Spatial correlation of permeability in cross‐stratified sediment with hierarchical architecture

Ritzi, Robert W.; Dai, Zhenxue; Dominic, David F.; Rubin, Yoram

doi:10.1029/2003wr002420

Cited by 104 publications

(174 citation statements)

References 43 publications

(94 reference statements)

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“…Grouping the same level I units differently into channel and interchannel unit types (Figure 3) also results in distinct permeabilty modes as shown in Figure 4c. Furthermore, it is likely that unit types still smaller in scale than the level I units can be defined as having distinct permeability modes [e.g., Ritzi et al, 2004]. Whether distinctions in permeability need to be made at any given scale depends on the context: what might be parsimonious for one purpose may not have enough detail for another.…”

Section: Conceptual Framework For Sedimentary Architecturementioning

confidence: 99%

“…[12] Sedimentary deposits are often conceptualized as having hierarchical organization and the conceptual hierarchy can be linked to permeability modes [e.g., Ritzi et al, 2004]. There may be contexts in which using a hierarchy of units is beneficial.…”

Section: Conceptual Framework For Sedimentary Architecturementioning

confidence: 99%

“…Importantly, Lu and Zhang [2002] and Ritzi et al [2004] related the spatial bivariate statistics for permeability to transition probabilities that represent the aquifer architecture Fogg, 1996, 1997]. Ritzi et al [2004] examined such relationships for cross-stratified deposits having hierarchical permeability modes and showed that the shape and range of the composite sample semivariogram can be determined largely by the cross-transition probabilities for those unit types that create large permeability contrasts and that occur in greater proportions. Ritzi [2000] showed that a sufficient condition for exponentiallike cross-transition probabilities is a relatively large coefficient of variation in the lengths of these units in the direction for which the sample semivariogram is determined.…”

Section: Introductionmentioning

confidence: 99%

“…[4] Recently, attention has been focused on linking semivariograms to permeability modes and to facies architecture [Davis et al, 1993[Davis et al, , 1997Allen-King et al, 1998;Ritzi et al, 2004;Dai et al, 2004a;Gaud et al, 2004]. In related work, expressions have been developed for bivariate spatial statistics, including the semivariogram in bimodal domains [Rubin, 1995], multimodal domains [Lu and Zhang, 2002;Zhang, 2002;Barrash and Clemo, 2002], and hierarchical multimodal domains [Ritzi et al, 2002[Ritzi et al, , 2004Dai et al, 2004b].…”

Section: Introductionmentioning

confidence: 99%

“…In related work, expressions have been developed for bivariate spatial statistics, including the semivariogram in bimodal domains [Rubin, 1995], multimodal domains [Lu and Zhang, 2002;Zhang, 2002;Barrash and Clemo, 2002], and hierarchical multimodal domains [Ritzi et al, 2002[Ritzi et al, , 2004Dai et al, 2004b]. Importantly, Lu and Zhang [2002] and Ritzi et al [2004] related the spatial bivariate statistics for permeability to transition probabilities that represent the aquifer architecture Fogg, 1996, 1997]. Ritzi et al [2004] examined such relationships for cross-stratified deposits having hierarchical permeability modes and showed that the shape and range of the composite sample semivariogram can be determined largely by the cross-transition probabilities for those unit types that create large permeability contrasts and that occur in greater proportions.…”

Section: Introductionmentioning

confidence: 99%

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Improving permeability semivariograms with transition probability models of hierarchical sedimentary architecture derived from outcrop analog studies

Dai

Ritzi

Dominic

2005

Water Resources Research

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[1] As analogs for aquifers, outcrops of sedimentary deposits allow sedimentary units to be mapped, permeability to be measured with high resolution, and sedimentary architecture to be related to the univariate and spatial bivariate statistics of permeability. Sedimentary deposits typically can be organized into hierarchies of unit types and associated permeability modes. The types of units and the number of hierarchical levels defined on an outcrop might vary depending upon the focus of the study. Regardless of how the outcrop sediments are subdivided, a composite bivariate statistic like the permeability semivariogram is a linear summation of the autosemivariograms and cross semivariograms for the unit types defined, weighted by the proportions and transition probabilities associated with the unit types. The composite sample semivariogram will not be representative unless data locations adequately define these transition probabilities. Data reflecting the stratal architecture can often be much more numerous than permeability measurements. These lithologic data can be used to better define transition probabilities and thus improve the estimates of the composite permeability semivariogram. In doing so, bias created from the incomplete exposure of units can be reduced by a Bayesian approach for estimating unit proportions and mean lengths. We illustrate this methodology with field data from an outcrop in the Española Basin, New Mexico.Citation: Dai, Z., R. W. Ritzi Jr., and D. F. Dominic (2005), Improving permeability semivariograms with transition probability models of hierarchical sedimentary architecture derived from outcrop analog studies, Water Resour. Res., 41, W07032,

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Section: Conceptual Framework For Sedimentary Architecturementioning

confidence: 99%

Section: Conceptual Framework For Sedimentary Architecturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Improving permeability semivariograms with transition probability models of hierarchical sedimentary architecture derived from outcrop analog studies

Dai

Ritzi

Dominic

2005

Water Resources Research

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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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Transverse mixing in three-dimensional nonstationary anisotropic heterogeneous porous media

et al. 2015

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Groundwater plumes originating from continuously emitting sources are typically controlled by transverse mixing between the plume and reactants in the ambient solution. In two-dimensional domains, heterogeneity causes only weak enhancement of transverse mixing in steady-state flows. In threedimensional domains, more complex flow patterns are possible because streamlines can twist. In particular, spatially varying orientation of anisotropy can cause steady-state groundwater whirls. We analyze steadystate solute transport in three-dimensional locally isotropic heterogeneous porous media with blockwise anisotropic correlation structure, in which the principal directions of anisotropy differ from block to block. For this purpose, we propose a transport scheme that relies on advective transport along streamlines and transverse-dispersive mass exchange between them based on Voronoi tessellation. We compare flow and transport results obtained for a nonstationary anisotropic log-hydraulic conductivity field to an equivalent stationary field with identical mean, variance, and two-point correlation function disregarding the nonstationarity. The nonstationary anisotropic field is affected by mean secondary motion and causes neighboring streamlines to strongly diverge, which can be quantified by the two-particle semivariogram of lateral advective displacements. An equivalent kinematic descriptor of the flow field is the advective folding of plumes, which is more relevant as precursor of mixing than stretching. The separation of neighboring streamlines enhances transverse mixing when considering local dispersion. We quantify mixing by the flux-related dilution index, which is substantially larger for the nonstationary anisotropic conductivity field than for the stationary one. We conclude that nonstationary anisotropy in the correlation structure has a significant impact on transverse plume deformation and mixing. In natural sediments, contaminant plumes most likely mix more effectively in the transverse directions than predicted by models that neglect the nonstationarity of anisotropy.

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Spatial correlation of permeability in cross‐stratified sediment with hierarchical architecture

Cited by 104 publications

References 43 publications

Improving permeability semivariograms with transition probability models of hierarchical sedimentary architecture derived from outcrop analog studies

Improving permeability semivariograms with transition probability models of hierarchical sedimentary architecture derived from outcrop analog studies

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

Transverse mixing in three-dimensional nonstationary anisotropic heterogeneous porous media

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