form of soil water retention curves [Ahl and Niemeyer, 1989;Tyler and Wheatcraft, 1990;Rieu and Sposito, 1991a, 1991b, 1991cPerrier et al, 1996;Perfect, 1999]. There has been considerable debate about the validity of the approaches presented in these papers because they generally neglect pore connectivity [Bird et al, 1996;Rieu and Perrier, 1998].…”

Section: Introductionmentioning

confidence: 99%

Water retention of prefractal porous media generated with the homogeneous and heterogeneous algorithms

Sukop¹,

Perfect²,

Bird³

2001

Water Resources Research

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Abstract. Fractal models of porous media are of interest in numerous scientific disciplines, including hydrology and soil science. This interest arises in part from the ability of these models to parsimoniously produce highly complex and richly structured geometries. Examination of the soil hydrology literature suggests that there are at least two different ways these models are being constructed. We review the two primary algorithms and compare the computed water retention behavior of the different media. Water retention is computed using a method that explicitly considers the connections between pores and to the atmosphere. The distributions of simulated water saturations (for 1000 realizations) around their median values as a function of applied tension were complex and multimodal for both homogeneous and heterogeneous prefractals. The range between the first and third quartiles for the water retention in heterogeneous prefractal structures was, on average, more than twice as large as that for the homogeneous prefractals. This suggests that relations between fractal parameters used to construct the porous media and the water retention behavior of the media can be more readily determined for homogeneous prefractals.

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Section: Introductionmentioning

confidence: 99%

Water retention of prefractal porous media generated with the homogeneous and heterogeneous algorithms

Sukop¹,

Perfect²,

Bird³

2001

Water Resources Research

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“…Maus et al (1999) conducted variogram analysis on magnetic data in Canada and found the data to exhibit scaling behavior as function of the horizontal distance. Studies in the soil science field have shown that the soil pore structure is fractal (Perrier et al 1996;Baveye et al 1998). Scaling behavior has also been noted for subsurface properties (namely the intrinsic permeability, K) as a function of space.…”

Section: Multifractal Modeling and Magnetic Datamentioning

confidence: 97%

Multifractal Characterization of Geologic Noise for Improved UXO Detection and Discrimination

Nyquist¹,

Boufadel²

2008

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This document has been approved for public release. Report Documentation PageForm Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. Executive SummaryPushing sensors and algorithms to the limit to minimize the chance of overlooking unexploded ordnance (UXO) increases the chance that noise will be misidentified as signal and money wasted excavating scrap metal or chucks of magnetic rock. Approaches to improve the signal to noise ratio typically follow one of three tracks: (1) development of new sensors that are either more sensitive, or less noisy; (2) fusion of data from multiple sensors so that the chances of confounding all of the det6ectors simultaneously is reduced; or (3) development of computer algorithms to extract the signal(s) from the noise. In the case of wide-area surveys that use methods such as helicopter-borne magnetometry, the battle against noise has focused primarily on instrument noise (e.g., thermal noise), platform noise (e.g., magnetic noise created by the helicopter), or interference created by multiple UXO targets in cluttered settings. What has been largely ignored is the "noise" created by the rock and soil that surrounds the buried ordnance.The goal of this pilot project was to investigate a new approach to the characterization and simulation of geologic noise using multifractal analysis that captures the scale-dependent variability arising from geologic heterogeneity in different environments. By combining geologic noise simulations with models for the geophysical signatures of UXO, the researchers aim to create synthetic datasets that can be used both to test and improve UXO discrimination algorithms developed by other researchers, and to develop more reliable estimates of the ratio of false positives to false negatives for a particular geologic environment.In this report we discuss the multifractal methodology and its application to three data sets: Isleta Pueblo, NM; Fort Ord, CA; and the Sierra Army Depot, CA, The S1 site at the Isleta Pueblo, which is underlain by volcanic rock, typifies a UXO site with high magnetic noise. Fort Ord is underlain by sedimentary rock that is largely non-magnetic, but apparently magnetic sediments have washed into topographic drainages, creating moderate levels of geologic noise distributed...

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“…We then seek for functions whose Laplace transforms are analytically obtained and asymptotes for sufficiently large t* are @*(t*) --f a3t*-5/2 and (a3 and a4 are constants) in models 3 and 4, respectively. The functions (22) we have chosen are @*(t*) = 4!4e~p(t')I~Erfc(t*'/~) (model 3), (12) @*(t*) = 4 e~p ( t * ) l~E r f c ( t * ' /~) (model 4), (13) …”

Section: Theorymentioning

confidence: 99%

Analysis on Eractal-Like Behaviour Expected for Migration of Radionuclides in Geologic Sorbing Media.

Kinoshita

Harada

Tsubata

et al. 1998

J. Nucl. Sci. Technol.

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In earlier work, we showed that within nonhomogeneous sorbing media the desorption process becomes fractal-like. In migration of radionuclides in geologic media, the adsorption is an essential factor retardating the migration. Moreover, geologic media is inherently nonhomogeneous. It is therefore probable that the migration is significantly influenced by the fractal-like feature. Based on this idea, we have analyzed migration behaviours by employing a new model and compared the results with those obtained using conventional models. The nuclides migrate in the media with the flow of ground water being continually trapped on adsorption sites and released (desorbed) to the flow. The concept of the overall residence-time distribution function for nuclides on the adsorption sites is introduced in the new model. This function obeys the power form,The migration behaviours predicted by our theory are qualitatively different from those by conventional theories, and the details of the differences are greatly dependent on the exponent a. In particular, the migration behaviour in cases of O O), for sufficiently large t ( t denotes time).

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Models of the water retention curve for soils with a fractal pore size distribution

Cited by 140 publications

References 31 publications

Water retention of prefractal porous media generated with the homogeneous and heterogeneous algorithms

Water retention of prefractal porous media generated with the homogeneous and heterogeneous algorithms

Multifractal Characterization of Geologic Noise for Improved UXO Detection and Discrimination

Analysis on Eractal-Like Behaviour Expected for Migration of Radionuclides in Geologic Sorbing Media.

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