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.

这项工作解决了具有不等式约束的互相关变量的协同仿真问题。在建立多并置协同克里格范式的基础上，提出了一种分层顺序高斯协同仿真算法。该算法与接受-拒绝采样技术的集成要求模拟值首先重现变量之间的双变量不等式约束，然后重现原始统计参数，例如全局分布和变异函数。另外，开发了鲁棒的回归分析以导出引入所需不等式约束的线性函数的系数。所提出的算法用于模拟铁矿床中的二氧化硅和铁，其中两个变量在二元关系中表现出不同的边际分布和明显的不平等约束。为了研究该方法的好处，将二氧化硅和铁与其他协同仿真算法进行了协同仿真，并对结果进行了比较。结果表明，常规的协同仿真方法无法考虑和再现线性约束特征，而线性约束特征是数据集性质的一部分。相反，所提出的分层协同仿真算法完美地再现了这些复杂的特征，并且更适合于实际数据集。结果表明，常规的协同仿真方法无法考虑和再现线性约束特征，而线性约束特征是数据集性质的一部分。相反，提出的分层协同仿真算法完美地再现了这些复杂的特征，并且更适合于实际数据集。结果表明，常规的协同仿真方法无法考虑和再现线性约束特征，而线性约束特征是数据集性质的一部分。相反，提出的分层协同仿真算法完美地再现了这些复杂的特征，并且更适合于实际数据集。