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Cokriging of compositional balances including a dimension reduction and retrieval of original units

Compositional data constitutes a special class of quantitativemeasurements involving parts of a whole. The sample space has analgebraic-geometric structure different from that of real-valued data. Asubcomposition is a subset of all possible parts. When compositionaldata values include geographical locations, they are also regionalizedvariables. In the Earth sciences, geochemical analyses are a commonform of regionalized compositional data. Ordinarily, there aremeasurements only at data locations. Geostatistics has proven to be thestandard for spatial estimation of regionalized variables but, in general,the compositional character of the geochemical data has been ignored.This paper presents in detail an application of cokriging for themodelling of compositional data using a method that is consistent withthe compositional character of the data. The uncertainty is evaluated bya Monte Carlo procedure. The method is illustrated for the contents ofarsenic and iron in groundwaters in Bangladesh, which have thepeculiarity of being measured in milligrams per litre, units for which thesum of all parts does not add to a constant. Practical results includemaps of estimates of the geochemical elements in the original concentrationunits, as well as measures of uncertainty, such as the probabilitythat the concentration may exceed a given threshold. Results indicatethat probabilities of exceedance in previous studies of the same data aretoo low

This research has been partly supported by the Spanish Ministry of Economy and Competitiveness under the project METRICS (Ref. MTM2012-33236); and by the Agencia de Gestió d’Ajuts Universitaris i de Recerca of the Generalitat de Catalunya under project Ref: 2009SGR424

Southern African Institute of Mining and Metallurgy (SAIMM)

Author: Pawlowsky-Glahn, Vera
Egozcue, Juan José
Olea, Ricardo A.
Pardo-Igúzquiza, E.
Abstract: Compositional data constitutes a special class of quantitativemeasurements involving parts of a whole. The sample space has analgebraic-geometric structure different from that of real-valued data. Asubcomposition is a subset of all possible parts. When compositionaldata values include geographical locations, they are also regionalizedvariables. In the Earth sciences, geochemical analyses are a commonform of regionalized compositional data. Ordinarily, there aremeasurements only at data locations. Geostatistics has proven to be thestandard for spatial estimation of regionalized variables but, in general,the compositional character of the geochemical data has been ignored.This paper presents in detail an application of cokriging for themodelling of compositional data using a method that is consistent withthe compositional character of the data. The uncertainty is evaluated bya Monte Carlo procedure. The method is illustrated for the contents ofarsenic and iron in groundwaters in Bangladesh, which have thepeculiarity of being measured in milligrams per litre, units for which thesum of all parts does not add to a constant. Practical results includemaps of estimates of the geochemical elements in the original concentrationunits, as well as measures of uncertainty, such as the probabilitythat the concentration may exceed a given threshold. Results indicatethat probabilities of exceedance in previous studies of the same data aretoo low
This research has been partly supported by the Spanish Ministry of Economy and Competitiveness under the project METRICS (Ref. MTM2012-33236); and by the Agencia de Gestió d’Ajuts Universitaris i de Recerca of the Generalitat de Catalunya under project Ref: 2009SGR424
Document access: http://hdl.handle.net/2072/282202
Language: eng
Publisher: Southern African Institute of Mining and Metallurgy (SAIMM)
Rights: Attribution 3.0 Spain
Rights URI: http://creativecommons.org/licenses/by/4.0/es/
Subject: Geologia -- Mètodes estadístics
Geology -- Statistical methods
Correlació (Estadistica)
Correlation (Statistics)
Geoquímica
Geochemistry
Anàlisi multivariable
Multivariate analysis
Title: Cokriging of compositional balances including a dimension reduction and retrieval of original units
Type: info:eu-repo/semantics/article
Repository: Recercat

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