A hierarchical cosimulation algorithm integrated with an acceptance-rejection method for the geostatistical modeling of variables with inequality constraints
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2020
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Madani, N.
Abulkhair, S.
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Stochastic Environmental Research and Risk Assessment, 2020; 34(10):1559-1589
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Nasser Madani and Sultan Abulkhair
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This work addresses the problem of the cosimulation of cross-correlated variables with inequality constraints. A hierarchical sequential Gaussian cosimulation algorithm is proposed to address this problem, based on establishing a multicollocated cokriging paradigm; the integration of this algorithm with the acceptance–rejection sampling technique entails that the simulated values first reproduce the bivariate inequality constraint between the variables and then reproduce the original statistical parameters, such as the global distribution and variogram. In addition, a robust regression analysis is developed to derive the coefficients of the linear function that introduces the desired inequality constraint. The proposed algorithm is applied to cosimulate Silica and Iron in an Iron deposit, where the two variables exhibit different marginal distributions and a sharp inequality constraint in the bivariate relation. To investigate the benefits of the proposed approach, the Silica and Iron are cosimulated by other cosimulation algorithms, and the results are compared. It is shown that conventional cosimulation approaches are not able to take into account and reproduce the linearity constraint characteristics, which are part of the nature of the dataset. In contrast, the proposed hierarchical cosimulation algorithm perfectly reproduces these complex characteristics and is more suited to the actual dataset.
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© The Author(s) 2020 This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons. org/licenses/by/4.0/.