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

Compositional data constitutes a special class of quantitative measurements involving parts of a whole. The sample space has an algebraic-geometric structure different from that of real-valued data. A subcomposition is a subset of all possible parts. When compositional data values include geographical locations, they are also regionalized variables. In the Earth sciences, geochemical analyses are a common form of regionalized compositional data. Ordinarily, there are measurements only at data locations. Geostatistics has proven to be the standard 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 the modelling of compositional data using a method that is consistent with the compositional character of the data. The uncertainty is evaluated by a Monte Carlo procedure. The method is illustrated for the contents of arsenic and iron in groundwaters in Bangladesh, which have the peculiarity of being measured in milligrams per litre, units for which the sum of all parts does not add to a constant. Practical results include maps of estimates of the geochemical elements in the original concentration units, as well as measures of uncertainty, such as the probability that the concentration may exceed a given threshold. Results indicate that probabilities of exceedance in previous studies of the same data are too 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

The Journal of The Southern African Institute of Mining and Metallurgy, 2015, vol. 115, p.59-72

Southern African Institute of Mining and Metallurgy (SAIMM)

Autor: Pawlowsky-Glahn, Vera
Egozcue, Juan José
Olea, Ricardo A.
Pardo-Igúzquiza, E.
Data: 2015
Resum: Compositional data constitutes a special class of quantitative measurements involving parts of a whole. The sample space has an algebraic-geometric structure different from that of real-valued data. A subcomposition is a subset of all possible parts. When compositional data values include geographical locations, they are also regionalized variables. In the Earth sciences, geochemical analyses are a common form of regionalized compositional data. Ordinarily, there are measurements only at data locations. Geostatistics has proven to be the standard 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 the modelling of compositional data using a method that is consistent with the compositional character of the data. The uncertainty is evaluated by a Monte Carlo procedure. The method is illustrated for the contents of arsenic and iron in groundwaters in Bangladesh, which have the peculiarity of being measured in milligrams per litre, units for which the sum of all parts does not add to a constant. Practical results include maps of estimates of the geochemical elements in the original concentration units, as well as measures of uncertainty, such as the probability that the concentration may exceed a given threshold. Results indicate that probabilities of exceedance in previous studies of the same data are too 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
Format: application/pdf
ISSN: 2225-6253 (versió paper)
2411-9717 (versió electrònica)
Accés al document: http://hdl.handle.net/10256/13738
Llenguatge: eng
Editor: Southern African Institute of Mining and Metallurgy (SAIMM)
Col·lecció: MICINN/PN 2013-2015/MTM2012-33236
Reproducció digital del document publicat a: http://www.saimm.co.za/Journal/v115n01p059.pdf
Articles publicats (D-IMA)
És part de: The Journal of The Southern African Institute of Mining and Metallurgy, 2015, vol. 115, p.59-72
Drets: Attribution 3.0 Spain
URI Drets: http://creativecommons.org/licenses/by/4.0/es/
Matèria: Geologia -- Mètodes estadístics
Geology -- Statistical methods
Correlació (Estadística)
Correlation (Statistics)
Geoquímica
Geochemistry
Anàlisi multivariable
Multivariate analysis
Títol: Cokriging of compositional balances including a dimension reduction and retrieval of original units
Tipus: info:eu-repo/semantics/article
Repositori: DUGiDocs

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