2006
DOI: 10.1029/2004wr003755
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Aquifer operator scaling and the effect on solute mixing and dispersion

Abstract: [1] Since aquifer parameters may have statistical dependence structures that are present across a huge range of scales, the concepts of fractional Brownian motion (fBm) have been used in both analytic and numerical stochastic settings. Most previous models have used isotropic scaling characterized by a single scalar Hurst coefficient. Any real-world anisotropy has been handled by an elliptical stretching random K field. We define a d-dimensional extension of fBm in which the fractional-order integration may ta… Show more

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Cited by 75 publications
(88 citation statements)
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“…We mention that the conditions of Theorem 2.1 of Kuelbs, Li and Shao (1995) can be weakened in a similar way. Then there exist positive constants c 4,6 and c 4,7 such that for all ε ∈ (0, 1),…”
Section: Small Ball Probability and Chung's Law Of The Iterated Logarmentioning
confidence: 99%
“…We mention that the conditions of Theorem 2.1 of Kuelbs, Li and Shao (1995) can be weakened in a similar way. Then there exist positive constants c 4,6 and c 4,7 such that for all ε ∈ (0, 1),…”
Section: Small Ball Probability and Chung's Law Of The Iterated Logarmentioning
confidence: 99%
“…, H N ) ∈ (0, 1) N . We should mention that several authors have been interested in applying anisotropic Gaussian random fields to stochastic modelling; see, for example, Bonami and Estrade [9] for bone structure modelling, and Benson et al [7] for modelling aquifer structure in hydrology. We hope that the results and techniques in this article will be helpful for studying more general anisotropic Gaussian random fields.…”
Section: Introductionmentioning
confidence: 99%
“…An interest to the anisotropic self-similar random fields is motivated by the applications coming from the climatological and environmental sciences (see [10,11]). Several authors have proposed to apply such random fields for modelling phenomena in spatial statistics, stochastic hydrology and image processing (see [2,3,4]). …”
Section: Definitionmentioning
confidence: 99%