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Mathematical Geosciences - Modern approaches for the spatial simulation of categorical variables are largely based on multi-point statistical methods, where a training image is used to derive... 相似文献
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de Carvalho Joao Pedro Dimitrakopoulos Roussos Minniakhmetov Ilnur 《Mathematical Geosciences》2019,51(6):793-810
Mathematical Geosciences - High-order sequential simulation methods have been developed as an alternative to existing frameworks to facilitate the modeling of the spatial complexity of non-Gaussian... 相似文献
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Ilnur Minniakhmetov Roussos Dimitrakopoulos Marcelo Godoy 《Mathematical Geosciences》2018,50(7):753-780
High-order sequential simulation techniques for complex non-Gaussian spatially distributed variables have been developed over the last few years. The high-order simulation approach does not require any transformation of initial data and makes no assumptions about any probability distribution function, while it introduces complex spatial relations to the simulated realizations via high-order spatial statistics. This paper presents a new extension where a conditional probability density function (cpdf) is approximated using Legendre-like orthogonal splines. The coefficients of spline approximation are estimated using high-order spatial statistics inferred from the available sample data, additionally complemented by a training image. The advantages of using orthogonal splines with respect to the previously used Legendre polynomials include their ability to better approximate a multidimensional probability density function, reproduce the high-order spatial statistics, and provide a generalization of high-order simulations using Legendre polynomials. The performance of the new method is first tested with a completely known image and compared to both the high-order simulation approach using Legendre polynomials and the conventional sequential Gaussian simulation method. Then, an application in a gold deposit demonstrates the advantages of the proposed method in terms of the reproduction of histograms, variograms, and high-order spatial statistics, including connectivity measures. The C++ course code of the high-order simulation implementation presented herein, along with an example demonstrating its utilization, are provided online as supplementary material. 相似文献
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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. 相似文献
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