Interval-valued kriging for geostatistical mapping with imprecise inputs

Bean, Brennan; Sun, Yan; Maguire, Marc

doi:10.1016/j.ijar.2021.10.003

Cited by 5 publications

(4 citation statements)

References 43 publications

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“…The nonnegativity constraint on weights { λ i , i = 1,⋯, k } ensures the non‐negativity of kriging variance (Bean et al., 2022) and restrains

\widehat{T}\left({\mathbf{x}}_{0},{\mathscr{l}}_{0}\right)

within the range [0,1] that gives an interpretable estimate on sand and non‐sand binary classification (Barnes & Johnson, 1984; Barnes & You, 1992; Deutsch, 1996; Herzfeld, 1989). The regularization coefficient β is set as c H + c V to balance the importance of interval estimation variance and the regularization term.…”

Section: Methodsmentioning

confidence: 99%

“…The nonnegativity constraint on weights {λ i ,i = 1,⋯,k} ensures the non-negativity of kriging variance (Bean et al, 2022) and restrains T(x 0 ,l 0 ) within the range [0,1] that gives an interpretable estimate on sand and nonsand binary classification (Barnes & Johnson, 1984;Barnes & You, 1992;Deutsch, 1996;Herzfeld, 1989).…”

Section: Interval Estimation Variance Minimizationmentioning

confidence: 99%

“…Change of support has been explored by mining and petroleum engineers (Journel & Huijbregts, 1978; Olea, 1999), soil scientists (Goovaerts, 1999, 2008), and ecologists (Gotway & Young, 2005) to handle upscaling issues or to synthesize different sources of data (Gotway & Young, 2002, 2007; Kupfersberger et al., 1998). Besides, kriged value can bear uncertainties by adopting interval‐valued random functions into kriging estimation (Bean et al., 2022; Diamond, 1988, 1989; Journel, 1986). Despite broad adoption in geological modeling, kriging methods suffer from the smoothing effect—whereby the local variability of estimates is mitigated through the minimization of estimation variance (Journel & Huijbregts, 1978).…”

Section: Introductionmentioning

confidence: 99%

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Borehole‐Based Interval Kriging for 3D Lithofacies Modeling

Song,

Tsai

2024

Water Resources Research

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Developing a three‐dimensional (3D) lithofacies model from boreholes is critical for providing a coherent understanding of complex subsurface geology, which is essential for groundwater studies. This study aims to introduce a new geostatistical method—interval kriging—to efficiently conduct 3D borehole‐based lithological modeling with sand/non‐sand binary indicators. Interval kriging is a best linear unbiased estimator for irregular interval supports. Interval kriging considers 3D anisotropies between two orthogonal components—a horizontal plane and a vertical axis. A new 3D interval semivariogram is developed. To cope with the nonconvexity of estimation variance, the minimization of estimation variance is regulated with an additional regularization term. The minimization problem is solved by a global‐local genetic algorithm embedded with quadratic programming and Brent's method to obtain kriging weights and kriging length. Four numerical and real‐world case studies demonstrate that interval kriging is more computationally efficient than 3D kriging because the covariance matrix is largely reduced without sacrificing borehole data. Moreover, interval kriging produces more realistic geologic characteristics than 2.5D kriging, while conditional to spatial borehole data. Compared to the multiple‐point statistics (MPS) algorithm—SNESIM, interval kriging can reproduce the geological architecture and spatial connectivity of channel‐type features, meanwhile producing tabular‐type features with better connectivity. Because the regularization term constrains kriged value toward 0 or 1, interval kriging produces more certainty in sand/non‐sand classification than 2.5D kriging, 3D kriging, and SNESIM. In conclusion, interval kriging is an effective and efficient 3D geostatistical algorithm that can capture the 3D structural complexity while significantly reducing computational time.

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“…The nonnegativity constraint on weights { λ i , i = 1,⋯, k } ensures the non‐negativity of kriging variance (Bean et al., 2022) and restrains

\widehat{T}\left({\mathbf{x}}_{0},{\mathscr{l}}_{0}\right)

Section: Methodsmentioning

confidence: 99%

Section: Interval Estimation Variance Minimizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Borehole‐Based Interval Kriging for 3D Lithofacies Modeling

Song,

Tsai

2024

Water Resources Research

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“…Kriging interpolation was developed in the 1960s to estimate gold deposited in a rock from a few random core samples (Beana, Sun & Maguire, 2022). Since then, kriging has found its way into other scientific disciplines.…”

Section: Kriging Interpolationmentioning

confidence: 99%

Spatial distribution prediction for the ground water quality in Mosul City (Iraq) using variogram equations

Ibrahim

Al-Tamir

2023

srees

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The GIS-aided spatial interpolation was applied on collected groundwater data to predict selected parameters (i.e., pH, electrical conductivity, and temperature) for the selected water wells distributed over Mosul City in Iraq. A descriptive statistical analysis was conducted on collected samples to explore the statistical indices. The skewness test was also employed to test the distribution of data sets around their mean values. The natural logarithms function achieved least skewness values and thus was applied to transfer data sets in order to adjust normality of the data sets distribution. Among all applied semivariogram models, the J-Bessel semivariogram model was optimal in terms of root mean square error (RMSE) values. The average standard errors were 0.2217, 740.5, and 1.209 for pH, EC, and temperature, respectively.

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