Sedimentary Porous Materials as a Realization of a Stochastic Process

Preston, Floyd W.; Davis, John C.

doi:10.1007/978-3-642-66146-4_6

Cited by 12 publications

(9 citation statements)

References 12 publications

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“…Simple stochastic models have traditionally been used to generate models of granular material. These often use a binary random field approach which treats the granular material as two phases of matter (solid particles and gas‐ or fluid‐filled ‘voids’) by simulating only the solid phase [e.g., Fara and Scheidegger , 1961; Preston and Davis , 1976; Sen , 1984; Koutsourelakis and Deodatis , 2005; Buscombe et al , 2010]. In such an approach, the particle geometries and packing characteristics at the scale approaching the individual grains are unrealistic even if the bulk properties such as porosity are adequately simulated.…”

Section: Discussionmentioning

confidence: 99%

“…Measurements of granular properties from images of planar sections through volumes of intact consolidated granular material [e.g., Fara and Scheidegger , 1961; Preston and Davis , 1976; Lin , 1982; Tovey and Hounslow , 1995; Prince et al , 1995; Van den Berg et al ., 2002; Neupauer and Powell , 2005; Torabi et al , 2008] and unconsolidated granular surfaces and vertical sections [e.g., Rubin , 2004; Carbonneau et al , 2004; Graham et al , 2005; Buscombe , 2008; Buscombe and Masselink , 2009; Warrick et al , 2009; Buscombe et al , 2010] are designed to give rapid yet highly accurate estimates of sediment structure (for example, packing, porosity, and dominant orientation) and particle properties (principally, particle size, shape, concentration, packing) in the field and laboratory. The goal is to estimate particle size statistics in situ using images of the surface of sediment which is interacting with fluid flows at a given instant in time.…”

Section: Introductionmentioning

confidence: 99%

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Advances in the simulation and automated measurement of well‐sorted granular material: 1. Simulation

Buscombe

Rubin

2012

J. Geophys. Res.

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[1] In this, the first of a pair of papers which address the simulation and automated measurement of well-sorted natural granular material, a method is presented for simulation of two-phase (solid, void) assemblages of discrete non-cohesive particles. The purpose is to have a flexible, yet computationally and theoretically simple, suite of tools with well constrained and well known statistical properties, in order to simulate realistic granular material as a discrete element model with realistic size and shape distributions, for a variety of purposes. The stochastic modeling framework is based on three-dimensional tessellations with variable degrees of order in particle-packing arrangement. Examples of sediments with a variety of particle size distributions and spatial variability in grain size are presented. The relationship between particle shape and porosity conforms to published data. The immediate application is testing new algorithms for automated measurements of particle properties (mean and standard deviation of particle sizes, and apparent porosity) from images of natural sediment, as detailed in the second of this pair of papers. The model could also prove useful for simulating specific depositional structures found in natural sediments, the result of physical alterations to packing and grain fabric, using discrete particle flow models. While the principal focus here is on naturally occurring sediment and sedimentary rock, the methods presented might also be useful for simulations of similar granular or cellular material encountered in engineering, industrial and life sciences.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Advances in the simulation and automated measurement of well‐sorted granular material: 1. Simulation

Buscombe

Rubin

2012

J. Geophys. Res.

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“… Buscombe and Masselink [2009] showed that the spatial autocorrelation algorithm was one of several suitable techniques which could be used within the calibration framework of Rubin [2004], including variograms and spectra. Buscombe [2008], drawing from work utilizing variance spectra of sedimentary rock thin sections to describe their stochastic geometry [e.g., Preston and Davis , 1976; Lin , 1982], described a technique using the two‐dimensional correlogram of an image in order to estimate the major and minor grain diameters. Furthermore, it was suggested that the diameter of some contour between 0 and 1 of the two‐dimensional surface of autocorrelation from an image of sediment should be related to the mean grain size, which in turn suggested that an uncalibrated estimate of mean grain size directly from the image might be possible.…”

