Robustness of variograms and conditioning of kriging matrices |
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| Authors: | Phil Diamond and Margaret Armstrong |
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| Institution: | (1) Department of Mathematics, University of Queensland, 4067 St. Lucia, Queensland, Australia;(2) Centre de Géostatistique et de Morphologie Mathématique, École des Mines de Paris, 35 Rue Saint-Honoré, 77305 Fontainebleau, France |
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| Abstract: | Current ideas of robustness in geostatistics concentrate upon estimation of the experimental variogram. However, predictive algorithms can be very sensitive to small perturbations in data or in the variogram model as well. To quantify this notion of robustness, nearness of variogram models is defined. Closeness of two variogram models is reflected in the sensitivity of their corresponding kriging estimators. The condition number of kriging matrices is shown to play a central role. Various examples are given. The ideas are used to analyze more complex universal kriging systems.Research performed while on leave at Centre de Geóstatistique et de Morphologie Mathématique, Fontainebleau. |
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| Keywords: | variogram robustness kriging conditioning number |
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