Numerical investigation of apparent multifractality of samples from processes subordinated to truncated fBm

Guadagnini, Alberto; Neuman, Shlomo P.; Riva, Mònica

doi:10.1002/hyp.8358

Cited by 29 publications

(53 citation statements)

References 72 publications

(117 reference statements)

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“…All scaling manifestations documented appear to be consistent with the interpretation proposed by [27], which is supported by theoretical [35,36], computational [19,27,29,37], and extensive experimental [17,18,20,21,33] evidence.…”

Section: Discussionsupporting

confidence: 83%

“…These cutoffs are intimately related to the breakdown in power-law scaling. Interpretations based on such modeling framework have been proven to be consistent with observations associated with a variety of laboratory and field scale hydrological and pedological data from sedimentary and fractured rocks [17][18][19][20]33]. With reference to ESS, a theoretical basis for Eq.…”

Section: Scaling Of Statisticssupporting

confidence: 54%

“…Following [11][12][13][14][15][16][17][18][19][20][21], statistical scaling of moments of velocity is investigated through the analysis of directional sample structure functions, i.e., qth-order statistical moments of absolute increments…”

Section: Scaling Of Statisticsmentioning

confidence: 99%

“…Indeed, the statistics of hydrological properties in aquifers and reservoirs exhibit dependences on various characteristic length scales, e.g., measurement volume and resolution, scale of observation, spatial correlation, and size of the sampled domain [10]. Scaling analyses of statistical moments of hydraulic conductivity and permeability data have been presented in many works, including [11][12][13][14][15][16][17][18][19][20]. In all these studies, measurement volumes are associated with a support scale ranging from the millimeter to the meter and data sets are collected on domains at the field (kilometer) or laboratory (decimeter to meter) scale.…”

Section: Introductionmentioning

confidence: 99%

“…Similar to [11][12][13][14][15][16][17][18][19][20][21], we do so by relying on the analysis of sample structure functions of order q > 0 of such increments. We then compare the scaling behaviors observed for static (i.e., local porosity and surface area) and dynamic (i.e., Lagrangian velocity) quantities, evaluated on the same rock samples.…”

Section: Introductionmentioning

confidence: 99%

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Statistical scaling of pore-scale Lagrangian velocities in natural porous media

et al. 2014

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We investigate the scaling behavior of sample statistics of pore-scale Lagrangian velocities in two different rock samples, Bentheimer sandstone and Estaillades limestone. The samples are imaged using x-ray computer tomography with micron-scale resolution. The scaling analysis relies on the study of the way qth-order sample structure functions (statistical moments of order q of absolute increments) of Lagrangian velocities depend on separation distances, or lags, traveled along the mean flow direction. In the sandstone block, sample structure functions of all orders exhibit a power-law scaling within a clearly identifiable intermediate range of lags. Sample structure functions associated with the limestone block display two diverse power-law regimes, which we infer to be related to two overlapping spatially correlated structures. In both rocks and for all orders q, we observe linear relationships between logarithmic structure functions of successive orders at all lags (a phenomenon that is typically known as extended power scaling, or extended self-similarity). The scaling behavior of Lagrangian velocities is compared with the one exhibited by porosity and specific surface area, which constitute two key pore-scale geometric observables. The statistical scaling of the local velocity field reflects the behavior of these geometric observables, with the occurrence of power-law-scaling regimes within the same range of lags for sample structure functions of Lagrangian velocity, porosity, and specific surface area.

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Section: Discussionsupporting

confidence: 83%

Section: Scaling Of Statisticssupporting

confidence: 54%

Section: Scaling Of Statisticsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Statistical scaling of pore-scale Lagrangian velocities in natural porous media

et al. 2014

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Anisotropic statistical scaling of vadose zone hydraulic property estimates near Maricopa, Arizona

et al. 2013

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[1] Fluid flow and mass transport in the vadose zone are strongly influenced by spatial variability in soil hydraulic properties. It has become common to characterize spatial variability geostatistically and to solve corresponding flow and/or transport problems stochastically. The typical (though not only) approach is to treat log saturated hydraulic conductivity, Y 5 log 10 K s , and perhaps other medium properties as statistically homogeneous, isotropic, or anisotropic multivariate-Gaussian random fields with unique variance and autocorrelation scale. A growing body of literature suggests that Y as well as many other variables may possess heavy-tailed, non-Gaussian distributions, and/or scaledependent statistical parameters representing a multiscale, hierarchical structure. Elsewhere, we have demonstrated that these important phenomena are difficult to detect, and are not fully tractable, with standard geostatistical methods. They are however detectable and tractable with a novel geostatistical method of analysis which treats such variables as samples from sub-Gaussian random fields subordinated to truncated fractional Brownian motion (tfBm) or truncated fractional Gaussian noise (tfGn). Each such field is a mixture of Gaussian components having random variances. The purpose of this paper is to explore the extent to which hydraulic parameters of unsaturated soils exhibit heavy-tailed distributions and statistical scaling of the above type. As a test bed we have selected an experimental site near Maricopa, Arizona, at which soil texture data have been collected in boreholes and trenches to a depth of 15 m over an area of 3600 m 2 . Since hydraulic parameters are difficult to measure to such depths we estimate them using a neural network pedotransfer model. Input data include percent sand, silt, and clay. Outputs include estimates of saturated and residual volumetric water content, saturated hydraulic conductivity, and (due to their wide applicability) parameters of the van Genuchten-Mualem constitutive model of unsaturated soil property variations with capillary pressure head. We find indeed that vertical and horizontal increments of our hydraulic parameter estimates exhibit heavy-tailed frequency distributions and statistical scaling which conform closely to our novel geostatistical framework. Its generality and applicability to the Maricopa site has far reaching implications vis-a-vis the geostatistical characterization of vadose zone properties and the stochastic modeling of flow and transport in unsaturated media at other sites.

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New scaling model for variables and increments with heavy‐tailed distributions

Riva

Neuman

Guadagnini

2015

Water Resources Research

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Many hydrological (as well as diverse earth, environmental, ecological, biological, physical, social, financial and other) variables, Y, exhibit frequency distributions that are difficult to reconcile with those of their spatial or temporal increments, DY. Whereas distributions of Y (or its logarithm) are at times slightly asymmetric with relatively mild peaks and tails, those of DY tend to be symmetric with peaks that grow sharper, and tails that become heavier, as the separation distance (lag) between pairs of Y values decreases. No statistical model known to us captures these behaviors of Y and DY in a unified and consistent manner. We propose a new, generalized sub-Gaussian model that does so. We derive analytical expressions for probability distribution functions (pdfs) of Y and DY as well as corresponding lead statistical moments. In our model the peak and tails of the DY pdf scale with lag in line with observed behavior. The model allows one to estimate, accurately and efficiently, all relevant parameters by analyzing jointly sample moments of Y and DY. We illustrate key features of our new model and method of inference on synthetically generated samples and neutron porosity data from a deep borehole.

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Numerical investigation of apparent multifractality of samples from processes subordinated to truncated fBm

Cited by 29 publications

References 72 publications

Statistical scaling of pore-scale Lagrangian velocities in natural porous media

Statistical scaling of pore-scale Lagrangian velocities in natural porous media

Anisotropic statistical scaling of vadose zone hydraulic property estimates near Maricopa, Arizona

New scaling model for variables and increments with heavy‐tailed distributions

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