Transition probability-based indicator geostatistics

Carle, Steven F.; Fogg, Graham E.

doi:10.1007/bf02083656

Cited by 439 publications

(369 citation statements)

References 14 publications

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“…First, note that the mean length of the units is the same for each curve in Figure 6. Thus the near-origin behavior, which is defined by the mean length [see Carle and Fogg, 1996], is identical for each curve. However, the effective structural range is different among the curves.…”

Section: As Given By Equation (A20)mentioning

confidence: 99%

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

Ritzi

Dai

Dominic

et al. 2004

Water Resources Research

104

167

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[1] Cross-stratified deposits can give rise to a hierarchy of permeability modes, across scales, corresponding to a hierarchy of sedimentary unit types. The shape of the sample semivariogram for permeability can be largely controlled by the shape of the crosstransition probabilities of unit types having the greatest contrast in permeability. The shape of those cross-transition probabilities can be, in turn, largely determined by the variance of the lengths of those unit types. A sufficient condition for an exponential-like semivariogram is the repeated occurrence of unit types having both a contrast in permeability and a large length variance. These relationships are shown through writing the identities for spatial correlation of permeability in a hierarchical and multimodal form and as a function of the transition probabilities for the sedimentary unit types. These relationships are also illustrated through analyzing data representing cross-stratified sediments within a point bar deposit.

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Section: As Given By Equation (A20)mentioning

confidence: 99%

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

Ritzi

Dai

Dominic

et al. 2004

Water Resources Research

104

167

View full text Add to dashboard Cite

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“…Existing strategies include: [a] indicator co-kriging with complementary variables, like probability kriging (Sullivan 1984) and cumulative distribution function of order statistics kriging (Juang et al 1998); [b] better characterization of indicator crosscovariance structures, like indicator principal component kriging (Suro-Perez and Journel 1991), successive kriging of indicators (Vargas-Guzman and Dimitrakopoulos 2003) or the use of transition probabilities (Carle and Fogg 1996); the Disjunctive Kriging (Matheron 1976, DK) estimation of the cpdf. None of these methods completely eliminate the order relation problems (Carr and Mao 1993;Carle and Fogg 1996).…”

Section: Introductionmentioning

confidence: 99%

Indicator Kriging without Order Relation Violations

Tolosana‐Delgado

Pawlowsky‐Glahn

Egozcue³

2008

Math Geosci

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Indicator kriging (IK) is a spatial interpolation technique aimed at estimating the conditional cumulative distribution function (ccdf) of a variable at an unsampled location. Obtained results form a discrete approximation to this ccdf, and its corresponding discrete probability density function (cpdf) should be a vector, where each component gives the probability of an occurrence of a class. Therefore, this vector must have positive components summing up to one, like in a composition in the simplex. This suggests a simplicial approach to IK, based on the algebraic-geometric structure of this sample space: simplicial IK actually works with log-odds. Interpolated log-odds can afterwards be easily re-expressed as the desired cpdf or ccdf. An alternative but equivalent approach may also be based on log-likelihoods. Both versions of the method avoid by construction all conventional IK standard drawbacks: estimates are always within the (0, 1) interval and present no order-relation problems (either with kriging or co-kriging). Even the modeling of indicator structural functions is clarified.

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“…volumes), obtained using conditioned SIS varying variogram ranges, were compared with those from the IK facies reconstruction, in order to test the hypothesis that the data spacing is sufficiently small to allow deterministic correlation of the wells. In theory, when the variogram range increases, and the proportions are kept constant, the mean dimensions of sand bodies should also increase (Carle and Fogg 1996;Ritzi 2000;Guardiola-Albert and Gómez-Hernández 2001). Figure 7 shows the mean size of sand bodies derived from SIS with several horizontal ranges, and the mean size of sand bodies from the IK reconstruction with the experimentally fitted ranges ( Figure 6).…”

Section: Suitability Of Data To Describe the Sand Bodiesmentioning

confidence: 99%

Large to intermediate-scale aquifer heterogeneity in fine-grain dominated alluvial fans (Cenozoic As Pontes Basin, northwestern Spain): insight based on three-dimensional geostatistical reconstruction

2007

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Facies reconstructions are used in hydrogeology to improve the interpretation of aquifer permeability.. In the absence of sufficient data to define the heterogeneity due to geological processes, uncertainties in the distribution of aquifer hydrofacies and characteristics may appear. Geometric and geostatistical methods are used to understand and model aquifer hydrofacies distribution, providing models to improve comprehension and development of aquifers. However, these models require some input statistical parameters that can be difficult to infer from the study site. A 3D reconstruction of a kilometer scale fine-grain dominated Cenozoic alluvial fan derived from a large number of continuously cored, closely spaced, and regularly distributed wells is presented. The facies distributions were reconstructed using a genetic stratigraphic subdivision and a deterministic geostatistical algorithm. The reconstruction is slightly affected by variations in the geostatistical input parameters because of the high-density data set. Analysis of the reconstruction allowed identification in the proximal to medial alluvial fan zones of several laterally extensive sand bodies with relatively higher permeability; these sand bodies were quantified in terms of volume, mean thickness, maximum area, and maximum equivalent diameter. These quantifications provide trends and geological scenarios for input statistical parameters to model aquifer systems in similar alluvial fan depositional settings.

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Transition probability-based indicator geostatistics

Cited by 439 publications

References 14 publications

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

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

Indicator Kriging without Order Relation Violations

Large to intermediate-scale aquifer heterogeneity in fine-grain dominated alluvial fans (Cenozoic As Pontes Basin, northwestern Spain): insight based on three-dimensional geostatistical reconstruction

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