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

详细信息    查看全文

• 作者：Ilnur Minniakhmetov ; Roussos Dimitrakopoulos
• 关键词：High ; order simulation ; Joint simulation ; Correlated variables ; Non ; Gaussian variables ; Decorrelation ; Diagonal domination ; Multi ; element mineral deposits
• 刊名：Mathematical Geosciences
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：49
• 期：1
• 页码：39-66
• 全文大小：
• 刊物类别：Earth and Environmental Science
• 刊物主题：Earth Sciences, general; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences; Geotechnical Engineering & Applied Earth Sciences; Hydrogeology;
• 出版者：Springer Berlin Heidelberg
• ISSN：1874-8953
• 卷排序：49

文摘

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.