Assessing heterotopic searching strategy in hierarchical cosimulation for modeling the variables with inequality constraints

A hierarchical sequential Gaussian cosimulation method is applied in this study for modeling the variables with an inequality constraint in the bivariate relationship. An algorithm is improved by embedding an inverse transform sampling technique in the second simulation to reproduce bivariate complexity and accelerate the process of cosimulation. A heterotopic simple cokriging (SCK) is also proposed, which introduces two moving neighborhoods: single and multiple searching strategies in both steps of the hierarchical process. The proposed algorithm is tested over a real case study from an iron deposit where iron and aluminum oxide shows a strong bivariate dependency as well as a sharp inequality constraint. The results showed that the proposed hierarchical cosimulation with a multiple searching strategy provides satisfying results compared to the case when a single searching strategy is employed. Moreover, the proposed algorithm is compared to the conventional hierarchical cosimulation, which does not implement the inverse transform sampling integrated into the second simulation. The proposed methodology successfully reproduces inequality constraint, while conventional hierarchical cosimulation fails in this regard. However, it is demonstrated that the proposed methodology requires further improvement for better reproduction of global statistics (i.e., mean and standard deviation).