Variograms of order w to measure departures from multiGaussianity

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Casson, David
Ortiz, Julian M.
The study of geostatistics involves the inference and modelling of multivariate random functions. Frequently, this includes the assumption of multipoint Gaussianity (“multiGaussianity”) of the underlying multivariate random function. The properties of a multipoint Gaussian random function allow for ease of mathematical operation and parametric modelling; facilitating a measure of uncertainty in estimation through sequential Gaussian simulation. The assumption of multipoint Gaussianity is rarely tested, and it is not guaranteed that such an assumption is appropriate for the spatial phenomenon under study. By identifying a “measure” of how far a phenomenon appears to deviate from bi-variate Gaussianity, it may be possible to better understand the accuracy of traditional Gaussian based predictive models. Ultimately such a measure of bi-Gaussianity may inform the selection of a different model for the random function and a as a result, a different approach to assessing uncertainty in estimation. Variograms of order ? provide a tool to quantitatively check the bi-Gaussianity of a data set. This approach also provides a metric that can be considered a “measure” of how close to bi-Gaussianity a given data set is. In this study, the variograms of order ? are applied to a number of reference data sets to generate a relative measure of bi- Gaussianity. Application of this tool in real world scenarios may allow for improved understanding of uncertainty in our estimates of mineral resources.
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