Mathematical Geosciences

, Volume 49, Issue 1, pp 39–66

# Joint High-Order Simulation of Spatially Correlated Variables Using High-Order Spatial Statistics

Article

## Abstract

Joint geostatistical simulation techniques are used to quantify uncertainty for spatially correlated attributes, including mineral deposits, petroleum reservoirs, hydrogeological horizons, environmental contaminants. Existing joint simulation methods consider only second-order spatial statistics and Gaussian processes. Motivated by the presence of relatively large datasets for multiple correlated variables that typically are available from mineral deposits and the effects of complex spatial connectivity between grades on the subsequent use of simulated realizations, this paper presents a new approach for the joint high-order simulation of spatially correlated random fields. First, a vector random function is orthogonalized with a new decorrelation algorithm into independent factors using the so-termed diagonal domination condition of high-order cumulants. Each of the factors is then simulated independently using a high-order univariate simulation method on the basis of high-order spatial cumulants and Legendre polynomials. Finally, attributes of interest are reconstructed through the back-transformation of the simulated factors. In contrast to state-of-the-art methods, the decorrelation step of the proposed approach not only considers the covariance matrix, but also high-order statistics to obtain independent non-Gaussian factors. The intricacies of the application of the proposed method are shown with a dataset from a multi-element iron ore deposit. The application shows the reproduction of high-order spatial statistics of available data by the jointly simulated attributes.

## Keywords

High-order simulation Joint simulation Correlated variables Non-Gaussian variables Decorrelation Diagonal domination Multi-element mineral deposits

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© International Association for Mathematical Geosciences 2016

## Authors and Affiliations

• Ilnur Minniakhmetov
• 1
• 2
• Roussos Dimitrakopoulos
• 2
1. 1.Department of Mining and Materials EngineeringMcGill UniversityMontrealCanada
2. 2.COSMO-Stochastic Mine Planning LaboratoryMcGill UniversityMontrealCanada

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