Multivariate Imputation of Unequally Sampled Geological Variables

Barnett, Ryan M.; Deutsch, Clayton V.

doi:10.1007/s11004-014-9580-8

Cited by 18 publications

(12 citation statements)

References 29 publications

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“…They believe that in cokriging estimates with variancebased cross-variograms, the variables can be measure with a different mean and scale. Foehn et al (2018) used the pseudo cross variogram to compute the linear model corregionalization to de-velop a methodology called regression cokriging in heterotopic data applied in meteorological data When the dataset is heterotopic, Barnett and Deutsch (2015) and Silva and Deutsch (2018) proposed multiple imputation (MI) to integrate secondary data into geostatistical simulations. The main idea of MI is to perform the geostatistical simulations in two steps.…”

Section: Mining Mineraçãomentioning

confidence: 99%

Geostatistical simulations with heterotopic hard and soft data without modeling the linear model of coregionalization

et al. 2021

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Most mining decisions are based on models estimated/simulated given the information obtained from samples. During the exploration stage, samples are commonly taken using diamond drill holes which are accurate and precise. These samples are considered hard data. In the production stage, new samples are added. These last are cheaper and more abundant than the drill hole samples, but imprecise and are here named as soft data. Usually hard and soft data are not sampled at the same locations, they form a heterotopic dataset. This article proposes a framework for geostatistical simulation with completely heterotopic soft data. The simulation proceeds in two steps. First, the variable of interest at the locations where soft data are available is simulated. The local conditional distributions built at these locations consider both hard and soft data and are obtained using simple cokriging with the intrinsic coregionalization model. Second, the variable of interest in the entire simulation grid using the original and previously simulated values at soft data locations is simulated. The results show that the information from soft data improved both the accuracy and precision of the simulated models. The proposed framework is illustrated by a case study with data obtained from an underground copper mine.

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Section: Mining Mineraçãomentioning

confidence: 99%

Geostatistical simulations with heterotopic hard and soft data without modeling the linear model of coregionalization

et al. 2021

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“…A sequential univariate outlier detection procedure (Ben-Gal, 2005) was applied to the data to find possible outlying values that deviate to a high extent from the other observations (Barnett and Lewis, 1974;Hawkins, 1980). During the procedure, the time series of the stations were compared pairwise for each year.…”

Section: Data Preprocessingmentioning

confidence: 99%

“…Because most modern data imputation methods start by assuming the missing data are MAR, imputation tools could have been applied in years with insufficient data density for proper interpolation. However, in every case, no method can provide an "automatic" solution to the problem of missing data, and any approach must be used with caution considering the context of the problem (Kenward and Carpenter, 2007); for instance, the accuracy of the imputed value will not be optimal, and the spatial correlation and intravariable relationships will be corrupted (Barnett and Deutsch, 2015).…”

Section: Derivation Of Amount-weighted Annual Mean Precipitation Tritmentioning

confidence: 99%

Isoscape of amount-weighted annual mean precipitation tritium (<sup>3</sup>H) activity from 1976 to 2017 for the Adriatic–Pannonian region – AP<sup>3</sup>H_v1 database

Kern

Erdélyi²,

Vreča

et al. 2020

Earth Syst. Sci. Data

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Abstract. Tritium (3H) as a constituent of the water molecule is an important natural tracer in hydrological sciences. The anthropogenic tritium introduced into the atmosphere unintentionally became an excellent tracer of processes on a time scale of up to 100 years. A prerequisite for tritium applications is to know the distribution of tritium activity in precipitation. Here we present a database of isoscapes derived from 41 stations for amount-weighted annual mean tritium activity in precipitation for the period 1976 to 2017 on spatially continuous interpolated 1 km×1 km grids for the Adriatic–Pannonian region (called the AP3H_v1 database), with a special focus on post-2010 years, which are not represented by existing global models. Five stations were used for out-of-sample evaluation of the model performance, independently confirming its capability of reproducing the spatiotemporal tritium variability in the region. The AP3H database is capable of providing reliable spatiotemporal input for hydrogeological application at any place within Slovenia, Hungary, and their surroundings. Results also show a decrease in the average spatial representativity of the stations regarding tritium activity in precipitation from ∼440 km in 1970s, when bomb tritium still prevailed in precipitation, to ∼235 km in the 2010s. The post-2010 isoscapes can serve as benchmarks for background tritium activity for the region, helping to determine potential future local increases in technogenic tritium from these backgrounds. The gridded tritium isoscape is available in NetCDF-4 at https://doi.org/10.1594/PANGAEA.896938 (Kern et al., 2019).

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“…A supersecondary approach was implemented here with sequential Gaussian simulation. This method requires homotopic sampling of all variables, so this approach was augmented with data imputation (Barnett and Deutsch 2015) to realize complete homotopic data sets. The supersecondary workflow followed incorporating data imputation is outlined in Figure 2.…”

Section: Modeling Workflowmentioning

confidence: 99%

Spatial Modeling of Geometallurgical Properties: Techniques and a Case Study

et al. 2015

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High-resolution spatial numerical models of metallurgical properties constrained by geological controls and more extensively by measured grade and geomechanical properties constitute an important part of geometallurgy. Geostatistical and other numerical techniques are adapted and developed to construct these high-resolution models accounting for all available data. Important issues that must be addressed include unequal sampling of the metallurgical properties versus grade assays, measurements at different scale, and complex nonlinear averaging of many metallurgical parameters. This paper establishes techniques to address each of these issues with the required implementation details and also demonstrates geometallurgical mineral deposit characterization for a copper-molybdenum deposit in South America. High-resolution models of grades and comminution indices are constructed, checked, and are rigorously validated. The workflow demonstrated in this case study is applicable to many other deposit types.

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Multivariate Imputation of Unequally Sampled Geological Variables

Cited by 18 publications

References 29 publications

Geostatistical simulations with heterotopic hard and soft data without modeling the linear model of coregionalization

Geostatistical simulations with heterotopic hard and soft data without modeling the linear model of coregionalization

Isoscape of amount-weighted annual mean precipitation tritium (<sup>3</sup>H) activity from 1976 to 2017 for the Adriatic–Pannonian region – AP<sup>3</sup>H_v1 database

Spatial Modeling of Geometallurgical Properties: Techniques and a Case Study

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Multivariate Imputation of Unequally Sampled Geological Variables

Cited by 18 publications

References 29 publications

Geostatistical simulations with heterotopic hard and soft data without modeling the linear model of coregionalization

Geostatistical simulations with heterotopic hard and soft data without modeling the linear model of coregionalization

Isoscape of amount-weighted annual mean precipitation tritium (&lt;sup&gt;3&lt;/sup&gt;H) activity from 1976 to 2017 for the Adriatic–Pannonian region – AP&lt;sup&gt;3&lt;/sup&gt;H_v1 database

Spatial Modeling of Geometallurgical Properties: Techniques and a Case Study

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Isoscape of amount-weighted annual mean precipitation tritium (<sup>3</sup>H) activity from 1976 to 2017 for the Adriatic–Pannonian region – AP<sup>3</sup>H_v1 database