Stochastic Reconstruction of Chalk Samples Containing Vuggy Porosity Using a Conditional Simulated Annealing Technique

Talukdar, Meenakshi; Torsæter, Ole; Howard, James W.

doi:10.1023/b:tipm.0000032737.59531.cf

Cited by 12 publications

(4 citation statements)

References 29 publications

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“…Numerous studies took advantage of the flexibility of the SA model to address this issue experimentally, essentially in the case of isotropic materials. The observed trend is that SA reconstructions combining the covariance with additional information are generally closer to the reference isotropic media than those produced from the covariance only (Rintoul & Torquato, 1997;Yeong & Torquato, 1998a,b;Cule & Torquato, 1999;Manwart & Hilfer, 1999;Sheehan & Torquato, 2001;Talukdar et al ., 2002Talukdar et al ., , 2004. In the less studied anisotropic case, Cule & Torquato (1999) observed that an SA process constrained by a volume average covariance depending on a vector distance leads exactly to the reference ordered anisotropic media, namely 2D checkerboards and arrays of squares.…”

Section: The Phase-retrieval Problemmentioning

confidence: 99%

“…The applicability of this empirical criterion requires several assumptions: (1) a covariance depending on two (h x , h y ) or three (h x , h y , h z ) variables and (2) the finiteness of the binary object attached to the evaluation of the reference covariance function. The SA-based isotropic numerical experiments referenced above (Rintoul & Torquato, 1997;Yeong & Torquato, 1998a,b;Cule & Torquato, 1999;Manwart & Hilfer, 1999;Sheehan & Torquato, 2001;Talukdar et al, 2002Talukdar et al, , 2004 do not fall within these assumptions: the accommodated radially averaged covariance depends on a single variable; the infinitesize limit is implicitly reached when considering hypothetical/ theoretical (isotropic) materials. The current criterion cannot apply accordingly to these studies, and it is observed that agreement between the correlation functions of the reference and reconstructed systems does not ensure that the structures of the two systems will match closely (Yeong & Torquato, 1998a).…”

Section: (5)mentioning

confidence: 99%

“…1. The simulated annealing (SA) strategy has emerged in recent years as another popular stochastic method to produce numerical media with specified correlation functions (Rintoul & Torquato, 1997;Hazlett, 1997;Yeong & Torquato, 1998a,b;Cule & Torquato, 1999;Manwart & Hilfer, 1999;Sheehan & Torquato, 2001;Talukdar et al ., 2002Talukdar et al ., , 2004Torquato, 2002). Within the SA optimization framework, the porosity and covariance (to which the GRF model is intrinsically limited) may be complemented or replaced by various statistical measures, including the lineal path function (Lu & Torquato, 1992), the chord length distribution (Torquato & Lu, 1993), the pore size distribution (Coker & Torquato, 1995) and the coarseness (Lu & Torquato, 1990).…”

Section: Introductionmentioning

confidence: 99%

“…A great deal of the answer is related to our ability to quantify the nature and quantity of information carried by the morphological constraints conditioning the model. Many authors have relied on the SA process of reconstruction to shed light on the information contained in the statistical functions that are implemented, essentially by comparing simulated media with reference ones (Yeong & Torquato, 1998a,b;Cule & Torquato, 1999;Manwart & Hilfer, 1999;Sheehan & Torquato, 2001;Talukdar et al ., 2002Talukdar et al ., , 2004. Following these works, and as far as isotropic media are concerned, the general observation is that SA reconstructions combining the covariance with additional morphological measures (commonly the lineal path function) are closer to reference media than reconstructions relying on the covariance only.…”

Section: Introductionmentioning

confidence: 99%

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Practical modelling of porous media from second‐order statistics: the phase‐retrieval problem and the interpretation of the covariance

Anguy

Trong

Ehrlich

2005

Journal of Microscopy

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Key words. Covariance, image modelling, models of random porous microstructures, phase retrieval problem. SummaryIn many disciplines, binary numerical porous media are commonly generated as realizations of a random process characterized by a limited set of morphological measurements, e.g. the conditioning and truncated Gaussian random field (GRF) model or the Monte Carlo simulated annealing (SA) reconstruction. Whether the output microstructures of a model are quantitative or qualitative depends largely on the information carried by the constraints that are implemented. We focus on the standard two-point correlation function, also referred to as the covariance. The isotropic situation has been previously extensively studied. Here, we concentrate on a vector distancedependent covariance. Relying on practical solutions to the phase-retrieval problem (retrieving an object from its Fourier modulus) encountered in general imaging, we show empirically that a finite binary two-or three-dimensional actual sample can be recovered systematically to within a pixel from its correlation integral (the volume average covariance to within a scale factor). In random modelling, this characteristic, describing uniquely a single sample of finite size, must be simplified, i.e. reduced to its statistical content, prior to be fitted in a random model (GRF, SA) as the characteristic of a series of realizations of a porous medium. We consider a common simplification, i.e. truncation, in which that part of the covariance relating to the small-scale features of the observed sample is preserved only. This arbitrary simplification is empirically supported by numerous published numerical experiments showing that the small-scale content of a volume-averaged covariance can be fairly well reproduced in realizations of various random models: its statistical nature is thus illustrated with the GRF model. The unique solution to the phase-retrieval problem confers an important sense to this numerical agreement: the correlation integral being the most complete descriptor, the actual sample and the model outputs are considered as true analogues over scales smaller or equal to the cutoff length attached to the truncation. Thus, awareness of the phase-retrieval problem supports on an empirical basis the generation of synthetic binary objects from a direct measurement on an available sample. IntroductionIn many disciplines including biology, medicine, petroleum engineering and water exploration, it may be of the greatest interest to generate numerical media from morphological information measured on a finite support [a two-dimensional (2D) digitized thin section or a 3D image obtained by X-ray microtomography] of size smaller than the whole system of interest. The conditioning and truncated Gaussian random field (GRF) model is an example of a widely used technique for producing synthetic media from a minimal set of morphological descriptors: the standard one-point and two-point correlation functions. The one-point correlation function is the classical s...

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