Section: Introductionmentioning

confidence: 99%

A universal approximation of grain size from images of noncohesive sediment

2010

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[1] The two-dimensional spectral decomposition of an image of sediment provides a direct statistical estimate, grid-by-number style, of the mean of all intermediate axes of all single particles within the image. We develop and test this new method which, unlike existing techniques, requires neither image processing algorithms for detection and measurement of individual grains, nor calibration. The only information required of the operator is the spatial resolution of the image. The method is tested with images of bed sediment from nine different sedimentary environments (five beaches, three rivers, and one continental shelf), across the range 0.1 mm to 150 mm, taken in air and underwater. Each population was photographed using a different camera and lighting conditions. We term it a "universal approximation" because it has produced accurate estimates for all populations we have tested it with, without calibration. We use three approaches (theory, computational experiments, and physical experiments) to both understand and explore the sensitivities and limits of this new method. Based on 443 samples, the root-mean-squared (RMS) error between size estimates from the new method and known mean grain size (obtained from point counts on the image) was found to be ±≈16%, with a 95% probability of estimates within ±31% of the true mean grain size (measured in a linear scale). The RMS error reduces to ≈11%, with a 95% probability of estimates within ±20% of the true mean grain size if point counts from a few images are used to correct bias for a specific population of sediment images. It thus appears it is transferable between sedimentary populations with different grain size, but factors such as particle shape and packing may introduce bias which may need to be calibrated for. For the first time, an attempt has been made to mathematically relate the spatial distribution of pixel intensity within the image of sediment to the grain size.

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“…Such a field is completely described, in a statistical sense, by the power spectrum Ψ ( k ), or equivalently its Fourier transform, the autocorrelation function R ( l ) (over l lags):

R (l) = \int_{- \infty}^{+ \infty} Ψ (k) e^{- i k l} d l

and

Ψ (k) = \frac{1}{2 π} \int_{- \infty}^{+ \infty} R (x) e^{- i k l} d l

where k and i are the wave number vector and imaginary unit, respectively. The centered, symmetrical 2D Fourier transform is the analytical equivalent to a diffraction pattern of a granular material body [ Preston and Davis , 1976] without the phase problem of capturing a 2D representation of a 3D volume. This transform has enjoyed widespread use in the description [ Prince et al , 1995] and reconstruction [ Liang et al , 1998] of granular material.…”

Section: Methods For Estimating Arithmetic Mean and Sortingmentioning

confidence: 99%

“…where k and i are the wave number vector and imaginary unit, respectively. The centered, symmetrical 2D Fourier transform is the analytical equivalent to a diffraction pattern of a granular material body [Preston and Davis, 1976] without the phase problem of capturing a 2D representation of a 3D volume. This transform has enjoyed widespread use in the description [Prince et al, 1995] and reconstruction [Liang et al, 1998] of granular material.…”

Section: Stochastic Properties Of An Image Of Sedimentmentioning

confidence: 99%

Advances in the simulation and automated measurement of well‐sorted granular material: 2. Direct measures of particle properties

Buscombe

Rubin

2012

J. Geophys. Res.

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[1] In this, the second of a pair of papers on the structure of well-sorted natural granular material (sediment), new methods are described for automated measurements from images of sediment, of: 1) particle-size standard deviation (arithmetic sorting) with and without apparent void fraction; and 2) mean particle size in material with void fraction. A variety of simulations of granular material are used for testing purposes, in addition to images of natural sediment. Simulations are also used to establish that the effects on automated particle sizing of grains visible through the interstices of the grains at the very surface of a granular material continue to a depth of approximately 4 grain diameters and that this is independent of mean particle size. Ensemble root-mean squared error between observed and estimated arithmetic sorting coefficients for 262 images of natural silts, sands and gravels (drawn from 8 populations) is 31%, which reduces to 27% if adjusted for bias (slope correction between observed and estimated values). These methods allow non-intrusive and fully automated measurements of surfaces of unconsolidated granular material. With no tunable parameters or empirically derived coefficients, they should be broadly universal in appropriate applications. However, empirical corrections may need to be applied for the most accurate results. Finally, analytical formulas are derived for the one-step pore-particle transition probability matrix, estimated from the image's autocorrelogram, from which void fraction of a section of granular material can be estimated directly. This model gives excellent predictions of bulk void fraction yet imperfect predictions of pore-particle transitions.Citation: Buscombe, D., and D. M. Rubin (2012), Advances in the simulation and automated measurement of well-sorted granular material: 2. Direct measures of particle properties,

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Sedimentary Porous Materials as a Realization of a Stochastic Process

Cited by 12 publications

References 12 publications

Advances in the simulation and automated measurement of well‐sorted granular material: 1. Simulation

Advances in the simulation and automated measurement of well‐sorted granular material: 1. Simulation

A universal approximation of grain size from images of noncohesive sediment

Advances in the simulation and automated measurement of well‐sorted granular material: 2. Direct measures of particle properties

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